(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 782535, 16768]*) (*NotebookOutlinePosition[ 865776, 19541]*) (* CellTagsIndexPosition[ 863449, 19474]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Fractional Calculus", "Title", CellTags->"Top"], Cell[TextData[{ "A ", StyleBox["Mathematica", FontSlant->"Italic"], " package to solve fractional differential equations" }], "Subtitle"], Cell["\<\ Gerd Baumann Department of Mathematical Physics University of Ulm D-89069 Ulm Germany Gerd.Baumann@physik.uni-ulm.de\ \>", "Author"], Cell[CellGroupData[{ Cell[TextData[ButtonBox["Initialization", ButtonData:>{"Content.nb", None}, ButtonStyle->"Hyperlink"]], "Subsubsection"], Cell[TextData[{ "Define the global variable $FractionalCalculusPath in such a way that the \ location of the package ", StyleBox["FractionalCalculus", FontWeight->"Bold"], " is uniquely defined." }], "Text"], Cell[BoxData[ \(Off[General::spell]\)], "Input", InitializationCell->True], Cell[BoxData[ \(Off[General::spell1]\)], "Input", InitializationCell->True], Cell[BoxData[ \(Off[Protect::pssl]\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(If[$OperatingSystem == "\", $FractionalCalculusPath = \ $TopDirectory <> "\"; AppendTo[$Path, $FractionalCalculusPath], $FractionalCalculusPath = \ $HomeDirectory <> "\"; AppendTo[$Path, $FractionalCalculusPath]];\)\)], "Input", InitializationCell->True], Cell["Load the package", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(<< FractionalCalculus.m\)], "Input", InitializationCell->True], Cell[BoxData[ \(" --> FractionalCalculus ready <-- "\)], "Print"], Cell[BoxData[ \("\[Copyright] Gerd Baumann, Norbert S\[UDoubleDot]dland 1996-1999"\)], \ "Print"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(NotebookClose[foxtitle]\)], "Input", InitializationCell->True], Cell[BoxData[ \(NotebookClose[foxtitle]\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], " Introduction" }], "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"Introduction"], Cell[TextData[{ "The term ", StyleBox["fractional calculus", FontSlant->"Italic"], " is by no means new. The subject is as old as calculus itself and goes \ back to times when Gau\[SZ], Leibniz, and Newton created differentiation as a \ new tool. Fractional calculus is a generalization of the ordinary \ differentiation by non-integer derivatives. " }], "Text"], Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgA]ZZATJZATJX00i6AZP0>]Y6ZTKJZTI6Z]Y6ZTKJZ ]Y6ZTKJZ]Y6ZTI6Z]Y6ZTKJZTI6Z][JZTI6Z0[JAZP0;][JZ]Y6Z][JZ]Y6Z ][JZ]Y6Z][JZ]Y6ZTKJZ]Y6Z][JZ00:fTJX01;JfZ[JAZ[JfZ[JAZP:f]ZX0 1Y6AZ[JfZ[JfZ[JAZ[JfZY6fZPBf]ZX00i6fZ[JfZ[JfZP08][JZ00FfTJZA ]ZZf]ZZfTJZA]ZX00[JfZP08TI6Z][JZ][JZ][JZTI6ZTKJZTI6ZTKJZ0[Jf ZP04]Y6ZTKJZ]Y6ZTKJZ0[JfZP0GTI6Z][JZTI6Z][JZTKJZ]Y6ZTI6ZTKJZ ]Y6ZTKJZ]Y6ZTKJZ]Y6ZTI6ZTKJZ]Y6ZTI6ZTI5ETI6ZTKJZ]Y6ZTKJZ][JZ 00>ATJX00kJfZY6AZY6AZP04TI6Z00>fTJZA]ZZfTJX00kJfZP;JfZX00m[J okJfZ[JfZP0<][JZ00BATJZf]ZZATJZf]ZX3f]ZZ0kJfZPBATJX01KJfZY6A ZY6AZY6AZY6AE@05TI6Z00>ATEFATJZATJX00Y6AZP03]Y6ZTKJZTI6Z00BA TJX01i6AEI6AZY6AZY6AZ[JfZY6AZY6AE@03TI6Z00>f]ZZATJZATJX00Y6A ZP:f]ZX7TI6Z00FA]ZZfTJZATJZA]UFATJX00[JAZP04TI6Z]Y6ZTI6Z]Y5E 0Y6AZP04]Y6ZTI6ZTI5E]Y6Z0Y6AZP07TI5ETI6ZTI6ZTI5E]Y6ZTI6Z]Y5E 00BATJX00kJAZY6AEKJAZP08TI6Z00nATEFATJZATEFATJZfTEFATJZfTJZA TEFfTJZATJZfTJZATJZATEFATJZATED02i6AZP06TI5ETI6ZTI6ZTI5ETI6Z TI5E0i6AZP03TI5ETI6ZTI6Z00^ATJX01I6AEI6AZY6AEI6AZY6AE@04TI6Z 00>ATEFATJZATJX00i6AZP03TI5ETI6ZTI6Z00FATJX00i6AEI6AZY6AZP0< TI6Z00>ATEFATJZATJX00i6AZP03TI5ETI6ZTI6Z00:ATJX01KJAEI6AZY6A ZY6AZY6AE@02TI6Z00002DQ8EFe]EDQ8EDQ8EFe8EDQ8EFe8EDQ8EFe8E@06 B4QE00M]B5E8B5E]B5E]B5E8B5E]B5E8B5D00Ve8E@04B4QEKDQEB4QEKDQE 0TQ8E@09KDQEB4QEKDQEB4QEKDQEB4QEKDQEB4QEKDQE0098B5D01fe8EDQ8 EFe8EDQ8EFe8EDQ8EFe8E@02B4QE00A]B5E8B5E]B5E]B5D?B4QE00=8B018 B5E8B5D00TQ8E@03B2AEB4QEB4QE00M8B5D00dQ804Q8EDQ8E@0=B4QE00=8 B018B5E8B5D03TQ8E@03B4P0B4QEB2AE00E8B5D00dQ804Q8EDQ8E@02B4QE 00=895E8B5E8B5D00TQ8E@03B2AEB4QEB4P000=8B5D00dQ804PTEDQ8E@03 B4QE00M8B01895E8B00TB5E895E8B5E895D00dQ8E@03B2@0B4QE94QE00A8 B5D00fe8EDQ8EDQ8E@04B4QE00=]B5E8B5E]B5D00dQ8E@03KDQEB4QEB4QE 0098B5D00fe8EDQ8EFe8E@02B4QE00=]B5E8B5E8B5D00Ve8E@08KFeEB4QE KFeEB4QEKFeEB6eEKFeEB4QE0Ve]E@06B4QEKFeEB4QEKFeEB4QEKFeE0dQ8 E@03B4P0B4QEB4QE0098B5D00dPT04Q8EDQ8E@0;B4QE00=8900TB5E8B5D0 14Q8E@04B4P0B4QEB4QEB4P03TQ8E@05B4P094QEB2@094QEB4P000=8B5D2 KFeE00FATJZfTJZA]ZZATEE]KJX00Ve]E@03B6eEKDQEB6eE00E8B5D00dQ] EDQ8EDQ8E@04B4QE0Y6AZP06TI5ETI6ZB4QEB4QE94QE92@00dQ8E@0894QE B4P092AE92AE92@092AE92@0B4QE0R@TE@0JB2@092AE92@092AE92@092AE 94P092@092AE92@092AEB4QE92@0B4QE92AE92@092AEB4P092AEB4QE92AE 92@092AEB4P0B4QEKFeE0TQ8E@0=92@092AE94P092AEB2AE94P0B2AE94QE B4QEB2AEB4QEB2@0B4QE00=890001TPTEDQ804PT04Q8EDPT04PTE@989000 2DQ804PTEDPT04PTEDPT02@T04PTEB@T04PTE@04B2@000=895E8900T9000 0R@T000702@0900092@0900002@092@092AE0098900014PTEDQ804PT04PT E@98900292@000DT95DT900T9000900T000012@T000<900092@092@00000 92@0001E92@0900092@0901E02@090000R@T0005000092AE92@092@09000 00HT900022@002@T02@T02@0EB@T02@TEB@T02@TE@@T90002b@TEB@T02@T 02@T000T02@T02@TEB@0000T02@T0000000292@00092AE02@092@002AE900092AE92@09000 92@0B2@092@0B2@092@0B2AE0TPT000794P0B2AE92@0B2@0B2AEB2@0B4QE 00989001B4P00006B4QE00U895E8B5E8B5E8B018B5E895E8B5E8B01895D0 0TQ8E@08KDQEB4QEKDQEB4QEKDQEB2AEB4QEB2AE1TQ8E@05B2AEB4QEB4QE B2AEB4P000M8B5D00dPTEDQ8EDQ8E@02B4QE00=89018B5E8B5D00TQ8E@03 B2AEB4QEB4P00098B5D03BA8EDPTEDQ804PTEDQ8EDPT02A8EDPT02A8EDPT EBA804PTEDQ80002B4QE00m89018B5E895DTB5E895E8B00T95E8B5E895DT B5E89018B5E895DTB01895D00dQ8E@05B2AE94P0B4QEB4QE92AE0098B5D0 22@T04PTEBA8EDPTEDQ804PTEDQ8EB@T00=8B5D05dPTEDQ802A8EDPT02A8 EDPTEBA8EDPTEDQ802@TEDQ804PTEBA804PTEBA8EDPT02A8EDPTEB@T04Q8 EDPT02A8EDPTE@02B4QE00TT95E8B5DT95E8B5DT9018B5DT95E8B5DT9000 0TQ8E@0;92AEB4P092AEB4QE92@0B4QE92@0B2AE92AEB4QEB2AE0098B5D0 1R@T04Q8EDPTEDPTEDQ8EDPTE@I8B5D00dPTEDQ8EDQ8E@04B4QE00E895E8 B5E8B5E8B5E895D014Q8E@06KDQEB4QEB4QEKDQEB4QEKDQE0dQ8E@04KFeE B4QEB4QEB4QE1Fe]E@04B4QEKDQEB6eEKDQE0dQ8E@06B4P0B4QEB4QEB4P0 B4QE92@014Q8E@0394QEB4QE92@00098B5D01dQ804Q8EDQ8EB@TEDQ802@T EDQ80002B4QE00ATEFATJY]KED00TQ8E@09 B6eEB4QEB4QEB4QEB6eEKFeEB4QEKFeEB4QE00>ATJX01Fe]EI6AZY6AZY6A EDQ]ZP02B4QE00A]KEE8B5E]KEE]KED2B4QE00=8KEE]KEE8B5D02dQ8E@04 KFeETI6ZTI6Z][JZ196AZP9]KED6B4QE00@T9018B5E8B5E8B5D292@000HT 95E8B5DTB5E8900T95E8B5D292@000=8B5E89018B5D00TQ8E@08B6eEB4QE B4QEKFeEKFfZKFeE92AE92@00TQ8E@03B2@0B4QEB4QE00=8B5D052@T04Q8 EDQ8EDPTEDQ804PTEDPT04Q804PTEDPT02@TEDPT02@TEDPT04PTEDPT04PT EDPT04PTEB@T009890000dQ8EFdT04PT0003B2@000A8B5E]9018901]B5D4 B2@000E895E8900T9018900T95D00R@T0003B2@092AEB2@0008T90004R@0 000T02@T000T000002@T02@0EB@T000002@T02@TE@0002@T02@002@T0000 02@T02@TE@8T900012@0000T02@T02@0E@@T900012@002@T02@TEB@000@T 900052@TEB@T02@T000T02@002@T02@002@T000T02@T02@002@T02@002@T 02@002@T02@TE@0T02@T000000ATJX00i6AEFe]ZVe]E@04B4QE00I895DTB018B5E895DTB5E89003B4QE 00LTB00T95E8B5DTB5E8B5E]KEFATJX00Ve]E@03B4QEKFeEKFeE0098B5D0 14PT02A8EDPT02A8E@A8B5D00dQ804Q8EDQ8E@02B4QE00E8B018B5E89018 B01895D01TPT000392@0B2@092@000A890001TQ8EFdT04Q8EFdTEDPT04PT E@9890003TPTEFdT04PTEDPT04PTEB@T04PTEB@T04PT04PTEB@T02@002@T 02@TE@8T90004R@TEB@T000T02@T02@0000TEB@0000T02@T000002@T0000 02@T02@002@T000T02@T0000008T900012@002@T02@T02@TE@f]ZZATJZA TJX00i6AZP04]Y6ZTI6ZTI5ETFfZ1Fe]E@05KFfZB4QEKFeEKFeEB4QE00A] KED2B4QE00=8B018B5E]KED00dQ8E@=]KED016e8EDQ]EFe8EDQ]E@9]KED0 1Fe]ZY6AEI6AZY6AZY6AE@02KFeE00=]KJZATJZATJX00i6AZP=]KED2B4QE 00E]KEFATEE]KEFATJZATED00Y6AZP03TI5EKFfZKFeE009]KED014Q8EDQ8 02@TEB@T00A8B5D01DQ804PTEDQ8EB@T02A8E@05B4QE00E89018B5E89018 B01895D00TPT0005B2AE94P0B2AE92@0B2AE009890002Ve804PTEDPT04PT 02@TEDPT02@T04PT02@004PT008T90001B@TEB@002@T04PT04PTE@02B2@0 01DT95DT9018900T05E8900T900T95DT900T000T900005DT9000000T9000 95DT0000900T9000000T900000000R@T000F000092@092@0900092@00000 92@092AE000092@002@0900002AE92@002@092@0900002@092@0001E92@0 02@00R@T0003901E92@00000008T90000b@002@T02@TE@0492@000M89018 95DT9018901895E8901895D00TPT0008B2AEB4P0KB@0B4QEKDP0B2AEB2@0 B2AE0TPT000392AEB2@0B2@000=8900014PTEDPT04PTEDPT00DT900012@0 000T02@T02@0008T900014PTEB@T04PT04PTE@=89001B4QE0DPT00000dQ8 E@03B4P0B4QEB2AE0098B5D2B2AE00Q8B01895E8B5E895E8B00T95E8B018 95D2B4QE00=895E8B5E895D00TQ8E@0:B2@0B4QEB2AE94QEB2@0B4QE92@0 B4QE92AEB4P00TQ8E@1^B2AEB4QEB2AEB4QE92@0B4QEB2AE94P0B2AE94QE B2AEB4P092AEB4P092AEB4P092AEB2@092AEB4P092AEB2AE92@092AE92@0 B2AE92@0B2AE92@092AE92@092AE92@092AE92@092AE92@092AEB2@094QE 92@092AE92@092AEB2@092AE92@092AEB2@092AE92@0B4QE92AEB2@092AE 92@0B2AE92@094QEB2@092AEB2AE92@092AEB2AE94P092AEB2AE94P092AE B2AE92@092AE92@092AEB2@092AE92@0B2AE94QE92@092AEB2AE92@0B2AE 92@092AE92@092AE92@0B2AE92AE94P092AE92@092AE92@092AE92@092AE 92@0B2AE92@092AE92@0B2AE92@0B2AE94QEB2@00TPTE@05B4QEKBAEB4QE TDQETFeE009]B5D00fe806dTEDQ8E@02KBAE0158B5E]95E8B01895E89018 B5E8901]B5E895E8B5E895E]901895E8B5E895E8B01895D00TQ8E@9895D2 B4QE00Q895E8B5E895E8B018B5E]B5E8B5E]B5D3B4QE00=]KEE8B5E8B5D0 0dQ8E@03KFeEB4QEKFeE00A8B5D00b@T04Q8EDQ8E@03B4QE00=8B018B5E8 B5D00TQ8E@07B4P0B4QEB4QE92@0B4QEB2AE94P000=8B5D00fe]EDQ8EFe] E@05B4QE00E8B018B5E8B5FATJY]KED00TQ8E@0892AEB4QEB4QEB2@0B4QE 92@092AE92@00TQ8E@0492@094QEB4QE92@00TQ8E@05KFeEB4QEKFeETI6Z TKJZ00>ATJX01ffAEFe]ZVe]EDQ8EFe]EDQ8EFe]E@02B4QE00=]KEE]KJY8 B5D01dQ8E@06B4P0KFeEB4QEB6eEB4QEKFeE14Q8E@=]KED2TI6Z00FATEFA TJZATJZATJZATED00Ve]E@03KFfZTI5ETI6Z00BATJX01;JfZY6AZY6AZ[Jf ZP>ATJX0196AEFe]ZVe]EFe]E@M8B5D01R@T04Q8EDQ8EDQ8EBA8EDQ80098 B5D02dQ804Q8EB@TEBA802@TEDPT04Q8EDPT04PTEDPT04PTE@03B2@000DT 901890189018901895D00dPT000392@0B2@092@0008T900012@TEB@T02@T 02@0008T90001TPTEDPT04Q804PTEB@T02@000@T900012@002@T02@T0000 008T900032@0000T02@0000T02@0000T02@002@T000T02@0000T02@0E@8T 90004P00EB@T000002@T000T02@002@T02@TEB@002@T000002@T000T02@0 000TEB@T000002@T008T0000100T02@002@T02@T0098900034PTEDQ804PT 04Q802@T04PT04PTEDPT04PTEDQ804PT04PTE@A890004Fe8EDQ804PTEDPT 04PTEDPT02@T04P002@T04PT02@T04PT02@T02@002@T02@TEB@0000392@0 00@T000T900T900T95D292@000dT95DT900T000095DT9000900T901895DT 90189018B5E8900TB5D00TPT00000dQ8E@0RB2AEB4QEB4P0B2AEB4QEB2AE B4P092AEB4QEB2AE92@0B4QEB2AEB4QEB2AEB4P0B2AEB4QEB2AEB4P0B2AE B4QE92AEB4QE92AEB2@0B4QE92AEB2AE92@0B2AEB4QEB2AE92@00TQ8E@0O B2AE94P0B2AE92AE92@0B2AE92@0B4QEB2@094QEB2AEB4QE92AEB2AEB4QE 92AEB4QE92@092AE92@092AE92@092AE92@092AE92@092AEB2@092AE92@0 92AE008T90003DPTEB@T02@TEDPTEB@T04PTEB@T02@TEB@T02@TEB@T04PT EB@T000292AE02a8B00T95DT900T95DT900T95DT900T95E8900T95DTB5DT 900T95E895DTB01895DT95DT901895DT900T95DT900T95DT900T95DT900T 95DT900T95DT900T95DT900T95DT900T95DT900T95DT900T95DT900T95DT 900T95E8900292AE00@T901895DT95E8900292AE00U8900T95E8900T95E8 901895E8901895E8B0000Ve8E@0?TDQETFeETDQEKDQEB2AEKBAEB2AEKDQE KB@0B2AEB4P0KBAEB4QEB2AEKDQE009895D03Fe8EDQ8EDPT06e8EDQ8EDPT EDQ8EDPT04PTEDQ8EDPTEDQ8EDPT0003B4QE00=895E8B5E890000TQ8E@06 B2AEB4QEB4QEB4QEKDQEB4P01TQ8E@05KFeEB4QEKFeEKFeEKFfZ009]KED4 B4QE00=]B5E8KEE8B5D00TQ8E@0392@092AE92@000=8B5D00bA804Q8EDQ8 000=B4QE00HT95E]KEFATJY]KEE8B5E8B002B4QE00/TB018B5E8900TB5E8 95E8B018B5DT95DT901895E8B0001DQ8E@05B4P0B4QEKFeETI6ZTI5E00:A TJX016e]EDQ8EFe]EFe]ZP9]KED01DQ8EFe]EDQ8EDQ]EFe]E@03B4QE00=8 B018B5E8B5D014Q8E@03KDQEB4QEKFeE00I8B5D016e]EFe]ZY6AZ[JfZP:A TJX01i6AEI6AZY6AZTQ8EFe]EI6AZVe]E@02TI6Z00>ATEFATJZATED00Y6A ZP0=TI5ETI6ZTI5EKI5ETI6ZKDQEKFeEB4QE92AE92@0B4QE92@0B4QE008T 9002B4QE00E8B00T9018B5E8B5E895D00dQ8E@0CB4P0B4QEB4P0B2AEB4P0 B2@0B4P0B2@0B4P092@0B2AE92@0B2AE92@0B2@0B4QEB2@0B2AE9000008T 90000b@0EB@T02@TE@0292@000AB5D04Ve8EFdTEDPTEFe8EDPTEFdT06e8EDPTEFdTEDQ8EFdT EDPTEDPT06dTEDQ8EFdT04PTEDPT00=895D034PT04Q8EDPTEDQ8EFe8EDPT EDQ804PTEDQ8EDPT04Q8EDPT0098B5D00dPTEDQ8EDPTE@03B4QE00I]B5E8 B5E8B5E8B5E8KEE]B5D2B4QE00M]KEE]KJY]KEE]KEFATJY]TEFAKJX00fe] E@I8B5D00b@T04Q8EDQ8E@09B4QE00=]KEE8B5E]KED014Q8E@9]KED2B4QE 00=8B01]KEE]KJX00Ve]E@98B5D02DPT02@TEB@TEDQ8EB@TEDQ802@TEDQ8 EBA80003B4QE00=]KEE8B5DT90001DQ8E@06KFeETI6ZTI5ETI6ZTI5EKFfZ 0fe]E@05B4QEKFeEKFeEB4QEKDQE0098B5D00fe]EDQ8EDQ8E@05B4QE00=] KEE8B5E8KED00TQ8E@03B4P0B4QEB4QE0098B5D01B@T04Q8EFe]EI6AZY6A E@03TI6Z00JATEFATJZATJY]KEFATJZATED7TI6Z00=]KEE8B5E8B5D00TQ8 E@0<92@092AEB4P092AEB4QE92AE92@094QEB4QEB2AEB4QE92AE0TQ8E@07 B4P0B4QEB4QEB4P092AEB4QE92AE0098B5D01dPT04Q8EDPT04PTEDPT04PT EB@T0003B2@0015]B5E8900T9018900T901895DT000T900T000T900T000T 95DT9018901895E8901895D00TPT008T90000dPT02@004PT000492@000lT 000T95DT900T900T0000900T000095DT0000900T0000900T05D0900T0000 0R@T0008000092@092@0000092AE92@002@092AE0R@T000:900002@0901E 900092@092AEB2@092@0B2AEB4P00TPTE@0:B4P0B2@0B4QEKB@0KDQEB2@0 B4QEKDP0B2AEB4P00dPT0006B4QEKB@0KDQEKDP0B4P0B2AE0dPT000592AE B2@092AE92@092AE00@T9002B2@000/T90189018901895DT9018901895DT 9018900T900T95D00b@T000=901E92@002AE92@0000092AE02@0900092@0 9000B2AE92@0B2AE00=8900000A8B5D04TPT04Q8EDPT04Q8EDPTEDQ802@T EDQ8EDPT02@TEDQ802@TEDPTEDPT04Q8EDPTEDQ8EB@TE@98B5D08dPT04Q8 EB@TEDPT04Q8EB@TEDQ802@TEDPTEDQ8EDPT04Q8EB@TEDPTEDQ804PTEBA8 EDPT02A8EB@TEDPT04Q8EDPT02A8EDPTEBA804PTEDQ802@TEBA8EDPTEB@T 02@TEB@T02@TE@0292@000HT95DT901895DT95DT900T95D292@001dT95DT 900T900T95E8900T95E8900T95DTB01895DT900T95DT900T95DT901895DT 900T95DTB00T95DT901895DT900T95DT901895DT901895DT90000R@TE@09 94P0B2AE92@092AE92@092AE92@092AE92@0008T95D04B@T04PTEB@T02@T EB@T02@TEB@T02@TEB@T02@TEB@T04PTEB@TEDPT02@TEB@T02@TE@0292@0 00lT95DT900T95E8901895DT95DT901895DT900T95E8901895E8B5E]95FA B5D016e8E@04KBAEB4QEB2AEKB@00TPTE@09KDQEB2AEKDQEB2@0KBAEB2@0 B4QEKBAEB4QE009895D01dQ8EDPTEDPTEDQ8EDPT04PTEDPT0002B2AE00I8 901895E8B5E895E8B5E895D2B4QE00E895E8B01895E8B5E8B0001dQ8E@06 KDQEB4QEB6eEKFeEKFfZKFeE0Y6AZP06TI5ETI6ZTI6ZTI5EKI6ZTFeE0Ve] E@03B6eEKFeEB4QE0098B5D02B@T04Q8EDQ8EDQ8EDPTEDQ804Q8EDPTEBA8 E@04B4QE00=]KEE8B5E]KED01DQ8E@03B4P092AEB4QE009]KED4B4QE00LT B5E8B01895DTB018B5DT95E890001DQ8E@03B4P0B4QEB4QE00E8B5D016e] EI6AZY6AZY6AZP9]KED024Q8EFe]ZVe]EFe]EFe]ZVe]EDQ8EFe]E@I8B5D0 0dQ804Q8EDQ8E@03B4QE00DT95E8B5E8B5DT95E8B0000TQ8E@0792@0B4QE B4P0B4QEKI6ZTI6ZTI5E00>ATJX0296AEI6AZVe]EI6AZY6AEI6AZVe]ZY6A ZP9]KED3B4QE00i895DTB00T95E8900TB5DT95E8900T95DTB01895E8B5DT 900TB5E8B004B4QE00/TB01895E8B5E8B5DT95E8B00TB5E89018B5E89018 95D01DPT0008B2AEKDP0B2AE92@0B2@092AE92@090000b@T0003B01E92@0 B2@000A8900032@TEDPT02@T02@TEB@002@TEB@T02@TEB@T02@002@TEB@0 0092AE92@092AE92@09000 92AE92@092AE92@092AE92@0B2AEB2@0B2AE0Ve8E@04KBAEKDQEKDQEKDQE 0VdTE@0^KDQEKBAEKBAEKB@0KDQEKBAEB4QEKBAEKDQEB2AEB2@0KDQEB2@0 B2AEKDQEB2AEKB@0B4QEKBAEB2@0KBAEB2@0B2AEKDQEB4QEB2@0B4QEB2AE B2@092AE92@092AEB4QE92@0B2AE94QE92@0B4QEB2AEB2@094QEB2@0B4QE 92@0B4QEB2AE14Q8E@06KDQEKFeEB4QEKFeEB4QEKFeE0i6AZP05TFfZTI5E KFfZTI5E92AE0098B5D02R@T04Q8EDQ8EDQ8EDQ]EFe]EFfAZY5]ZVfAEFe] E@98B5D012@T02A8EDPTEDQ800E8B5D2KFeE00=8B5E]KEE8B5D00Ve]E@06 B4QEKFeEB4QEB4P0B4QE92@014Q8E@0394QEB4P0B4QE00U8B5D3KFeE00e8 B5E]KEE]KEE]KEFAKJY]KEFATJY]KEE8KEE]B5E]KEE8B5E]KED00TQ8E@03 KFeEB4QEB4QE00A8B5D00dQ804Q8EDQ8E@04B4QE00=8B00T95DT900024Q8 E@07B4P0B4QEB4QE92AEB4QEB4P0B4QE00A]KED2TI6Z00BATEFATJZAKJY] KED2B4QE00LT901895DT95E8B5DT95E8B00T95D00R@T000C94QEB4QEB2@0 94QEB2@092AEB4P092AEB4QEB4P0B4QE92@0B4QE92AEB2@092@0B2AEB4P0 B2AE009890006I58EFe806e8EFdT04PTEFe804PT04PTEDQ806dT06e8EDPT 06e806dTEFe806e8EFdT04PT04PTEB@T02@002@T02@004PT04Q8E@03B2@0 01U895E89018901895E8900T0000900T00009000000T9000000T9000000T 9000000T9000900T0000900T95D0000T900T000T90000TPT0004B4P0KB@0 B2AEKDP00TPT000392@0900092@000ATJX2KFeE14Q8E@0:92AE B4QEB4QEB4QEB4P0B4QE92AEB4P0B4QETI6Z0Ve]E@98B5D00fe]EDQ8EDQ8 E@06B4QE00=]KEE8B5E8B5D00dQ8E@0392AEB4QEKFeE00=8B5D00dQ804Q8 EDQ8E@03B4QE00=]KEE8B5E]KED00dQ8E@05KFeEB4QEKFeEKFeEKFfZ009] KED01Y6AZVe]EI6AZY6AZY6AEI6AZP9]KED3B4QE00=8KEE8B5E]KED00dQ8 E@04KFeEB4QEB4QEKFeE0dQ8E@03B6eEKFeEB4QE0098B5D00dQ804Q8EDQ8 E@02B4QE00=]KEE8B5E]KED00Ve]E@A8B5D016e]EFe]ZY6AEI6AZPA]KED2 B4QE00XTB5DT901895DTB5DT9018B5DT9018B5DT95E8B5D292@000B2@0B2AEB4QEB2AEKDQETFeE]Y6ZTFeEKDQE B4QEB2@092@092AEB2AE0TQ8E@0QB2AE92@092AEB2@092AE92@0B2AE92@0 92AEB2@092AE92@0B2AE92AEB2@092AE92@0B2AE92@092AEB2AE92@0B4QE 92AEB2@092AEB2AE92AEB4P0B2AEB4QEB2AEB4P000=8B5D016e]EDQ8EFe] EDQ8E@A]KED01dQ8EFe]EFe]ZVe]EFe]ZY6AEI6AZP02KFeE00M8B5DT9018 B5DT95E89018B5E895D01DQ8E@03B4P0B4QEB4QE0098B5D00dQ802@TEDQ8 0003B4QE00]8B018B5E]KEE]KEFATJY]KEFATJZATEFATJZf]ZZA]ZX01;Jf ZP08TI6Z][JZTI6Z][JZTI6ZTI5ETI6ZTI5E0fe]E@0=B4QEKFeEKFfZB6eE TFeEKI6ZTI5ETI6ZTI5ETI6ZTI5ETI6Z][JZ00:ATJX0196AEDQ8EFe]EDQ] ZPA]KED01fe]ZVe8EDQ8EDQ8EB@T02@TEB@T0002B4QE00=8B018B5E8B5D0 0TQ8E@03KDQEKFeEB4QE009]KED2B4QE00e]B5E8KEE8B5E8B5DT900TB5DT 901895DTB5E8900TB5E8B5DT900014Q8E@0592@0B4QE92AE92@0B4QE008T 90002R@TEBA804PTEDQ8EBA802@TEDPTEB@T02A8EDPT00=8B5D062@T02@T EDQ804PTEDQ8EDPT02A8EDQ806e8EFe804Q8EDPT06dTEDQ806dT04Q8EFdT 04Q806dTEDQ806dT04PTEFe804PTE@=8900026e8EFe806dTEDQ804PT04PT EDPT04PTE@8T90004R@0EB@T02@0000T02@0000T02@0000T02@0000T02@T 000002@T000002@T000002@T02@TE@8T90001DPT04PTEDQ804PT04Q8E@02 B2@000DT95DT900T95DT900T05D00R@T000AB2@092@0B2AEB2@0B2AEB2@0 92@0B2AEB2@092@0B2@092@0901E92@0900092@0900000@T90004DPTEB@T 04PTEB@T000T02@T02@TEB@T04PTEB@T04PTEB@T04PTEB@T02@TEB@T02@0 000492@000D0000T9000000T900000000b@T0008900092@0900092AE9000 92@0901E02@00b@T0008900092@092@092@0900092@002@0900012@T0003 900092AE92@0004T900000=8B5D0;TPT04Q8EB@TEDQ8EDPT04Q8EB@TEDPT EDQ8EB@T04PTEB@T04PTEB@TEDQ8EB@T02@TEDPT02@TEDPTEDQ8EB@T04PT EB@T04PTEBA804PTEB@T04PTEDQ8EB@T04Q8EB@T04PTEDQ804PTEB@T02@T EDPTEB@T04PTEB@T04PTEB@T04PTEB@T008T95D01b@T02@TEB@T02@002@T EB@T02@0E@0292@0018T95DT900T95DT900T000T95DT900T05DT900T95E8 9018B5DT95DT901895DT95DT901895D292@000`T95DT900T900T95DT900T 95DT900T95DT900T95DT900T95D292@0014T05DT900T95DT900T05DT900T 95DT900T95E8900T95DT900T95DT900T95DT900T95D00b@T000K92AE92@0 92AE900092AE92@0901E92@092AE92@092AE92@092AEB2@092AE900092AE 92@092AE92@0B2AE92@092AE92@092AEB2@0B2AE0098B5D016e8EFe]EI5] EKJAE@:AKED2KDQE0TPTE@9]B5D01DQ8EDPT04PTEDPTEDPT000292AE00=8 900T95DT90000R@TE@0EB2@092AE92@092AE92@0B2AE92AE94QE92@0B2AE 92@092AE92@0B2@094QEB2AE92@0B4QEB2AEB4QE92@00098B5D01TPTEDQ8 EFe]EFe]EDQ8EFe]E@98B5D00fe]EDQ8EFe]E@04KFeE00A]KJZATEFATJZA TJX4B4QE00ATJX01;JfZY6AZY6AZY6AE@Ff]ZX2TI6Z00BA TEFATJZf]ZZATJX2][JZ00FATJZf]ZZATJZATJZf]ZX01I6AZP05TKJZTI6Z TI6ZTI6ZKFeE00BATJX01[JfZ[JAZY6fZY6AZY6AEI6AZP=8B5D02B@T04Q8 EB@TEDQ8EDPT02A8EDPT02A8EDQ80003B4QE00 92@0900002@0900002@0900002@0900002@0900002@0900092@090000b@T 000LB2@0B2AEB2@092AEB2@092@092AE900002@0900002@0900002@092@0 901E02@092@0900002@0900002@0900092@0900092@092AE92@0900012@T 000ATJY]KEE]KED00Ve]E@04B4QEKFeEB4QE92AE0TQ8E@002AE92@092AE02@0900092AE92@0 92AE92@0B2AE92AE92@0B2AE92@00R@TE@0C92@092AE92@092AE92@092AE B2@092AE92@092AE92@092AE92@092AE92@092AE92@092AE92@0009895D0 ;b@T04PTEDPTEDPTEDPT02A8EDPTEB@T02@TEB@T02@TEB@T02@TEB@T02@T EB@T02@TEB@T02@TEB@T02@TEB@T02@TEB@T04PTEB@T02@TEDPTEB@T02@T EBA8EDPT02@TEDQ804PTEDQ8EDPTEB@T04Q8EDPTEDQ8EDPTEDQ8EDPTEDQ8 EFe8EFe]E@02TI6Z0fe]E@05B4QEKFfZKFeEKFeEKFfZ009]KED00fe]ZVe] EI6AZP02TI6Z00M]KEE]KJZATJY]KEFATEE]KJY]KED01TQ8E@0692@0B4QE 92@0B4QE92AEB4QE16e]E@04B4QEB4P0B4QEB4QE0fe]E@98B5D00dQ804Q8 EDQ8E@08B4QE00M8B018B5DT95E8B00T95E8B5DTB5D01DQ8E@04KFeETI6Z TI6ZKDQE0TQ8E@0592@094QEB4P092AEB4P00098B5D00b@T04Q8EB@T0003 B4QE00TTB01895DTB018B5DT9018B5DT95E8B00T95D00TQ8E@0JB4P0B4QE KFeEB4QEB4P092AEB4QE92AEB2@094QE92@092AE92@094QEB2@092AE92@0 94QEB2AE94P0B2AE02@092AEB4P092@092AE0R@T000;94QEB2AEB4P0B4QE 94QEB2@092AE92@0B4QE92AE92@00098B5D00b@T02@TEDQ80007B4QE00LT B018B5E]9018B5E]9018901]90000dPT0006KDQEB2@0KBAEB2@0B2AEB4P0 0TPT000?B2AEB2@092@0B2AEB4P0B2@0KDQEKDP0B2@092@0900092@00000 92@09000008T90005DPT02@002@T02@0000TE@0002@T000002@T000T02@0 02@T02@0000T02@002@T000002@TE@0T02@0000T000292@000D0000T9000 000T900T05D00R@T0003900092@092@0008T900012@TEDPT04PTEB@T0098 90002dQ8EDPT04PT04PT02@T02@0000T02@T000T02@T02@0000392@000000092@092@092@0000092@0900002@0900002@0 900002@0900092AE12@T0006900002@0900092@0900002@00R@T0005901E 02@092@092AE900000DT900192AE0002B4QE01i895E8B5E895E8B01895E8 900T95E8900T95E8B5E8900T95E895DT901895DT900T95E895DT901895DT B01895DT95E895DTB01895DT901895DT9018B5D292AE0198B5E895DTB018 95DT95E8B00T95DT900T95E8900T95E895DT901895DT900T95DT900T95D2 92@000LT95DT900T95DT900T95DT900T95D00R@T000;901E92@002@092AE 92@0B2AE92@092AE92@092AEB2AE008T900014PTEB@T02@TEB@TE@8T9000 3b@TEB@T02@TEB@T02@TEB@T02@TEDPT02@TEB@T02@TEB@T02@TEB@T02@T E@0292@000@T05DT900T000T95D392@00092AE92@092AE92@092AEB2@092AE B4QE92AEB2@092AEB4QEB2@094QE0TPTE@06B4QEB2AEB2AE92AEB4QEB2@0 14Q8E@04KDQEB4QEKDQEKFeE0Y6AZP03TI5EKFeEKFeE009]KED016e]ZVe8 EFe]ZTQ]E@=]KED00dQ8EFfAZVe8E@02B4QE00I]KEE]KJY]KEE]KEE]KJY] KED2B4QE00A8B018B5E8B5DT9002B4QE00A]KEE]KJY]KJY]KED2B4QE00LT 9018B5E8B5E8B5E8B00T95E]KED01dQ8E@03B6eEB4QEB4QE0098B5D01Fe] EDQ8EFe]EFe8EDQ]E@03B4QE00A8B00T900T95DT900292AE00U8B00T95E8 B5E8B5E8B018B5DT900TB5E8B0000dQ8E@0>92AEB4P0B4QEB4QEKDQEB4QE 94QEB2AE94QE92@092AE92@092AEB4P00TQ8E@05B4P0B4QEB4QEB4QEB2AE 0098B5D04R@T02@TEBA802@TEDQ8EB@T02@TEDQ8EDQ802@TEDQ804Q8EB@T EDQ802@TEDQ804Q8EB@T0098B5D00b@T04Q8EDQ8E@0292@000 KDQEB6eEB4QEB2@094QEB2AEB4QE92@092AE92@092AE92@092AE92@00dQ8 E@0@92@092AE92@092AEB4P092AE92@0B4QEB2@092AEB4P092AEB4P092AE B4QEB4P01DQ8E@0892AE92@092AE92@0B4QEB4P0B4QEB4P00dQ8E@07B4P0 B4QEB2AE94P092@0B2@092AE008T900022@TEB@T02@002@TEB@T02@002@T EB@0008T9002B2@000A895E89018900T9002B2@001=895E8900T9018900T 000T9000000T90000000900T00009000000T9000000T9000000T95DT0000 1B@T000GB2@092@0901E92@0900092@0000092@0900092AE02@0900092@0 900092@0901EB2@092@0B2@092@0B2@092@0B2@0008T90003B@TEB@002@T 000T02@T000T02@T02@002@T04PTEDQ804PT04Q8E@02B2@000=8B5E8B018 95D00R@T0008900002@092@092@0000092AE92@090000R@T0003000092@0 0000008T90001B@002@T02@T02@T02@0000292@000@T000T900T900T0002 92@000XT95DT900T0000900T000T9000900T900T95DT000292@000KFeEB4QEB4QE B4QE92@092AEB4P092AEB4QE94P0B2AE92AEB4P092AE44Q8E@05KFeEKFfZ KFeEB4QE92@000=8B5D032@T02A8EDPT02A8EDPTEDQ]EI6AEFe]ZY6AEI6A ZVe]EI6AZP9]KED2B4QE00LT95E8B5E8B5E8B5DT95E8B00T95D01DQ8E@8T 90001R@TEDQ8EB@T04PTEDQ8EBA8E@=8B5D292@024Q8E@0392@0B4QEB4QE 00I8B5D02B@TEDQ804PTEDQ804PT04PTEDPT04PTEDPT000492@000LT000T 900T9000000T900T05DT90000TPT000OB4P0B2@0B2@092@0000092@09000 92AE92@0000092@092AE000092@0000092@0001E900002@0000092@002@0 900092@092AE92@0B2@0B2AEB4P0B2@0B2AE008T90001R@002@T000002@T EB@T02@0008T90000dPTEB@004PT000292@000DT000T900T900T900T0000 0R@T0003900092@0001E00ATJX00fe] EDQ8EB@T0004B4QE00E]KEE8B5E8B5E8B5E]KED00Y6AZP=]KED3B4QE00=] KEE8B5E8B00034Q8E@08B4P0B4QE92@0B4QE92@092AE94P0B2AE0R@T0004 92AE92@092@0B4QE0R@T0007B4QE92@092AEB4QE92@0B4QE92AE00E8B5D0 0i6AZVe]EI6AZP03B4QE00A]KEFATJY]KEFATED2KFeE00E]B5E8B5E8KEFA TJY]KED00TQ8E@04KFeEB4QEKFeEKFfZ0Y6AZP03B4QEKFeETI5E00:ATJX0 2Ve]EDQ8EDQ8EDQ8EB@T04Q8EDQ804Q8EB@TEB@T00A8B5D012@T04PTEB@T EDQ800=8B5D02R@T02@TEDQ8EDQ804Q8EB@TEDQ804Q8EDQ806e]E@Y8B5D0 1DQ804Q8EDQ8EB@T04Q8E@03B2@000ATJX01Fe]EDQ8EDQ8EDQ8EDQ80004B4QE0Ve]E@98 B5D00fe]ZY6AEFfAZP02KFeE00nATEFATJZATJY]KEE8B5E8B00T95DT900T 95E8B00T95E8900TB5E895DT95D00TQ8E@8T90001B@TEB@T02@T02@TEFe] E@0292@000DT95DT900T95E8B5E8B00014Q8E@04B4P0B4QEB4QEB4P01DQ8 E@0392@0B4QEB4QE0098B5D00b@T04PTEB@T0002B2@000@T9018900T95D0 000292@000P0000T900T0000900T000T9018901895D292@001ATJY]KEE]KED00TQ8 E@0492@0B4QETI6ZTI5E0Y6AZP05KFeEB4QEB4QEB4QE94QE00A8B5D00fe] EI6AZY6AE@02KFeE00I8B5E]TJZAKJY8B5E]KJY]KED2TI6Z00=8KEE]B5E8 B5D00TQ8E@07B4P092AE94P0B4QE92@0B4QE92@00098B5D012@TEB@T04Q8 EDQ80098B5D2KFeE00A8B5DT95DT9018B5D392@000=8B5DT9018B5D01TQ8 E@0692@0B4QEB4QEB4P0B4QE92AE0dQ8E@8T90000dPTEB@T04PT000492@0 00L0000T95DT9000000T9000000T90000TPT000392AE92@092@000=89000 2DQ8EB@T02@0000T02@0000T02@T02@002@T0002B2@001M8B01895DT9018 900T95DT9018900T900T0018900T901895E8901895E8901895DT90189018 95DT9018900T901895D012@T000QB2@092@092@092@0900092AEB2@0B4QE B2@0B2AEB4P0B2@0B2AEKDQEKDP0B4QEKDQEKFeETFeEKFeETI5EfY6Z][JZ TFeETI5E]Y6ZTI5ETFeEB4P0B2AEB2@092@092AE008T90000dPT02@TEDPT 0002B2@000ATJX01Fe]EI6AZ[JfZTQ8EI6AZP02][JZ00U]KEE8B5E]KEFA]ZZA TJY8B5E]B5E8KEE]B5D01DQ8E@07KFeEB4QEB4QEB4QEKFeEB4QEKFeE0098 B5D2KFeE0TQ8E@03B2@0B4QEB4QE0098B5D00b@T04Q8EDQ8E@03B4QE00B2AEB4P0B2AEB2@0B4QEKDQEB4QE KDQETFeEKFeE]Y6Z]Y5ETI5E][JZ0[JAE@06TI6Z]Y5E]Y6Z]Y5ETI5EB2@0 0R@T0007900092@0B2@092@0B2AEB2@0B2AE00=890000b@T04PT02@T0003 92@000DT05D0900T900T000T95D00R@T0003B2AEB2@092AE008T90002R@T EB@T02@0000T02@T02@TEB@T02@TEB@002@TE@8T90001dPT02@T02@T02@T 04PTEB@T04PTE@0192@00004B4QE050T95E8B5DT901895DT95E8901895E8 B5DT900T95E895DT901895DT901895DT900T95DT901895DT901895DTB018 95DTB01895DT901895DT95DT901895DT901895DT95DT900T95DT900T95DT 901895DT901895DT95DT900T95DT900T95DT900T95DT900T95E8900T95DT 900T95DT000T95DT900T000T900T95D0900T900T95E8900T95DT900T95E8 B5DT900T95DT900T95DT900T95DT901895DT95DT901895DT900292AE028T 900T95E895DT900T95E8900T95DT900T95DT901895DT95E8900T95DT900T 05E8900T95DT000T95DT900T95DT900T95E8900T95E8900T95DT900T95DT 900T95DT900T0003B4QE0Ve8E@07B2AEB4P0B2AE92@0900092AE92@0008T 95D08R@T02@TEB@002@TEB@T02@TEB@T02@TE@0002@TEB@T02@TEB@T0000 02@0000T02@TEB@002@T02@TEB@0000T02@TEB@T02@TEB@T02@TEB@T04PT EB@T04PTEB@T02@TEDPT008T95D03dPT04Q8EDQ8EDQ8EDPTEDQ8EDPTEDQ8 EDPTEDQ8EB@T04PTEB@TEDQ8EDPT0002B4QE00Y8B018B5E8B5E8B5E]B5E] KEFATJZf]ZZATJZf]ZX2TI6Z00>ATEFAKJY]KED0196AZP06TI5EB4QE][JZ ][JZB4QETI6Z0[JfZP03KFfZB4QETI5E00:ATJX4B4QE0Ve]E@0:B6eEKDQE B6eEKDQEB6eEKDQEB6eEKDQEB6eEKDQE0TQ8E@09KFfZKFeEB4QE92@0B4QE 92AEB2@094QEB4P00098B5D022@TEDQ804Q8EDQ804Q8EDQ804Q8EB@TE@98 B5D02DQ804Q8EDQ8EDQ8EI6AEI6AZVe]EDQ8EFe]E@02TI6Z00FATEE8B5E8 B5E8B5E8B0000dQ8E@08KFeEB4QEKFeEB4QE92@0B4QEKFeETI6Z0TQ8E@03 92AEKFeEKFeE0098B5D2KFeE00U]KJY]TJY]KEFATJY]KEFATJZATEFATJZA TED00Y6AZP05KDQEB4QEB4QE94P0B2AE00=8B5D00b@T04Q8EDQ8E@03B4QE 00XT9018B5E8B5E8B00T95DT900T95E8B5DT95DT900;B4QE00PT900T95E8 B00T95DT900T95E895DTB5D292@000LT000T900T900T900T05DT900T0000 0R@T000502@092@0900092@092AE009890002b@004PT06e8EFe804PT02@T 000002@T02@002@T02@TE@0292@000A8900T95E8901895D3B2@000@T95E8 9018901895D2B2@00TQ80004B2AEB4P0B2@0B4QE0TPT0008B2AEB2@0B2@0 92@0B2@092AEB2@0B4QE14PT000592@0B2@0B2AEB2@0B4P00098900014Q8 EDPT04Q8EFe800:AKED03Fe]EMZfZ[JAZ[JAZ[JAEKJAZY6AZY6AEKJAZY6A EI6AZY5]EDQ8E@0492@000TT95E8900T90189018B00T901895DT901895D0 0R@T000392AE900092@0008T90000b@0000T02@T000892@00R@0000392@0 900092@000HT90001TPTEB@T02@TEDPT02@T04PT008T90000098B5D064PT EDQ804PTEDQ804PTEDQ8EDPT02A8EDPT02@TEDPT02@TEDPT02@TEDQ8EB@T 02@TEDPT02@TEB@T02@TEDPT02@TEDQ8E@9895D06R@T04Q8EB@TEDPT02@T EDQ8EB@T02@TEDQ804PTEB@TEB@T02@TEB@T02@TEB@T02@TEB@T02@TEB@T 04PTEB@T02@TEB@T02@TEB@T008T95D0@B@T02@TEB@T02@T0000EB@T02@T EB@T02@0EB@T02@TEB@T02@TEB@T04PTEB@T04Q8EB@T02@TEB@T02@TEDPT EB@T02@TEDPT02@TEB@T02@TEDPT02@TEDPT02@TEB@T02@TEB@T02@TEB@T 04PTEB@TEB@T04PTEB@T02@TEB@T02@TEB@T02@TEDPT02@TEB@T04PTEB@T 02@TEB@002@TEDPTEB@T02@TEB@002@TEB@T02@TEB@T04PTEDQ8E@02KDQE 01]8B5E]B5E]B5E8B5DT900T95DT900T95DT900T95DT901895DT900T95DT 900T95DT900T95DT900T95DT900T000T95DT900T95DT900T95D00R@T000> 001E92@092@092AE900092@092AE900092AE92@092AEB2AE94QEB2@00R@T E@04B2AE92@0B4QEB2@00dQ8E@0=B2AEB2@092AEB4P0B2AEB4QEB2AEB4P0 B2AEB4QEB2AEB4QEB2AE00A8B5D00fe8EI6AZ[JfZP03][JZ0Y6AZP05TI5E KFfZTI5ETI6ZTI5E00>ATJX02=ZfZY6fZTQ8EKJAZ][JZ[JfZVe]EDQ8E@:A TJX00fe]EDQ8EFe]E@03B4QE00A]KEE]B5E8KEE]KJX2KFeE00U8B5E]KJY] KEE8B5E]KEE8B5FATEFATJY]KED00dQ8E@04B4P094QEB2AE92AE0TQ8E@03 B4P0B4QEB4QE00A8B5D00dQ804Q8EDQ8E@03B4QE00FATJY]KEE]KEDT95E] KED00Y6AZP03KFeEB4QEB4P000A8B5D00fe]EDQ8EDQ8E@06B4QE00RATJY8 B00T9018B5FAKEFATJY8B5DT9002B4QE00A]KEFAKEE]KEE8B5D2KFeE0Y6A ZP04]Y6ZTI5ETI6ZKI5E14Q8E@0394P0B4QEB2AE0098B5D00fe]EDQ8EB@T 0002B4QE00I8B00T95DT900T95DT900T95D292@00TQ8E@04B4P0B4QEB4QE B4P01DQ8E@0792@092AE92@092AEB4QE92@0B4QE00f]ZZATEE8B5D00[JfZP03KFfZKFeE f][o00:f]ZX01i6AZTQ8EI6AEI6AZY5]EDQ]EDQ8E@02KFeE00M8B5E]KEE8 B5E8KEE]B5E]KEE8B5D00Ve]E@=8B5D01Ve]EI6AZVe]EDQ8EFe]EB@TE@98 B5D014PTEBA804Q8EB@T00E8B5D00dQ804Q8EDQ8E@02B4QE00M8B018B5E] KJZATEE]KEDT95E8B5D00Ve]E@03B4QEKDQEB4QE0098B5D00fe]EDQ8EFe] E@03B4QE0Ve]E@98B5D01DQ802@TEDQ8EI6AEFe]ZP02B4QE00=]KJZATEE8 B5D00TQ8E@0392@0B4QEKFfZ009]KED5TI6Z00bA]ZZfTJZATEE8B5E8B018 B5E8B01895DTB5DT9018B5E8KED8B4QE00LT900T95DT9018B5DT95E8B00T 95D01dQ8E@0392AEB4P0B4QE008T90001TQ8EB@T02@TEB@T04Q8EB@TE@ATJX4B4QE00PTB5E8B5DT9018B5E]KEE]B5E8 B5E8B002B4QE00`T9018B5E8B5E8B5DT9018B5DT900T95DT900T95E8B00T 95D3B4QE00=8B018B5E8B0000TQ8E@0392@092AEB4QE0098B5D01B@T02@T EB@T02@T02@TE@0292@000DT95DT900T900T95DT00000R@T000<900092@0 000092@0000092@0B2@0B2AE92@0B2@0KDP0KBAE0R@T0003900002@09000 008T90001B@TEB@T04PT02@T02@TE@03B2@000DT9018900T9018900T9000 0TPT0003B4P0B2AEB4P00098900014Q8EDPT04PT04PT008T9003B2@000A8 95E8B018B01895D2B2@001XT9018B00T95E89018B5E]B5E8B01]B5E8B5FA KEFf]ZZATJZAKEFf]Z[J]ZZf]Z[J]ZZfTEFf]Z[J]ZZf]ZZf]UFfTJZATJY] B5E8B00492@000A8900T901895DT9002B2@000ATEE8B5E8B5D01dQ8E@9]KED01TQ8EFe]EI6AZTQ8EI6AEFe]E@:A TJX026e]EDQ8EFe]EI6AZY5]EFe]EDQ8EFe]ZP98B5D01Fe]EI6AEFe]EFe] EFe]ZP02KFeE0i6AZP04TI5EKFeEB4QEKDQE0dQ8E@9]KED00dQ8EFe]EI6A ZP05B4QE00PT9018B5E8B018B5DT900T95E8B5DT9004B4QE00@T9018B5E8 B5DT95D6B4QE00M8B018B5E8B5E]KEE8B5DTB01895D00b@T0008000092@0 02@0900092@092AE900002@00R@T000>900092@092@0B2AEB2@0B000B4QE B2@0B4QEB2@0900002@092@090000R@T00049000B2@092@090000TPT0005 B2AEB2@092@0B2@092AE00=890001TQ8EDPT04Q804PT04Q804PTE@=89000 0b@T04PTEDPT0002B2@000E8B5E8901]B5E89018B0000TPT0007B2AEB2@0 B2@0B4P0KDQEB4P0KDQE009]KED01]ZfZ[JfZY5]EI5]EKJfZ]ZfZP:f]ZX0 2;JAZ]ZfZ[JfZ]ZfZ[JAZ[JAEI5]EFe8E@8T90003dPT02@TEDPT04PTEB@T 04PT02@T02@TEDPT04PTEDPT02@TEB@T02@002@TE@0792@000TPTEB@T02@TEDPT02@TEB@T02@TEB@T02@TEB@002@TEB@T02@T EB@T02@TE@0T02@0000TEB@0000TEB@T02@TE@0002@T02@TEDPT02@TEB@T 02@TEB@T02@TEB@T02@TEBA802@TEB@T02@TEDPT02@TEB@T02@TEDPT02@T EB@T04PTEB@T04PTEDQ8EB@TEDPT04PTEB@T02@TEB@T02@0EB@T02@002@T E@8T90002b@TEB@T04PTEB@T02@TEDPT04PTEBA804PTEDQ8EB@TE@03B4QE 00ZATJZfTJZf]ZZfTJ[JfZZATJZfTJZATJZAB5E]B5D2B4QE00DT900T95DT 900T95DT90000R@TE@0492@092AE92@092AE0R@T000;901E92@092@092@0 92AE92@092AE92@092AE900092AE008T90000b@TEB@T02@TE@0292@000A8 95E8901895E8B002B2AE00LT901895DT95E8B00T95E8901895D00TQ8E@03 KDQEB4QEB2AE0098B5D02DPTEDQ8EDQ8EDQ8EDPTEBA8EDPT04Q8EDPTE@08 B4QE012ATJY]KEE8B5FATJZf]ZZATEFATJY]KEFf]Z[Jf_nf]Z[J]_m8KEE8 B5E]KEFATJX5][JZ00?J]ZZATJZATED016e]E@03KFfZKFeEKFfZ009]KED2 TI6Z00BATEE]KEE]TJZATJX2KFeE00>fTJZATJY8B5D00TQ8E@03KFeEB4QE B4QE00M8B5D016e]EFe]ZVe]EDQ8E@:ATJX026e]EDQ8EI6AEI6AZ[JfZY6A ZVe]EDQ8E@=]KED02TQ8EFe8EFe]EI6AZVe]EI5]EFe]ZVe]EDQ8EFe]E@>f ]ZX03mZfZ[JfokJfZ[JAZTQ8EFe]EKJfZ[JfokJfZ]ZfZVe]EDQ8EI6AEKJf ZVe]E@05B4QE00A8KEE]B5E8B5E8B5D2KFeE00U8B5E]KEE8B5E8B5E]KEFA TJZATEE]KJY]KED01DQ8E@09KFeEB4QEB4QE92@092AEB4P092AEB4QE92@0 0098B5D01dQ804Q8EDQ8EDQ802@TEDQ802@TE@0292@000U8B5DT901895DT B00T95DT901895DT900T95D00b@T0003900092@09000008T90001B@002@T 02@002@T02@0E@0292@00dPT000?B2AEB2@092@0000092@092AE92@09000 92@0900092@0B2@092AEB2@092AE00=8900014PTEB@T04PT02@T00A89000 1DQ804PTEDPT04PTEDQ80002B2@000Q8B5E890189018B5E8B018901895E8 B002B2@000TT901]B5E]B5E8B01]B5E]KEFAB5Ff]Z[J]ZX00][JZP04TFeE ]Y6Zf[JZ][JZ0]ZfZP0;][JZf[JZf]ZZ]Y6Zf[JZ]Y5ETFeEKFd0B4QEB2@0 B2AE00=890003dPTEDQ804PT04PT04PTEB@T04PT02@TEDPT02@TEDPT02@T 04PTEB@T04PT000<92@000E8900T9018901895DT90000TPT00fTJZAKEE]B5D014PT0009B4QEB2@0B2@0B2@0B2AEB2@0B4P0B2@092@0 0098900392@000f]ZZAKEE8KED00TQ8E@06TI5ETI6ZTKJZ][JZf][of]ZZ0fe] E@03B4QETI6ZTKJZ00JATJX02I6AEI6AZY6AEFe]ZY6AEFe]ZVfAEFe]ZY6A E@05TI6Z00FATEE]KEFATJZf]ZY]KED00TQ8E@03KFeEKDQEB6eE0098B5D0 16e]EDQ8EDQ8EB@TE@E8B5D026e]EFe]ZVe]EDQ8EI6AZ[JfZY6AZ[JfZP:A TJX2TI5E0Ve]E@09B4QETI5EKFeEB4QEKFeETFfZKFeETI6ZB4QE00:ATJX4 ][JZ017J]_nffZ[J]_nA]ZZATJY]KEE8B5FATJ[JfZZATJY8B5FATJZATEE8 B5E8B018B5E]KED01dQ8E@06KFeEB4QE92@0KFeETI6ZKFeE0TQ8E@03TI6Z KFeEB4QE0098B5D01TQ804Q8EDQ8EDQ8EDQ802@TE@=8B5D00dQ804Q8EDQ8 E@02B4QE00ATJX2KFeE00Q] KJY]KEE]KEE8KEE8B5E]KEE]B5E]KED6][JZ00?JfZZf]ZZf]ZX00kJfZP03 TI6Z][JZ][JZ0098B5D01;JfZY6AZVe8EBA8E@A8B5D01TQ804Q8EDQ8EDQ] EFe]ZVe]E@98B5D00i6AEFe]ZTQ8E@03B4QE00=]KEE8B5E8B5D014Q8E@03 92@092AEB4P00098B5D016e]EDQ8EDQ8EDQ8E@8T90003b@TEDQ8EDQ8EB@T 02@TEB@T02@TEB@T04Q8EB@T04Q8EB@T02@TEBA804PTE@0592@000DT000T 900T000T900000000b@T0003000002@09000008T9002B2@000A895E8900T 900T000292@000M8900T90189018900T9018900T900014PT000:B4QEB2@0 B2@0B2@0B4P0B2AEB4P0B4QEKB@0B4QE0dPT0003B4P0B2@0B4QE00989000 3dQ8EDPT04PT04PT04Q804PT04PTEDQ806e]EI5]EKJAZY6AEI5]EKJAEMZf ZP02f]ZZ00?J]ZZATEGJ]ZX00[JfZP;J]ZX00m[JZ]ZfZ][JZP03f[JZ00Bf TEFAKEE]B5E8B004B2@000E895E89018B01895E8B0000TPT0003B2AEB2@0 B4P0009890001B@T04PT02@T02@T02@TE@0592@000@T95E8900T95E89002 92@000E8900T9018900T95E890000R@T000392AEB2@092@0008T90001R@T EB@T04PTEB@T02@TEDPT004T95D000=8B5D0>4PT02A8EDPT02A8EDPTEB@T 02@TEB@T04Q8EB@TEB@T04PTEB@TEDPT02@TEDPT02@TEB@T02@TEB@T02@T EDPT02@TEB@T02@TEDPTEB@TEB@T02@TEDQ8EB@TEDPTEB@T04PTE@0T02@T 02@TEB@T04PTEB@T04PTEB@T02@TEB@T02@TEB@T02@TE@0T02@T02@TEB@T 02@002@TEB@T02@002@TE@8T90000b@TEB@T02@T000292AE00`TB018900T B5E8900T95DT9018B5DT900T95E8900T95DT900292AE02@T900T95DT900T 95DT901895DT95E895DT901895DT95DT900T95DT900T95DT000T900T95DT 900T95DT900T95E8B00T95E8900T95E8B5DT9018B5DT9018B5FATJZf]Z[J ]ZZf]Z[J]ZX5][JZ01BfTJZATJZAKEE]B5E8B5E895DT900T95E8900T95DT 900T95DT900T95DT900T95DT900T95DT900005D292@0014T95DT0000900T 900T95DT900T000T95DT900T95DT900T95E8901895E8B5E8901]B5D00TQ8 E@0?KDQEB4QEKDQEB4QEB2AEB2@0B4QEB2@0B2AEB2@0B4QEB2AE94QEB2AE B4P0009895D3B4QE00A895E8B5E895E8B002B4QE00A895E8B5E8B5E]B5D2 B4QE00hTB5E8B5E]KEFATJY]KEFATJY]KEFATJZffZ[Jf_oJfZZA]ZY]B5E] KED2B4QE00=]KEFATJZA]ZX0196AZP04TI5ETI6ZTI6ZTI5E0Y6AZP9]KED0 0fe]ZVe]EFe]E@03KFeE0Y6AZP05][JZTI5EB4QEB2@094QE0098B5D00dQ] EDQ8EFe8E@06B4QE0Ve]E@05B4QEKFeEKFfZKFeETI6Z00:f]ZX0196AZ[Jf ZY6AZY6AZP:f]ZX0396AZVe]EFe]EFe]ZVe]EDQ]EFe]EFe8EI6AZVe]EDQ8 EI6AZPBf]ZX01;JfokKJZ]ZfZ[KJo`:f]ZX01KJfokJfZ[KJZ[JfZY6AE@02 B4QE0i6AZP03TI5EKFfZTI5E00E8B5D01fe]EI6AEFe8EB@TEFe]EI6AZVe] E@02B4QE00E8B018B5E8B5E8B5E8B0000dQ8E@0592@0B4QEB4QEB4QEB4P0 00A8B5D04R@T04Q8EB@TEB@T04Q8EB@T02@TEB@T02@TEDQ8EB@T02@TEDQ8 EB@T04Q8EDQ804Q8EB@TE@0000 92@002AE92@092AE92@092AE92@092AEB2@0B4QEKDQEB4QEKBAE0Ve8E@0B B4QEKDQEB4QEB2@0B4QEB2AEB4QEB2AEB4QEB2AEB4QEB2@0B4QEB2AEB2@0 B4QEB2AEB2@00TQ8E@04B2@0B4QEB4QEB2AE0dQ8E@0AKDQEB4QEB2AE92@0 B4P092AEB4P0TI6Z][JZTI6ZTI5E]Y6Zf][of]ZZf][o][JZKFeE0098B5D0 2fe]EDQ8EI6AZ[JAZY6AZY6AEI6AZY6AEI6AZ[JfZY6AE@02TI6Z00JATEFA TJZATJY]KEFATJY]KED2TI6Z0kJfZP05KFfZB4QEB4QEB4QEB4P00098B5D0 1Ve8EDQ8EDQ]EFe8EDQ]EFe]E@98B5D016e]EDQ8EDQ8EFe]ZP9]KED014Q8 EKJfZ[JfZY6AZP:f]ZX2TI6Z00nf]ZZATJY]KEE]KEE]KJY]KEFATJY]KEE] KJZATJZf]ZY8B5E]KEFATJZf]ZX00Y6AZP>f]ZX01=[JokJfZ[Jfom[JZP:f ]ZX01]ZfZY6AZTQ8EDQ8EFe]EDQ8E@9]KED2B4QE00]8B018B5E8B5DT95E8 B018B5E]KEE]KJY8KEE8901]KJX00Ve]E@98B5D016e]EDQ8EDQ8EB@TE@A8 B5D00b@T04Q8EDQ8E@05B4QE00/T9018B5DT95E8B018B5DT95E8B00T95E8 B00T95DT90000TQ8E@03B4P092AEB4QE0098B5D01DPT02@T04PTEB@T02@0 000292@0018T000T900T0000900T000T9000900T90000000900T000T900T 0018901895E8900T9000000392@000=8900T901890000TPT000?92@0B2@0 B2@0B4P0B2@0B4QEKDP0B4QEKDP0B2@0B4QEB2@0B4QEB2@0B4P000A89000 1dQ804PT04Q804PTEDPT04Q8EFe80002B2@000M8B01]B5E]B02fTJ[J]ZZA TEFAKED00]ZfZP?JfZX01KJAEKJAZ][JZ[JfZ]ZfZP02f]ZZ00cJ]_oJ]Z[J ]Z[J]Z[JfZ[J]ZZf]ZZfTEE]B5E8B0189018B5D2B2@000A895E8B0189018 B002B2@000=8B5E89018B5D00TPT0005B4P0B2@0B2@092@0B2@000DT9000 1R@TEB@T02@T04PTEB@T02@TE@8T90000dPT02@T02@TE@0292@000ATEE8KEE8B5D0 14Q8E@03KFeEB4QEB4QE00=8B5D01fe]EDQ8EDQ8EDQ8EFe]EDQ8EFe]E@02 B4QE0Y6AZP09TI5EKFeETI6ZTI6Z][JZTI6Z][JZTI5EKFfZ00A]KED01fe] ZY5]EI6fZY5]EDQ]EFe]EKJfZP02TI6Z0kJfZP08f[Kof]ZZ]]ZZ][JZf[JZ f][o][JZKI6Z0dQ8E@9]KED6B4QE00I8B018B5E8B5E]KEFATJY]KED2B4QE 0Ve]E@A8B5D00dQ802@TEDQ80004B4QE00E8B00T95E]KEE8B5E]KED00TQ8 E@8T90001R@TEB@T02@TEDQ804Q8EB@TE@98B5D01dQ802@TEB@T04Q8EB@T EDQ8EDQ80003B4QE1B@T000>B2AE92@092@092AE900002@0900002@09000 02@0900092AE02@092@00dPT0009000002@0900092AE92@09000B2AEB2@0 B2AE00=8900024PTEDQ804PTEDQ804PT04Q804PTEDQ8009890002TQ804PT 04Q8EDPT04Q8EDPT04Q8EDPT04Q8EDPT0098B0004VdT04Q8EFe804Q8EFe8 04Q8EFe8EI6AEMZfZY6AEKJAZ]ZfZ][JZ_oJZ_oJokJfZ[JAZ][JZPCJ]ZX0 5m[JZ_oJZ]ZfZ]ZfZ][JZ]ZfZ[JfZY6AEKJAZVe804PTEDQ804PT04Q8EFdT 04Q804PTEDPT04Q8EDPT04Q8EDPT04Q80002B2@000=8B5E]901895D00TPT 000492@092AE92@0901E1R@T0007B2@092@0B2@092@092AE92@0900000LT 90000b@002@T02@TE@0292@00DPTE@4T9001B4P00002B4QE00U895E8B5E8 95E8B5DT95E895E8B00T95DT90000TPTE@0@94P0B2AEB2AE92@092AEB2AE 92@092AEB2@092AE92@092AE92@092AEB2@092AE0TPTE@0594P0B2AE92AE 92@0B2AE008T90002B@TEB@T02@TEB@T02@TEDPT02@TEB@T02@TE@0292@0 01`T95DT900T95DT900T000T900T95D0900T000T95DT9000900T95DT900T 95DT900T95E895DT9018B5DT95DT900T95DT901895DT900T95E8900292AE 0118900T95E895DT900T95DT901895DT95DT900T95DT901895DT900T95DT 900T95D292@000@T95DT901895DT900292AE00M895DT901895E8B01895E8 B5FATJX00][JZP0Ff][oomZZf][of[JZTI6Z]Y6Zf]ZZf[JZf]ZZf[JZ]Y6Z TI5EKDQEB4QEB2@092AE92@0B2AE92@092AE92@092AE0R@T0007B2AE92@0 92AE02@092AE92@092AE00001E92@092@092AEB2@092AEB2AE92@0B2AE92AE B2@0B4QEKDQEB4QE1fe8E@0;B4QEKDQEB4QEB4P0KDQEB2AEB4P0B4QEB2@0 B4QEB2AE0098B5D01DPTEDQ806e8EDPTEDQ80002B4QE00A]B5E895E8B5DT B002B4QE00HT95E8B5E8B5E8B5FAKEFATJX3][JZ00JATJY8B5E]KEE]KJZA TJZf]ZX2TI6Z00Bf]ZZATJZATJZATED3TI6Z00VATEFATJZATJZAKEE]TJZA KEE]KJZATEE]KJX016e]E@98B5D016e]EDQ8EDQ8EFe]E@98B5D00fe]EDQ8 EFe]E@02B4QE00DT9000000T95E8B00TB5D00TQ8E@06TI6Z][JZTI6Z][JZ TI6ZTI5E0Y6AZP08KDQEKFeETI6ZTI6ZTI5EKFfZKFeETI6Z0[JfZP=]KED0 1;Jfom[JZ[Jfom[JZP:f]ZX02=[Jom[JZ[JfZVe]ZTQ8EFe]EKJAZ[JfZP98 B5D00dQ804Q8EDQ8E@03B4QE00/T95E8B5E8B5E]B5E]TEFAKEE]TJY8B5E] KEE]KJY8KED01dQ8E@03B4P0B4QEKFeE0098B5D012@T04Q8EB@TEB@T0098 B5D01B@TEDQ802@TEDQ802@TE@0292@000LT95DT900T95E8B00T95E8B5DT 90000dQ8E@09B4P092AEB4QEKFeEB4QEB2@092@092AEB2@000ATEFA TJZATJX00Ve]E@98B5D4KFeE0dQ8E@9]KED01TQ8EDQ]EFe]EDQ8EFe]EI5] ZPE8B5D01b@TEDQ802@TEDQ8EB@T04Q8EDQ80002B4QE00I8B01]KEFATJY] TEE]B5E8B5D3TI6Z16e]E@05TI6Zf]ZZKFeEB4QEKFfZ00>f]ZX02M[JZ][J okJfZY6AZVe]EDQ8EI6AZTQ8EFe]E@02][JZ00>ATJY8B5E8B5D014Q8E@07 92@0B4QE92AEB2AEB4P0B4QEB4P000E8B5D00fe]EDQ8EDQ8E@0;B4QE014T 95E8B00T95DT900T95E8B5DT9018B5DT900T95DT900T95E8B018B5E8B00T 95E8B0000dQ8E@08B4P092AEB4QEKFeEB4QEKFeEB4QEB2@00R@T0004B2@0 92AE92@0B2@01B@T000=B2@092@092AE900092@0000092@0900002@09000 02@092@00000008T900024PT02@T04PTEB@T04PT02@T04PT02@000989000 1B@T04PT02@T04PT04PTE@02B2@000M8B01895E]B018B5E]9018B018B5D0 0Ve8000>B4QEKB@0B4P0KDP0B4P0KDQEB4P0KDQETFeEf]ZZ]Y5E][JZomZZ f]ZZ0_ooZP;J]ZX3f]ZZ00?J]Z[JfZ[JfZX01=ZfZP06][IETFeEB4QEB4P0 B2@0B2AE0TPT000BB2AEB2@0B2AEB4P0B2AEB2@0B4P0B2@0B4QEB2@0B4P0 B2AEB2@092@0B2@0B2AEB2@0B2AE0dPT000492@0B2@092@0B2@00b@T0007 92AE92@092AEB2@092AE92@0B2AE008T90001B@TEB@T02@T02@TEDPT0004 92@000A8900T9018900TB5D1B2@00003B4QE011895DTB01895E895DT900T B5E8900T95E8900TB5E8900T95DT900T95DT900T95D292@002HT95DT900T 95DT900T95DT900T95E8900T95E895DTB01895DT95E895DTB00T95DT000T 95DT900T95DT900T95E8900T95DT900T95DT900T95DT900T95DT900T95DT 900T95DT900T95DT900T95D292@001@T95DT900T95DT901895DT900T95DT 900T95E895DT901895DT95DT900T95E8900T95DT900T95E895D292@000U8 95DT901895DT900T95DT900T000T900T95D00b@T000@92AE92@0B2AE92@0 B4QE92@092AEB4P092AEKDQETI6Z][JZom[of_ooomZZf][o0m[JZP03omZZ f][oomZZ00:f]ZX01M[JZ_oJokJAZY6AEI5]E@02B4QE00I8900T95DT900T 95DT900T95D292@000B00092@092@092@0B2@092AE92@0B2@092@092AE92@092AE92@0 B2@00B@T000014Q8E@0QB2AEB4QE92@0B4QEB2@092AEB4P092AEB2AE92@0 92AE92@0B2AE92@092AE92@092AEB2@092AE92@0B2AE92@092AE92@092AE B2@094QEB2@092AEB4P092AE92@092AE008T90002R@TEB@T02@TEB@T02@T EB@T02@TEB@T02@TEDQ8E@8T90001b@0EB@T02@TEB@T02@TEB@T02@TE@02 92@002HT05DT900T95DT000T95DT900T95DT900T95DT900T95DT900T95DT 900T95DT900T95E895DT900T95E8900T95E895DT900T95DT900T95DT900T 95DT900T95DT900T95DT900T95DT900T95DT900292AE00LT9018B5E895E8 B5E]TEFf]Z[Jf_l00][JZP03f][of]ZZf_oo00;of_l06M[Jom[JZ][JZ]Zf Z[JAZ][JZ_oJZY6AZ[JAEI5]ZTQ8EDQ804PTEDQ8EB@T02@TEDPT02@TEB@T 02@TEB@T02@TEB@002@T000TE@0292@000dT95D0000T900T95DT900T95DT 900T95DT900T95DT901895DT90000R@TE@0;92@0B2AE92@0B2AE92@092AE B2@092AEB2@0B4QEB2AE009]B5D01DQ8EFe8EDQ8EFe804PTE@03KDQE00A8 B5E]B5E]B5E]B5D2B4QE0Ve8E@03B4QEKDQEB4QE0098B5D026e8EDQ8EDQ8 EDQ8EB@T04Q8EB@T02@TE@98B5D012@TEDPT02A8EDPT00=8B5D01Fe]ZY6A EFe]ZTQ8EFe]E@02TI6Z00Ff]ZZATJZATJZA]UFfTJX00Y6AZP05TI5EB4QE KFeEKFeEB4QE009]KED4B4QE00@T9018B5E8KEE]KED3B4QE00A8KEE8B5E] B5E8B004B4QE00]8B00T95DTB01895E8B018B5DTB01895DTB01895DTB5D0 0TQ8E@05KFeETI6ZKFeEB4QEKFeE00JATJX02I6AEKJAZ[KJom[JZ[JfokJf ZY6AZVe]ZTQ]E@03TI6Z00Jf]ZY8B5FATJZATJZf]ZY]KED6B4QE00@T900T 95DT95E8B008B4QE00HT9018B5DT9018B5DT95DT9003B4QE00]]KEE8B5E8 B5E8B5DT9018B5DT95DT9018B5DT95DT90000TQ8E@0392@092AE92@00098 B5D00b@T02@TEDQ80002B4QE00B4P0KDP0B4P0KDQEB4P0KDQETI5E f[JZf]ZZ]Y5Ef]ZZom[ooonZomZZ0][JZP06f][of[JZf[JZf[JZf]ZZomZZ 0[JAZP07f[JZ][IE][JZTI5EKFeEKDP0B4QE0098900034Q8EFdT04Q804PT EDQ804PTEDPT06e8EDQ806e804PTEDQ800A8900022@T04PT04PTEDPT02@T 04PT02@T04PT00HT90001dPT02@T02@TEB@T02@TEB@T02@TE@0292@000B2@092@092@0900092@0900002@09000 92@0000092@0900092@090000R@T0003901EB2@092@000A890005DQ8EDPT 04PT04Q8EDQ804PTEFe804Q8EFe804Q806e8EDQ806e804Q806e804Q8EFe8 04Q8EFe8095]EKJAZP02f[JZ02Nf]Z[JfZ[ofZ[JfZ[of_oJfZ[J]Z[JfZ[J ]ZZf]Z[J]Z[ofZZf]ZZAKEFfTEFf]Z[J]ZZfTJZAKEE]B5E8B018901]B5E8 B0189018B01895E8B0189018B01]B5E8B01]9018B5E]B0189018B5E89018 95D00TPT0004B2AEB2@092@0B2AE0R@T0005B2@092AEB2@092@0901E008T 900012@TEB@T02@T04PT008T90001B@002@T02@T02@T02@0000392@000Q8 95DT900T900T95DT900T95E8900T9001B4QE00002TQ8EDPTEDQ8EDQ8EB@T 04Q8EDPTEBA804PTEDPT008T95D03R@T04Q8EB@T04PTEB@T02@TEDPT02@T EDPT02@TEB@T02@TEDPT02@TE@8T90006R@TEDPTEB@T04PTEBA802@TEDPT EB@T02@TEB@T02@002@TEB@T02@TEB@T02@TEB@T02@TEB@002@TEB@T02A8 EB@002@TEB@T02@TE@8T90007b@TEB@T02@TEB@002@TEB@T02@TEB@T02@T EB@T02@TEB@T02@TEB@T02@TEB@T02@TEB@T02@TEDPTEB@T02@TEDPTEB@T 04PTEB@T02@TEB@T02@TEB@T02@0E@0292@000`T95DT900T95DT900T95DT 900T95DT901895DT900TB5E895D2B4QE00jf]Z[Jf_oof_oJfZ[ooooJf_oo oj[Jf_oJfZ[Jf_oJfZ[of_oooooJfZX2f[JZ01[ofZZf]ZZAKEFfTJY]B5E8 B5E8900T95DT900T95E8900T95DT901895DT900T95DT000T95DT900T95DT 900T95DT000T95DT000T95D292@0018T95DT900T900T95DT901895DT9018 95DT900T95DT901895DT901895DT95DT900T95E8B002B2AE00@T9018B5E8 95E8B5D4KDQE00=8B01]B5E895D00TQ8E@03B2AEB4QEKDP00098B5D2KDQE 00A8B5E]B5E8B5E]B5D2B4QE00LT9018B5DT9018B5DT9018B5DT90000TQ8 E@0992@0B4QE92@0B4QE92AEB4QE92AEB4P0B4QE00A]KED02I6AZ[JfZY6A ZY6AZY6AEI6AZVfAEFe8EFe]E@03B4QE00E8KEE89018B5DTB5E8B5D00Ve] E@04KFfZKFeEKFfZKFeE0TQ8E@0=B4P0B4QEB4QE92@0B4QEB2AE92@0B4P0 92AEB4P092AEB4P092AE00KFeETI6ZKFeE]][of[JZ94QE92@0B2@0B4QEB4P092AE B4P092AE92@00TQ8E@0392AEB4QE92@00098B5D01dQ804Q8EB@TEDQ802@T EDQ8EDQ80002B4QE00A8B018B5E8B5E]KED2B4QE00TT9018B5DT9018B5DT 95DT900T95DT900T95D00TQ8E@07B4P092AE92@0B4P092AEB4QEB4P000=8 B5D00fe]EDQ8EDQ8E@02KFeE00A8B5E]KEE8B5E8900292@00118900T900T 900T900T95E8900T901895DT9018900T9018000T9018900T901805D392@0 00HT0000900T0000900T0000900492@000PT000T900T900T95E8900T95E8 900T9003B2@000A8B5E8B01]B018B5D2KDP000m8B5E]B018B5E]B018B01] B5E]B01]B5E]B01]KEFfTJ[J]Z[JfZZfTJ[ofZX00]ZfZP;JfZX01=[JomZf Z[JfZ[JAZP;JfZX01mZAEI5]EFe8EFe]EKJAEKJAZY6AE@02KDQE0198901] B5E8B01]B5E8B01]B5E]B01895E]B01895E8B0189018B5E]B018B01]B5E8 9018B002B2@000M8B0189018900T9018900T901890001B@T000@B2@092@0 92@0B2@092AEB2@092AEB2@092@092AE92@092AE92@0B2@092@092AE0R@T 0003B2@092@0B2@0008T9001B2AE0B@T00000dQ8E@0ZB2AEB4QEB2AE94P0 B2AE94QE92@0B4QE92@0B2AE92@092AE92@0B2AE92@092AE92@092AE92@0 92AEB2@094QE92@092AE92@092AE92@092AEB4QEB2AE92@0B2AE92@092AE 92@092AE92@092AE92@092AE92@092AE0R@T000392AE92@092AE008T9000 12@TEB@T02@T02@TE@8T900012@TEB@T02@T02@TE@8T90003B@TEB@T02@T EDPT02@TEDPT02@TEB@T02@TEB@T02@TEB@T02@TE@0292@001DT95DT900T 95DT900T95DT000T900T95DT900T95DT900T95DT900T95DT900T95E8900T 900T95E8B5E890000TQ8E@05TI6Zf]ZZf][of]ZZf][o00;oool03=[Joooo oooJoooooooJZ][JoooJZ][JomZfZ][JZ_oookJAE@:ATJX026e8EDQ8EDPT EDQ8EB@T02@TEB@T02@TE@8T90001b@TEB@T02@T02@T02@TEB@T02@TE@03 92@001DT95DT900T95DT000T95DT900T95DT900T95DT900T95DT900T95E8 95DT900T95DT900T95E8900T95E890000R@TE@0>B4P092AEB2AE94P0B2AE B4QEB2AEKDQEB4QEKDQEB4QEKDQEB2@0KDQE0TQ8E@9895D00dQ806e8EDQ8 E@02B4QE00=]B5E8B5E]B5D01DQ8E@0592AEB4P092AEB4P092AE008T9000 1b@TEDQ8EB@T04Q8EBA804Q8EDPTE@03B4QE00a]KEE]KJZf]ZZATJZATEE] KJZATEE]KJY]KEE8B5E]KEE]B5D3B4QE00M8B018B5E]KEE]KEFATJY]TEFA TJX00Ve]E@98B5D024PTEBA8EDPT02A8EDQ8EB@T04Q8EB@TE@98B5D01DQ8 02@TEB@T000T02@TE@03B4QE00NATEE]KJY]KEFATJY]KEE]KJZATED01;Jf ZP0CKFeE][JZB4QETI6Z][JZ]]ZZf]ZZTI6ZKFeEB6eE]Y6Z][JZ][Ko][JZ KFeEKFfZ][JZf[JZ][JZ00E8B5D00b@TEDQ8EB@T000292AE0R@T00I8B5D0 0b@T02@TEB@T0007B4QE00A8B00T95DT900T95D3B4QE00PT900T95E8B5DT 900T95DT9018B5DT95D2B4QE00B2@092AE94P0B2AE92@0 92AE92@092AE92@092AE92@092AE92@092AE0R@T008T95D292@0018T95DT 900T95DT900T95E8900T95DT900T95E8900T95E8900T95DT900T95E8900T 95E8900292AE00U8900T95E895DT901895E8B5E89018B5E895D00TQ8E@04 KDQEB4QEKDQEB4QE0Ve8E@03B4QEKDQEB4QE00=8B5D02fe8EDQ8EDQ8EFe8 EDQ8EB@T02@TEDQ802@TEDQ802@TE@02B4QE00XT95DT9018B5DT95E8B00T 95DT9018B5DT95E8B002B4QE00A8B00T95E8B01]KED2TI6Z00BATEFATJZA KJY8KED4B4QE00=]KEE8B5E8B5D014Q8E@0CTI5EKFfZKFeEB4QETI5EB4QE 94QE92@0B4QEKFfZKFeEB4QE92AEB4P0B4QEKI6ZKDQEB4QEKFeE0098B5D0 1B@T02@TEBA806e8ZY6AZP04][JZ00bATJZf]ZZATJZf]ZZATJY]KEFf]ZY8 B5Ff]Z[J]ZZf]ZZATJX2B4QE00FATJZf]Z[JfZZf]ZZATJX00kJfZP05KFeE 94QEB4QEB2@094QE0098B5D01b@T04Q8EB@T04Q8EB@T04Q8EB@TE@0292@0 00/T95E8B5E8B5DT900T95DT9018B5DT900T95E8B5E]KED00TQ8E@0392@0 92AE92@00098B5D01B@T02@TEB@T04Q8EDQ80002B4QE00`T9018B5E8B5DT 900T95DT9018B5DT9018B5DT95E8B00T95D2B4QE0Ve]E@08KFfZKFeEB4QE KFeEB4QEB2@092@0B2@00R@T0006B2@092@0B2@092@0B2AE92@00TPT0008 92@0B2AE92@0B2AE92@0B2@092AEB2@00R@T000;000092@002AE900092@0 000092@092AE900092@0001E008T90000b@TEDPT04PT0004B2@001M895E8 B0189018B01]B5E8901]B5E8B01]B018B5E]B018B01]B018B5E]B5GJ]UGJ fZ[J]ZZf]Z[J]ZZfTJ[J]ZZf]UD00[JfZP09f]ZZf[JZf]ZZf[JZ]Y6ZTFeE ]VeETFd0KDQE00:ATED0295]ZVe]EFe8EFe804Q8EFe804Q804PT009]B5D0 3dQ804PTEDPT04PTEFe804Q804PTEFe804Q806e804Q8EDPT06e804PT04Q8 0003B2@000PT9018900T9018900T9018900T9018900292@000U8900T900T 95E8900T900T95DT900T000T95D00R@T0004900092@092@092AE0R@T0003 B2@092AE92@00092@092AEB2@092AE92@092AE92@0B2AE92@092AE92@092AE92@092AE 0R@T000>92AE92@092AE92@092AEB2@092AE92@0B2AE94QEB2@0B4QEB2AE KFeE0][Jo`0AKEE]KEE8B5D00TQ8E@0:92@0B2AE92@0B4P092AEB4P092AE B4QE92@0B4P00TQ8E@0892@094QEB4QEB4QEB4P092AEB2@094QE14Q8E@03 92@092AEB4QE00:f]ZX00fe]Z][JZY6AZP02TI6Z00>f]ZY]KJY]KED00Y6A ZP0=KFeETI6ZB4QETI5ETI6ZTI5EB4QETI6Z][JZTI6Z][JZf][oTI5E0098 B5D00dPT04Q8EB@00005B4QE00]8B00T95DT900T95E8B018B5DTB01895E8 B5E8B00T95D00TQ8E@0392@092AE92@000=8B5D02B@T04Q802@TEDQ8EB@T 04Q8EB@TEDQ802@TE@02B4QE00LT95DT900T95DT95DT900T95DT90001TQ8 E@0592AEB4P0B4QEKFfZKFeE0098B5D00fe]EDQ8EDQ8E@02B2@000dT95DT 900T900T9018900T9018900T95E8900T9018901895DT90000TPT0003B2AE 92@0B2AE008T90001B@002@T02@T02@T02@0000292@000PT0000900T900T 000T900T000T95DT9004B2@000=8B5E8B01]95D00TPT000BB4P0B2@0B4QE B2@0B4QEB2@0B4P0KDQEB4P0TFeEKDQETFeE]Y6Z]Y5EKFeETFeEKFeETI5E 1=ZfZP06][JZ]Y6Zf[JZf]ZZTFeE]Y5E0i5]E@03TI5Ef[JZTI5E009]KED0 5fe804Q8EDQ806e8EDQ806e804Q8EFe804PTEDQ804PTEDQ806dT04Q8EFe8 04Q8EFe804Q8EDPT04Q804PTEDPT04Q80002B2@000hT9018900T95E8900T 9018900T901895DT9018B5DT900T95DT901895D292@000f]ZX2f]ZZ 01JfTEFATEGJ]Z[J]ZZf]Z[J]ZZf]ZZfTJZAKEE]B018B01895E89018B5E8 B0189018B5E]B01895E8B0189018B5D2B2@000=8B0189018B0000TPT000B B2AEB2@0B2@0B2@092AEB2@092@0B2@092@0B2@092AE92@0B2AEB2@092@0 B2@092@0B2@00R@T000;B2@092@092@0B2@092AE92@092AEB2@092AEB2@0 92AE00@T90000dPT02@TEB@T0001B2@00003B4QE00A8900T95E8B01895D2 92AE00e8B00T95DT95DT901895DT900T95DT900T95DT901895DT900T95D0 0R@T000:92AE92@092AE92@092AE92@092AEB2@092AEB2@00R@TE@0H92@0 92AE92@092@092AE92@092AE92@092AE92@092AE900092AE02@092@092AE 92@092AE92@092AE92@092AE92@092AE0R@T000792AE92@092AE92@092AE 92@092AE008T90001B@TEB@T02@TEDPT02@TE@0292@000@T95DT900T900T 95D292@00092AEB2@0B2@0B4QEB4P0KDQEB4P0KDQEB4QEKDP0KFeEf]ZZ omZZom[o0_oJZP04f]ZZf[JZ]Y5ETI6Z0[JAE@0@]Y6Zf]ZZomZZf[JZKFeE B2AEB4P0B2@092@0B4QEB2@0B4QEB2@0B4P0B2AEB4P00TPT000@B2AEB2@0 B4P0B2@092@0B2@092@0B2@0B2AE92@0B2@092AEB2@092AE92@0B2@00R@T 0004B2@092AE92@0B2@00R@T000EB2@092@0B2@092@0B2@092@0B2@092@0 B2AE92@092AEB4P092AEB2@092AE92@0B2@092@092AEB2@092@0004TB000 00=8B5D064Q802@TEDQ804PTEB@T04Q8EB@TEB@T04Q8EB@T02@TEB@T04PT EB@T02A8EB@T04Q8EB@T04Q8EB@TEB@T02@TEB@T02@TE@8T90002b@TEB@T 02@T04PTEB@TEDPT02@TEB@T02@TEB@T02@TE@0292@000TT95DT900T95DT 95DT900T000T95DT900T95D00R@T000<92AE92@0900092@092AE92@092AE 92@092AE92@092AE92@00R@TE@0492@092AE92@092@00R@TE@0692@092AE 92@092AE92@092AE0R@T000@92AE92@092AE92@092AE92@092AEB4P092AE 92@0B4QEB2AEB4QEf]ZZf][ooonZ0oooo`05f][oom[ooooooonZom[o00;o ool06?oJom[oZ_oJooooom[JoooJomZfZ[JAZ[JfZ][JZ[JAEI6AZY5]EDPT EDQ804PTEDQ8EB@T02@TEDPTEB@T02@TEB@T02@TE@8T90003b@TEB@T02@T 02@TE@0T02@TEB@T02@002@TEB@T02@TEB@T02@TEB@T02@TE@0292@0028T 95DT901895DT900T95DT900T95E8900T95E895DT900T95E895DT900T95DT 900T95E8900T95E8900T95E895E8900T95E8901895DT95E8B00T95E895E8 B5E895E89018B5D2B2AE00@TB01895E8B5E895D2B4QE01M895E8B5DTB00T 95E895DT9018B5DT900T95DT900T95DTB00T95E8B00TB5E895DT901895DT B01895E8B018B5DT95D00R@T000D92AEB2AE92@092AEB4P092AEB4P092AE B4P092AE92@092AE92@0B4QE92AEB4P092AE92@092AE92@00R@TE@0=92@0 92AE92@092AEB4P092AEB4P092AEB4QE94P092AEB4P094QE00A8B5D0196A Z[JfZY6AZ][JZP;Jf_l02M[JZ[JfZ][Jom[JokJfZY6AZVe]EKJfZ][JZP02 ][JZ00KJf_oJfZZf]ZZf]_oof_nATJX2B4QE00Q8B00TB5E8B5E8B5DT9018 B5DTB5E895D392@000fTED01;I]EI5]EI5]EKJAZP:f]ZX0 0fe8EB@T04PT0002B2@000=8B5E89018B5D014PT0003B2AEB2@0B2@00098 900034PTEDPT04Q804PT02@T04PT02@T04PT02@T04PTEB@T04PT008T9000 34PT02@TEB@T04PT02@T04PT02@T04PT02@T04PT02@T04PT008T90002DPT 02@T04PTEB@T02@TEDPT02@TEB@T04PT000292@00B@TE@4T9001B2@00002 B4QE029895E8B5E8900T95E8901895E8B5DT901895E8B5DT901895DT900T 95E895DT900T95E8900T95DT901895DT900T95DT900T95DT900T95DT900T 95DT900T95E8900T95E8900292AE00hT900T95DT900T95DT900T95DT900T 95DT900T95DT900T95DT900T95D292@000AB5FAK@2fKED00Y5]E@09]VeE TFeETFeETFd0KDQEKFd0TDQEKFeEKDP000>AKED07KJAEKI]EI5]EI58EFe8 04PT02@T04PT02@T04PTEDPT04Q8EFe804PT04Q8EDPT04Q804PTEDPT04Q8 04PTEDPT04Q802@T04PT04PTEDQ804PTEB@T0002B2@000=8B01895E89000 14PT008T900054PT02@T02@T02@T04PTEDPT02@T04PT02@T04PT02@TEDPT 02@TEDPT02@T04Q802@T04PT02@T04PT00B4P0B2@092@0B2@092AEB2@092@0B2@0B2AE92@0 B2@092@0B2@092@01DPT0009B2AEB2@0B2AEB2@0B4QEB2@092@09000B2AE 00HT900024PTEDPT04PTEDPT04PTEDQ804PT04Q8E@9890001B@T04PTEB@T 04PT02@0000292@000@000189018B01]B5D2KDP000>AB5FAKEFfTED00]ZA E@:fTED05MZAEKJAZ[I]EI5]EFe]EFe806e]EI5806e8EI5]EFe]095]EKI] EKJAEI5]EFe8EDPT02@T04PTEDPT04Q8E@02B2@00218B5E8901]B5E89018 B5E]9018B01895E89018B01895E8901895DT9018900T9018901895E8B018 95E8B018900T901895E8900T95DT9018900T95E8900T95E8900292@00198 900T95E8900T95E8900T9018900T901895DT901895E8900T95E8900T95DT 901895DT9001B2AE0003B4QE03189018B5DT95E8B5DT901895DT901895DT B5E89018B5DT95DT900T95E8900T95DT900T95DT901895DT900T95E8900T 95DT901895DT901895DT900T95DT000T900T95DT900T95DT000T95DT900T 000T95DT900T000095DT000T900T95DT900T95D292@000L095DT900T05DT 900T95DT900T95D00R@T000392AE92@092AE008T900014PTEB@T02@T02@T E@8T90008dPTEB@T02@TEB@T04PTEB@T04Q8EB@T02A8EDPTEDQ8EI6AZ][J Z_ooooooZ_oJooooZ][JoooJZ]ZfZ_ooom[JooooZ][JZ][JoooJZ][JZ]Zf Z_oJoooJZ][JZ][JoooJZ][JoooJo`02f]ZZ01CofZZf]ZZAKEE]B5E8B5DT 901895DTB01895DT95E8900T95DT900T95DT900T95DT900T95DT900T95D2 92@000ATEE]KJY]KED00[JfZP04B4QE KFfZTI6Z][JZ0Y6AZP98B5D292@00TQ8E@0A92@0B4QEB4QEB4QE92@0B2AE B4QE92@0B4QE94QEB4QE92@0B4QE92@092AE92@092AE0098B5D01R@TEB@T 04Q8EB@T04Q8EB@TE@I8B5D00fe]EDQ8EFe]E@02KFeE00Y]KJY]KEE8B5E] KEE8B5E]KEE8B5E]KEE8B5E]KED5B4QE00=]KEE8B5E]KED00TQ8E@9]KED3 B4QE00=]KEE8B5E]KED00TQ8E@9890000b@T04PTEDPT0004B2@000M895E8 901895E8901895E8901895D014PT0003B4P0B2AEB2@000=890000b@T04PT 02@T0002B2@000A895E890189018900292@00dPT0003B2AEB2@092@00098 90000dPTEDPT04PT000292@000Q8901]B5FAB5FAK@2AKEFfKEFAKEFfKED2 ]Y5E00KJTEGJTJ[J]UGJTJ[JTEGJTJX2fY5E00CJ]UFfTEFfTEFfTED5TFeE 00A]B01]B5E]B01895D2B2@000e8B5E89018901895E89018B01895E89018 B01]B01895E8B018B5D00TPT000=B4P0B2@0B2@0B2@092@0B2@092@0B2@0 B4P0B2AEB2@0B4P092@00098900292@001=8900T9018900T9018900T95E8 900T9018900T95E8B00T9018900T95E8900T9018900T901890000R@T0003 B2@092@092@0005890000098B5D06dPTEDQ8EDPTEBA804PTEB@T04Q8EB@T 02@TEB@T02A8EB@T04PTEB@T02@TEDPT02@TEB@T04PTEB@T04PTEB@T02@T EB@T02@TEB@T04PTE@0292@000HT95DT900T900T95DT900T95D292@000@T 95DT900T900T95D292@00R@TE@0492@092AE92@092AE0R@T000e92AE9000 92AE92@092AE92@0B2AE92@092AE92@092AE92@092AE92@092AE92@0B2@0 92AE92@092AE92@092AEB2@092@0B4QEB2AEB4QEKFeE][JZom[of_nZoooo om[ooonZf]ZZf[JZf][ooooof[JZf]ZZom[o][JZom[ooooof]ZZom[ooooo f][of]ZZf[JZf][oomZZf]ZZ00;J]ZX03]ZAZY5]EFe]EFe8EDQ804PTEB@T 04Q8EB@T04PTEB@T02@TEDPT02@TE@8T90003B@TEB@T02@TEB@T02@TEB@T 02@TEB@T02@TEB@T04PTEB@T02@TE@0292@0024T95DT900T95DT901895DT 900T95DT900T95E8900T95DT900T95DT900T95DT900T95DT900T95DT900T 95DT900T95E8900T95E895DT900T95DT900T95DT901895DT90000TPTE@0I 92@0B2AEB2AE92@0B2AE92AEB2@0B4QE92@0B2AE94QEB2AEB4P0B2AE92AE B4QEB2AEB4QE92AEB4QEB2@094QEB2AEB4P092AE0098B5D01R@T04Q8EB@T 02@TEDQ802@TE@8T90001B@TEB@T04Q8EB@TEB@T0002B4QE00DTB01895DT B5E8B5E8B0000TQ8E@06B4P0B4QEB4QEKFeEKDQEKFeE0Y6AZP=]KED3B4QE 00e8B018B5E8B5DT95DT900T95DT900T95E8B5E8B01895DTB01895D00TQ8 E@03TI6Z][JZ][JZ00:f]ZX0196AZTQ8EI6AZY6AE@:ATJX01;JfZY6AZVe] EFe]E@98B5D3KFeE0kJfZP05TI6ZKFeEB2AE94QEB2AE0098B5D00b@T04Q8 EDQ80002B4QE01DTB5DT900T95E8B01]KEE8B5DT95DT900T95E8B018B5E8 B00T95E8B5DT9018B5DT900T95DT9018B5DT900014Q8E@9]KED00dQ8EFe] EDQ8E@02KFeE00=8B5E]KEE]KED014Q8E@9]KED4B4QE00=]KEE8B5E8B5D0 0fe]E@05KFfZB4QEKFeEKFeEB4QE009]KED034Q8EFe]EDQ8EDQ804PTEDQ8 02@T04PTEB@T04PTEDPT02@T0098900012@T04PT04PT04Q8009890002R@T EDPT04PT04PT02@T04PT04Q8EDPT02@T04PTE@8T900034PTEDPT04PT04PT 04PTEDPT02@T04PT02@T04PTEDPT02@T00=890002DPTEB@T04PT02@TEB@T 02@004Q80958EI580002TFeE00FfKEFAKEFAKEFAKEFfKED00]ZAE@0:fY6Z fY5EfY6ZfY5EfY6Zf[IEfY6ZfY5E]Y5E]Y6Z0[JAE@04]VeETFeETFeETFeE 0Ve80008B4P092AEB2@0B2@0B4QEB2@0B4P0B4QE0TPT000AB4P0B2@0B2AE B4P0B2@0B4P0B2@0B4QE92@0B2AE94P0B2AE92@0B2AEB2@092@0B2AE0098 90007TPTEDPT04PTEB@T04PT04PTEB@T04PTEB@T04PTEB@T04PT02@T04PT EB@T04PT02@T04PTEB@T04PT02@T04PTEB@T04PT02@TEDPT02@T04PTEB@T 04Q8E@4T90000098B5D08TQ802@TEDQ802@TEDPTEBA8EDPT02@TEDPT02@T EDPTEB@T04PTEB@T04PTEB@TEB@T04PTEB@T02@TEB@T02@TEDPT02@TEDPT 02@TEB@T02@TEB@T02@TEB@002@TEB@T02@TE@8T900012@0EB@T02@T02@T E@8T90002B@0EB@T02@T02@T02@TEB@T02@0EB@T02@TE@0392@000`T95DT 901895DT900T95DT901895DT900T95DT900T95E8900292AE00HT901895DT 900T95E895DTB002B2AE00i8B5E]KEGJ]Z[Jf_oooj[ooooJf_oooj[JfZ[J TJ[JfZ[of_oJfZ[Jf_l2f]ZZ00SJ]Z[JfZ[of_oJf_oooooooj[ooooof_l2 f]ZZ0]ZfZP0Gf]ZZf[JZTFfZTFeEKDQEB4QEB2AE92@0B2AE92@0B4QE92AE 92@0B2AE92@0B2AE92@092AE92@092AE92@0900092AE008T90000b@TEB@T 02@TE@0292@001DT95DT900T95DT901895DT900T95DT900T95DT900T95DT 900T95DT901895DT900T05DT900T95E8900T95D00R@T000:92AE900092AE 92@092AE92@0B2AE92@092AE92@00TPTE@0P92@0B2AE92@092AEB4QE92@0 B4QEB2AE94P0B2AE92AEB2AEB4QEB2@0B4QE92AEB2AE94P0B2AE94P0B2AE B4P094QEB4QE94QE92@092AEB4QE92@0B4QE92@092AE0TQ8E@0792@0B4QE B4QEB4QE92@092AEB4P000A8B5D014PTEDQ804Q8EB@T00M8B5D00dQ]EFe8 EFfAZP02KFeE0TQ8E@9]KED04BA8EDPTEDQ8EDQ8EDQ802@TEDQ802@TEDQ8 EB@T02@TEBA8EDPTEB@T02A8EDQ8EKJAZP09][JZ00NATJZATEFATJY]KJZA TJY]KEFATED00Y6AZP0:KFeE][JZ][JZ]Y6Z][JZKFeE94QEB2@094QEB4P0 1DQ8E@0492@0B2AE92@092AE0dQ8E@0692@092AE92@092AE92@092AE0R@T 000992AE92@092AEB4QE92@092AE92@092AEB4P00098B5D00fe]EDQ8EDQ8 E@02B4QE00=]KEE8B5E8B5D00dQ8E@9]KED00dQ8EFe]EDQ8E@02B4QE00=] KEE8B5E]KED00TQ8E@03KFeEB4QEB4QE009]KED00fe]ZVe]EDQ8E@02B4QE 00=]KEE8B5E8B5D00TPT0003B2AEB2@0B2@000=8900014PTEDPT04PT04PT E@9890001R@TEDPT04PT04Q804PT04PTE@I8900292@00TPT000592@0B2AE B2@0B2@0B4QE00A890002B@T04PTEDPT02@T04PTEB@T04PT02@T04PT0002 92@000E]B5FAB02AB5FAKEFfTED00Y5]E@06TDP0KDQETDP0TFeETDQETFd0 0[I]E@;JTED00mZAZ]ZfEMZAZP03fY5E00>fTJZfTEFfTED00Y5]E@06TDP0 B4QEB2@0B2@092@0B2AE0TPT000;B4QEB4P0KBAEB4P0B2AEB2@0B4P0B2AE KDP0B2AEB4P000A890004B@T04PT02@T04Q804PTEDPT02@T04PTEDQ804PT 02@T04PTEB@T04PT02@T04PT02@T0002B2@000XT95E8900T9018900T9018 95DT9018900T901895D292@000LT95E8900T900T95DT9018900T90000DPT E@000TQ8E@0OB2AEB4QEB2AE92@0B4QEB2@092AEB2AE94P0B2AE92@0B2AE 94QE92@092AEB2@092AE92@092AE92@0B2AE92@092AE92@092AE92@092AE 92@092AE92@092AE008T90000b@002@TEB@T000292@000PT95DT000T900T 95DT900T95DT900T95D392@001TT95DT900T95DT95E8B5E8900T95E895DT 900T95E8900T95E8900T95E8900T95DT900T95E8900T900T95E8B00T95E8 900T95D00TQ8E@0>KDQEf]ZZf][oooooomZZf][oomZZf]ZZf[JZ]Y6Z]Y5E ]Y6Zf[JZf]ZZ0]ZfZP05f]ZZf[JZf]ZZf[JZf][o00;of_l0F][JZ]ZfZ]Zf Z][JZ]ZfZ][JZ[JAZY5]EFe8EDQ8EDPTEB@T04PTEBA8EDPT02@TEDPT02@T EB@T02@TEB@T02@TEB@T04PTEB@T02@TEDPT02@TEB@T04PTEB@T02@TEB@T 02@TEB@T02@TEB@T02@TEB@T02@TEB@T02@002@TEB@T04PTEB@T02@TEB@T 02@TEB@T02@TEB@T02@TEB@T02@TEB@T02@TEDPTEB@T02@TEB@T02@TEB@T 04PTEB@T02@TEDPTEB@T02@TEB@T02@TEDQ8EB@T04PTEB@T02@TEDPTEB@T 04PTEB@T04Q8EB@T04Q8EB@TEDPT04PTEDQ802@TEDQ8EDPTE@98B5D07DPT EB@T04PTEBA802@TEB@T04Q8EB@T02A8EDPTEBA804PTEDQ8EB@TEDQ802@T EDQ8EB@TEB@T04Q8EB@T02@TEB@T02A8EDQ8EBA8EDPTEBA8EFe]E@04B4QE 0Ve]E@03TI6ZKFeETI6Z00I8B5D03b@T02@TEFe]EDQ8EB@TEDQ8EB@TEDQ8 04Q8EB@TEDQ802@TEBA804PTEDQ]E@02][JZ00VATJZf]_nf]Z[Jf_nf]Z[J f_nATJY8B5E]KED00TQ8E@05B4P0KFeE][JZf][o][JZ00:ATJX01KJfZ[KJ ZY6AZY6AZY6AE@02B4QE00/TB5E895DT900TB5E8B5E895DTB018B5DTB5DT 901895D00TQ8E@0@B4P092AE92@092AE92@0B4QE92AE92@092AE92@0B4QE B4P092AEB4P092AEB4P014Q8E@05B4P0B4QEB4QEB4P0KFeE00=8B5D3KFeE 0TQ8E@03KFeEB4QEB4QE0098B5D00dQ804Q8EFe]E@03B4QE0Ve]E@06TI6Z B4QEKFeEKFfZKDQEB6eE14Q8E@06B2@0B4QEB2@092@0B2@0B2AE0TPT0004 92@0B2@0B2@092@014PT000AB2AEB2@0B2@0B4P0B2AEB2@0B2AE92@0B2AE B2@092@0B2AE92@092AEB2@092@0B2@00098B0001DPT04PTEDPT02@T04PT 000292@014PT0006900092AE92@092@0TDQETFd00Y58E@07TFeETDP0KDQE KDP0KDQETDQE]Vd000:fKED2fY5E00BfTEGJTJ[o]UGJ]UD2fY5E00_JTJ[J ]UGJTJ[J]UFfTJZfTEFfKEFAKEE]B018901895D00dPT000[B4QEB2@0B4P0 B4QEB4P0B2@0B4P0B2AEB4P0B2@0B4P0B2AEB2@092AEB2@092AEB2@092@0 B2@092AEB2@092@0B2@0B2AE92@0B2AEB2@092@0B2@092@0B2AE92@0B2AE 92@0B2AE92@0B2@094P0B2AE92@0B2@092@0B2AE008T90002DPT02@T04PT 02@T04PT02@T04PT02@T04PTE@0194P00002B4QE01Q895E8B5DT9018B5E8 900T95DTB5E8900T95E8B5DT900T95E8900T95E8900T95DT900T95E8900T 95E8900T95DT901895D292@000`T95DT900T900T95DT900T95DT900T95DT 900T95DT000T95D292@000@T95DT900T900T05D292@001DT05DT900T95DT 901895E8B01895DT900T95E8B5DT901895DT900T95DT900T95DT900T95DT 901895DT90000R@TE@04B2@092AEB4P092AE0dQ8E@0AB01]B02fKED00mZAE@0@ TFeETDP0TDP0TDQE]VeEokIEokJZokIEfY6Zoi5EokJZfY5Eoi5EokJZf[IE f[JZ0]ZAE@0F]VeEKDP0B2AEB2@0B4QEB2@0B4P0B2@0B4P0B2AEB2@0B2AE B2@0KDP0B4P0KDQEB4QEKB@0B4P0B2AEB2@0B4P014PT000492AEB2@0B2@0 92@00TPT0007B2AE92@0B4QE92@0B2AE92@0B2@0008T90002dPT02@T04PT EB@T04PT02@T04PT02@T04PT04Q8EDPT000292@000I8900T9018900T95E8 B00T95D1B4P00003B4QE01Y895E8B5DT95E8900T95E895DTB01895DT9018 95DT9018B5DT900T95E8900T95DT901895DT900T95E8900T95DT900T95DT 900T95D392@000PT95DT900T000T900T95DT900T000T95D292@000DT95DT 900T95DT900T95D00R@T000R92AE92@0900092AE92@092AE92@092AE92@0 92AEB2@092AE92@0B2AE92AEB4QE92@0B2AEB4QEB2AEB4QEf[JZf][oom[o f_nZom[of]ZZoooof][ooonZom[of_ooom[ooooo0_oJZP06]Y6ZTFeE]Y6Z ]Y5E]Y6Z]VeE0]ZAZP0:]Y6ZfY5EfY6ZfY5E]Y6ZfY5E]Y6Z]VeETDQETFeE 0kJAZP0B]Y5E]Y6Z]Y5ETFeE]Y6ZTFeE]Y6ZTI6ZB2@094QE92@0B2AE92@0 B2AE92@092AE92@092AE0R@T000AB2AE92@0900092@0B2AE92@092AE9000 92AE900092AE92@092AE92@092AE92@092AE008T90002B@TEB@T02@TEB@T 04PTEB@002@TEDPT02@TE@0292@001@T95E8900T000T95DT901895DT9018 95DT900T95DT900T95E8900T95DT901895DT900T95DT9018900292AE00a8 900T95DT95E8900T95E89018B5DT95E895DTB5E8900T95D2B4QE00A895DT 900T95DT9003B4QE00U8900TB5E8B5DTB01895DTB5DT901895DTB5D00TQ8 E@8T9002B4QE00=895E8B00T95D01dQ8E@07KDQEB6eEKDQEKFfZTI5ETI6Z TI5E00:ATJX00i6AEFe]ZTQ8E@02B4QE00=8B00T95DT90000R@TE@05B4P0 B4QEB4QEB4QE92@00098B5D03i6AZ[JfZ[JfZ][Jom[JZ][Jom[JZ][Jom[J Z][JokJfZ][Jom[JZ[JfZY6AZP02][JZ00?JfZ[Jf_oJfZX00][Jo`04f]ZZ f][of][of]ZZ0Y6AZP07KFeEB4QEB4QE92@092AEB4P0B4QE00=]KED2B4QE 00TT900T95DT900T9018B5DT900T95DT900T95D00R@T000592AE92@092@0 92AE92@000M8B5D2KFeE00E8B5E]KEE]KEE8B5E]KED00dQ8E@9]KED00dQ8 EFe]EDQ8E@03B4QE00M]KEE8B5E]KEE8B5E]KEE8B5E]KED00TQ8E@05B4P0 B4QEB4QEB4QEKFeE00=8B5D2B2@000m8B0189018900T95E8900T9018B018 900T9018901895E8901895E8901895D00TPT000392@0B2@0B2@000=89000 14PTEDQ802@T0000008T90001B@002@T02@T04PT02@TE@02B2@00b@T0004 B2@092@0B2@0B2AE0R@T0005B2AEB2@0B4P0]TQE]VeE00;JTED01]ZAZ]ZA EI58EI5]EMZfEOoJZPCo]ZX06?nfEOnfZ_nAEOnAZ]ZAEOnfEOnAZ_nfEOnA EOnfZ]ZAEOnfZ_nAEOnfZ]ZAEI5]EFe804PT04Q804PTEDQ804PT04PTEB@T 0098900034Q804PTEFdT06e8EDQ806dT04Q804PTEDQ806e804PT04Q8E@98 90007DPTEDPT04PT02@T04PTEDPT04PTEDQ804PT02@T04PT02A804PT04PT EDPT04Q8EDPT04Q802@T04PT02@TEDPT02@TEDPT02@TEB@T02@TEB@T04PT E@0292@000A895DT901890189001B2AE0003B4QE01e8B01895E8B00T95E8 B5DT901895DT95E8900TB5DT95E8900T95E8900T95DT901895DT900T95E8 900T95DT901895DT901895DT900T95DT000T95D00R@T008T95D00b@002@T 02@TE@0292@0002@TEB@T02@T02@TEB@T02@002@TEB@002@T 02@TEB@T02@0EB@T02@TEB@T04PTEB@T02@TEB@T02@TEB@T02@0EDPT02@T EB@T02@TEB@T02@TEB@T02@TEB@T02@TEDPT02@TEB@T02@TEB@T02@TEDPT EB@T02@TEB@T04PTEB@TEDPTEDQ802@TEB@T04PTEDQ802@TEDPTEB@T04PT EDQ804PTE@98B5D04DQ804PTEBA8EDPT02@TEB@T02A8EDPTEBA802@TEDQ8 EDPT02@TEBA8EDPT02A8EB@T0002B4QE00DT9018B5DT95E8B5E8B0000dQ8 E@03B4P0B4QEB4QE00=8B5D01DQ]EFe]EFe8EDQ]EFe]E@04TI6Z00>ATEE] KJY]KED00dQ8E@0592AEB4P092AEB4QE92@000I8B5D01B@T096AZ]ZfZ[KJ om[Jo`02f]ZZ00CJf_oJfZ[Jf_oJf_l2f]ZZ00?Jf_nf]ZZATED00[JfZP08 ][Kof]ZZf][of][of]ZZ][Kof]ZZf][o0][JZP03][JZKFeEB4QE0098B5D0 12@T02@TEDQ8EDPTE@E8B5D01B@T02@TEDPTEB@T02@TE@0292@000hT95DT 900T95DT95E8B00T95DT900T95E8B5DT9018B5E8B00T95E8B003B4QE0Ve] E@03B4QEKFeEB4QE009]KED2B4QE0Ve]E@03B4QEKFeEKFeE0098B5D2KFeE 0dQ8E@03KFeEB4QEB4QE00=8B5D02fe]EDQ8EFe]EDQ8EFe8EDQ8EDQ804PT EDPT04PTEB@T0002B2@000E895E8900T901895DT90000dPT0004B4P092@0 B2@0B2AE0TPT0003B2AEB2@0B2AE009890001B@T02@002@T02@T02@00003 92@000Q895DT90189018901895E8900T900T95D5B2@000=895E8901]B000 0[I]E@CJTED02[JAEI5]0=ZfZ_nfEOnfZ_nAEMZfZ_nAEOnfZ]ZAZP;JTED0 1?nfEOnAZ_nAEOnAZP;oTED02?nAZ]ZAEOnfZ]ZAEMZAZ[I]EFe806e8E@=8 90004TQ8EDPT04PT02@T04PT04PTEDQ806e804Q8EFdT06e804PTEDQ804PT 04Q806e8EDPT04Q8009890000dQ804PTEDQ80002B2@000i8B01890189018 95E8901895DT9018900T9018901895DT901895E8900392@000E8B00T9018 900T901890000R@T000592AEB2@092@0B2@094QE0058B00000=8B5D07dPT EDQ8EB@TEDQ804PTEB@TEBA804PTEB@T02@TEDPT02@TEDPT02@TEB@T04PT EB@T04PTEB@T02@TEDPT02@TEB@T02@TEB@T02@TEDPT02@TEB@T02@002@T E@0392@000DT95DT900T05DT900T95D00R@T000DB2AE92@092AE92@09000 92AE92@092AE92@092AE92@092AE92@0B2@092AE92@0B2AE92@0B2AEB4QE 0TPTE@0ATEFfKJZf TED00i5]E@14B4QEB2@092AEB2@092AE92@092AE92@092AE92@0B2AE92@0 92AEB2@092AE92@092AE92@092AE92@092AE92@092AE92@092AE92@092AE 92@092AE92@092AE92@092AE92@092AE92@092AE92@0B2AE92@092AE92@0 92AE900092AE92@092AEB2@092AE92@0900092AE92@092AE92@0901EB2@0 92AEB2@092AEB2AE92@092AEB2@092@092AE92@0B2AE0R@TE@0=B2@0B4QE 92AEB4QEB2AEB2@094QEB2AE92AEB4QEB2@094QE92@00098B5D01b@T04PT EBA8EB@T04Q8EB@TEDPT0002B4QE00dT9018B5E8B5DT900T95DTB01895DT B5E895DT9018B5DTB5E895D00dQ8E@0:KFeEKDQEB4QEB6eEKFeEKFfZTI6Z TI5ETI6ZTI5E0Y6AZP0>B6eEB4QE94QEKDQEKFeEKFfZKFeE92@0B4QEB4P0 B4QEKFeEB4QEKFeE0TQ8E@0>TI5E][JZf][of[JZ][JZ]][o][JZf]ZZ][JZ f]ZZf][o][JZf][o][JZ0Y6AZP09f]ZZf][of]ZZ][JZf]ZZ][JZf]ZZ]]ZZ TI6Z00;Jf_l01KJfZY6AZTQ8EDQ8EDQ80003B4QE00U]KEDT900T95E8B00T 95E8B01895DTB5DT900014Q8E@0792AEB4P092AEB4P092AE92@092AE00AB02fTEGJTED00]ZAE@0LfY6Z fY5Ef[IETDQEfY5EokJZokIEoi6ZokJZokIEokJZokIEomZZokIEokJZokIE okJZoi5EokIEokJZoi5EokJZfY6ZfY5EfY6Z]Y5ETDP0KDQE0TPT000>B4QE B2@0B2@0B2AEB2@0B4P0B2@0B4QEB2@0B4P0KDQEB2@0KDP0B2AE0TQ80007 KDP0KB@0B4QEB2@0B2AEB2@0B4QE0098900044Q804PT04Q804PT02@T04PT EDPT02@TEDQ804PT02A804PT02@T04PT02A804PTE@f]ZX0496AZTQ]EDQ8EDPTEDQ8EFfAEFe]EDQ8EFe8EBA8 EB@T04Q8EB@T02@TE@0002@T00A8B5D00b@T04Q8EB@T0004B4QE00=8B018 B5E8B0000TQ8E@03B4P0B4QEB4QE00I8B5D00fe]EDQ8EDQ8E@02B4QE00A] KEE8B5E8B5E]KED3B4QE00=]KEE8B5E8B5D00TQ8E@07KFeEB4QEKFeEB4QE KFeEB4QEKFeE0098B5D00fe]EDQ8EDPT0002B2@000HT9018900T95E8B018 900TB005B2@000=895E8B01890001DPT000:B4P0B2@0B2@0B4P092@0B2@0 92@0B2AEB2@092AE0TPT0003B4P0B2@0B4P00098900054PTEDQ804PT04PT 04Q806e806e8EDPT04Q8EFe80958EMZAEKJAEMZAEKJAEMY]EMZAEMZAZY5] 0;I]E@;o]ZX00onfEOnfZ_nfZP02okJZ00GJ]Z[o]Z[ofZ[o]Z[o]UD00onf ZP0YokIEf[JZoi5EokJZf[IEfY5ETFeEKDP0B2AEB4QEB2@0B2AEB4P0B2@0 B4P0B2AEB2@0B4P0KBAEB4P0B2@0KDP0B4QEB4P0KDP0B2AEB4P0B4QEB2@0 B4P0B2@0B4P0B2@0B4P0B2AEB4P0B2AEB2@0B2AEB4P092@00098900022@T 04PT04PTEDPT04Q8EDPT02@TEDPT008T90001DQ802@TEB@T02@T02@TE@02 92@000E8900T900TB018900T90000DPTE@000dQ8E@0LB2@0B4QEB2AEB4P0 B2AEB4P092AEB4QE92AEB2@092AEB2AE92@0B2AE92AE92@0B2AEB4QE92@0 B2AE92@0B2AE92@092AE92@092AE92@092AE0R@T000792AE92@092AE92@0 92AE92@092AE008T90001B@TEB@T02@TEB@T02@TE@0292@002AB5FATEFAKED00Y5]E@:fKED06kJAEI5]EI5]EOnf EOoJZ]ZAEOnfZ_nfEOnfZ_nfEOoJZ_nfZ]ZfZ]ZAEMZfZ]ZAEOnfZ_nfEOnf Z_nfEMZfZ_nfEMZAZ]ZAEI5]EI5804Q80003B2@001I895E8B01895E89018 B01895E8B01895E8B01895E]B01895E8B01]B01]B5E89018B01895E89018 95DT901895D3B2@000/T9018900T901895E8900T95E8900T95E8B018900T 90000TPT000592@0B2@092AE92@0B2@0008T900024PT02@T04PTEB@T04PT 02@TEB@T04PTE@4TB0000098B5D06DPTEDQ8EDPT04Q8EB@TEDQ8EB@TEDPT 04PTEB@T04PTEBA802@TEDPT02@TEB@T04PTEB@TEDQ802@TEDPTEB@T02@T EB@T04PTE@0292@000E895DT900T95DT900T95D00R@T000X92AE900092@0 92AE92@092AEB2@092AEB2@092AE92@092AE900092AE92@092AEB2@092AE B2@092AE92@0B2AE92@0B2AE92@092AE92@0B2AE92AEB2@092AEB4P0B2AE KFeEf]ZZf][of]ZZf][oom[of]ZZ0_oJo`04f]ZZf[JZfY6Z]Y6Z0mZfZP03 omZZf[JZomZZ00KJ]ZX00mZAZ]ZfZ]ZfZP02fY6Z00BfTEFfTJZfKEFAB5D2 TFeE01bAKJZAKEFAKEE8B5E8900T95DT901895DT900T95E8900T95DT9018 95DT900T95DT901895DT900T95DT900T95DT900T95DT000T95DT900T95D2 92@000@T95DT000T900T95D292@000@T05DT900T900T95D292@000fKED09kJAEMZA Z]ZAEMZAEMZfZ_nfEOnfZ_nfEMZfZ]ZAEKJAEI58EFe804PT04Q804PTEDPT 02@T04Q8EFe806e8EDQ804PTEFe804PT04Q804PTEDQ804PTEFe804PT04Q8 EDPT06e804PT04PTEDPT02@T04Q8E@02B2@000AKED03958 EI5]EFe8EFe806e8EI5]EMZfZ_oJZ_nfEMZAEKJAZ[I]00>AKED016e804Q8 EFe8EFe8E@:AKED2]VeE00VfTEFfKEFAKEFAB01]B5E]B018B5E8B01895D0 0TPT0008B4QEKDP0B4P0KDQEB2@0B4P0B2@0B4QE0TPT0004B4P0B2@0B4P0 B4P01dPT000@94P0B2AEB2@092@0B2AE92@0B2@092@0B2@092@0B2AE92@0 B2@092AE92@0B2@00R@T0008B2@092@0B2@092AEB2@092AE92@0B2@00R@T 004T95D192@00DPT00000dQ8E@0aB2AEB4P092AEB2AEB4P092AEB2AE92@0 B2AE92AEB2@092AE92@0B4QE92@0B2AE92@092AEB4P092AE92@0B2AE92@0 92AEB2@092AE92@092AE92@092AE92@092AE92@092AEB2@092AE92@0B2AE 92@092AE92@0B2AE92@092AE92@0B2AE92@09000B2AE0092AE92@0 92AEB2@092AE92@0900092AE92@0900092@092AE900092AE0b@T000592AE B2@092AE92@0B2@0008T95D022@T04PTEDPT06e8EKJAZ]ZfZ]ZAEI6AE@GJ ]ZX02onfZ][JZ_oJZ]ZfZ][JZ]ZfZ][JZ_nfZ][JZ_oJZ][JZP04f[JZ00CJ TJZAKEFfTJ[JTJX2f[JZ00GJ]UGJ]Z[JTJZfKEFAKED00Ve8E@0EB2@092AE 92@0B2AE92@092AE92@092AE92@0900092AE92@092AE92@092AE92@092AE 92@092AE900092AE008T900022@0EB@T02@T02@TEB@T02@TEB@T02@TE@8T 90001b@TEB@T02@T02@002@TEB@T02@TE@0292@000@T95DT9018900T95D2 92@000m895DT900T95DT900T000T95DT901895DT900T95DT900T95DT900T 95DT90000R@TE@0J92@092AE92@092AEB2@092AE92@0B2AE92@0B2AE92AE B2@092AE92@0B4QE92AEB4QEB2AEB4P0B2AE94P092AEB4P092AEB4QE92AE 0TQ8E@B2AE92@092@0B2@092AE B2@0KDQEfY6ZfY5E]Y6ZTI6Z]Y6Z][JZf[IE0]ZfZP;ofZX00m[JZ]ZfZ_oJ ZP05f[JZ00SofZ[J]Z[J]Z[JfZ[J]Z[JTJZAB5FfTED3f[JZ00SJTJ[JTEFf TJZfKJY]B5FAB5E8B01895D392@000TT95E8900T95DT000T900T95DT9018 900T95D00R@T000592AE92@092@092@092AE008T90001R@TEB@T02@T02@T EB@T02@0E@8T90001b@TEB@002@TEB@T02@TEB@002@TE@0292@000TT95E8 900T95DT900T95DT000T95DT900T95D00R@T000F901E92@092AEB2@092AE 92@092AE92@092AE92@0B2AE92@0B2@092AEB2@092@0B2AE92@0B2AE92@0 92AEB2@00R@TE@0:92@0B2AE92@094QEB2@092AEB2AE94P0B2AE94QE0TQ8 E@07B2AE94QEB4P092AEB4P092AE92@00098B5D012A8EDPTEDQ8EB@T00=8 B5D02B@T04Q8EDQ804Q8EDQ804Q8EFe8EDQ]EFe]E@02B4QE00E]KJY]KEE] KEE]KEE8B5D00fe]E@0:B4QEKFeEKFfZKFeEKFfZKFeETI6ZTI5EKFfZKFeE 0TQ8E@04B6eEB4QEB4QEB4P00R@TE@98B5D012A804Q8EFe]EFe]E@98B5D0 2i6AZ]ZfZ][Jooooom[JZ][Jooooom[Jooooom[JZ][Jo`04oooo00GJf_oo oooJfZ[Jf_oJfZX00kJfZP06TI6ZKFeE92AEB4QE92@0B4QE0Ve]E@0392AE 92@092AE008T90002B@TEB@T04Q8EB@TEB@T02@TEDQ802@TEB@T0003B4QE 00DT95DT9018B5DT95E]KED00TQ8E@05KFeEB4QEKFeEKFeEB4QE009]KED0 1dQ8EFe]EFe]EFe]EFe]ZVe]EDQ8E@03KFeE00M8B5E]KEE8B5E8B5E]KEE8 B5E]KED00dQ8E@05B4P0B4QEB4QEB4QEKFeE0098B5D00dQ804Q8EDQ8E@02 B4QE0dPT000792@0B2@092@0B2@092@0B2AEB2@0008T90001DPT02@T04PT 04PT02@T0002B2@000@T901895E8900T9002B2@000TT9018900T900T000T 901895DT9018901895D00TPT0006B4P0B2@0B2AEB2@0B4QEB2@00b@T0006 900092@0B2AEKDP0TFeE]Y5E0]ZfZP0;f[IEf[JZokJZokJZokIEomZZokJZ omZZokJZomYEokJZ00_ofZX04OnfZ_oJZ]ZfZ]ZAEI5]EFe804Q8EFe804Q8 06dTEDPT04Q804PT04Q8EDPT04Q8EDQ80002B2@000E8B5E89018901]B5E8 B0000TPT000592@0B2@0B2@0B2AEB4P0009890001B@T04PT04PT02@T04PT 000292@000B4P0B2AEB2AE94P092AEB2@092AE94QEB4P0B2AE94QE92@0B2AE 92@00dQ8E@03B2AE94P0B2AE00I8B5D00fe]EDQ8EFe]E@03KFeE00M]KJY] KEE]KJY]KEE]KJY]KEE]KJX01Fe]E@05KFfZKFeEKFeEKFfZKFeE00E8B5D0 0b@T02A806e]E@07B4QE00=8KEFf]Z[JfZX00][Jo`03oooooonZoooo00?o ool03][JZ_ooom[Jooooom[Jom[JZ][Jom[JZ[Jfom[JZY6AZ[JfZY6AZVe] E@98B5D00b@T04Q8EB@T0002B4QE00DT900T95DT9018B5DT95D00TQ8E@8T 90001B@TEB@T02@TEDQ8EB@T0002B4QE00=8B018B5E8B5D016e]E@04B4QE KFeEKFfZB4QE1Fe]E@98B5D00fe]EDQ8EFe]E@04B4QE00=]KEE8B5E8B5D0 0dQ8E@9]KED3B4QE00E]KEE8B5E8B5E8B5E]B5D014Q8E@08B4P0B2AE92@0 92@0B2AE92@092AEB2@012@T0008B2@092@0B2AE92@0B2AE92@0B2AE92@0 0TPT000792@0B2@0B2AE92@0B2AE92@092AE008T90000dPT04PTEDPT0002 B2@000=8B5E8901890000dPT008T90000b@TEB@T02@TE@02B2@000U8B02A B5FfTEGJTJ[J]UGJ]Z[o]Z[ofZ[J]ZX00ooJZP03okJZomZZokJZ00KofZX0 0oooZ_oJZ_oJZP04omZZ00_o]Z[J]ZZfTEE]B01]B5E]B01]B5E8B01]B5E8 B01895D00Ve8000?B4QEB4P0KBAEB4P0B2AEB4P0KB@0B4QEKDP0KDQEB2@0 B4QEB2@0B2AE92@0009890002DQ8EDPT02@T04PTEB@T02@TEB@T02@TEDPT 000292@000f[IE fY6ZfY5E]Y6Zf[JZTFeETFfZf[JZfY5Ef[JZomZZf]ZZomZZ]Y6Z0Y5]E@?J ]ZX2fY6Z0[I]E@0GTDQEKDQEKDQEKDQEB4P092AE92@0B2@092@0900092@0 92AE92@0900092AE92@092AE92@092AE92@092AE92@092AE008T90003R@0 EB@T02@TEB@T02@TEB@002@T02@TEB@T02@TEB@T02@TEB@T02@TE@8T9000 0b@0EB@T02@TE@0292@000Q895DT000T900T95DT000T95DT000T95D292@0 02dT000T95DT000T900T95DT900T95DT900T95DT900T95E8900T95DT900T 95DT900T95E8900T95E8900T95DT901895DT901895DT9018B5DT9018B5E8 900TB5E895E8B5DTB00T95E8900TB5E8B5DT9018B5DT95E8B018B5DT900T B5D00TQ8E@03B4P0B4QEB4QE00I8B5D01Ve]EDQ8EFe]ZVe]EDQ8EFe]ZP=] KED00i6AZVe]EFe]E@03KFeE00A]KJZAKEE]TJZATJX2KFeE00I]KJZATEE] KEE]B5E8KEE]B5D4B4QE00e]B5E8B018B5E8B5E]KEDT95E8B5DTB01895FA TEFf]_oJf_oJfZX00][Jo`04oooof][ooooof][o0oooo`06f]ZZf][of]ZZ f][of]ZZf][o0[JfZP04KFfZKFeEKFeEKFeE1DQ8E@0492@092AEB4P0B4QE 0fe]E@0792AE92@092AE92@0B4QE92AE92@000E8B5D2KFeE00I8B:Y8B5E8 B5E]KEE8B5E]KED7B4QE00=]KEE8B5E]KED01dQ8E@03KFeEB4QEB4QE00a8 B5D01dQ804Q8EDQ8EDPTEDQ802@TEDPT000492@0010T95DT901895DT900T 95E8900T9018900T9018900T9018900T95E8900T95E8900292@000=8900T 900T00000R@T00=890002R@T04PTEDPT04PT04Q8EDPT02@T02@TEDPT02@0 008T9002B2@000I8B5E]B02AB5FfTEGJ]UGJ]ZX2okJZ0ooJZP03okJZomZZ omZZ00KofZX01OooZ_oJZ_oooooJZ_ooZP05omZZ01OJTEFAKEE]B5E]B018 901]B5E89018B5E]9018B018B5E]B01]B5E]B018B01]B5E8B01]B018B5E8 B0189018B01]B5D00TQ80098900012@TEDPT02@T04PTE@8T900024PT02@T 02@T04PT02@T02@TEB@T04PT00PT900012@TEB@T02@T02@000@T90001@0T EB@T04PT04Q8EDPT0001B4QE00008dQ8EFe8EDQ8EDQ8EDPTEDQ804PTEDQ8 EDPT02@TEDPTEBA804PTEB@T02A8EDPTEB@T04PTEB@T04PTEB@T04PTEBA8 EDPT02@TEB@T02@TEB@T04PTEB@T02@TEB@T04PTEB@T04PTE@0292@000DT 95DT900T05DT900T95D00R@T000392AE900092AE008T900012@TEB@002@T 02@TE@8T90001B@TEB@T04PTEB@T02@TE@0292@000HT95E8900T95DT900T 95DT9002B2AE00JAKEFfTJZfTJZAKEFATJZfTJX4f[JZ00oo]Z[JTJZfTEGJ TJZAKEE]B5E]B02fKJZfTJZfTEGJTJ[JfZ[ofZ[JTJZAB5D00Y5]E@04B4QE 92@0TI6ZTFeE0Ve8E@0;TDQEKDQEKDQEKDQEB2AE92@092AE92@092AE92@0 92AE008T90002dPTEB@T02@T02@TEB@T02@TEB@002@T02@TEB@T02@0E@03 92@000HT95DT900T900T95DT900T05D292@000hT95DT900T000T95DT000T 95DT900T95DT900T05DT900T95DT900T95D292@000HT95DT900T900T95DT 900T95D292@001hT95DT000T95DT900T95DT900T95DT900T95DT901895DT 900T95DT900T95DT900T95DT900T95E895DTB00T95E895DT901895DT95E8 B5E895DTB018B5D2B2AE00HTB01895DT95E8B00T95DT9002B4QE00E895E8 B5E8B018B5DT95D00TQ8E@03B4P0B4QEB4QE0098B5D044Q]EFe]EFe]EDQ8 EFe]EDQ8EFe]EDQ8EFe]EFe]ZVe]EI6AZVe]EFe]ZVe]EFe]ZP9]KED016e] ZVe]EFe]EFe]ZP9]KED0196AZVe]EDQ8EFe]E@E8B5D01R@TEDQ8EDQ8EFe] EDQ8EDQ800=8B5D00i6AEKJfZ[JfZP02f][o00OJfZ[ooooooooooj[Jf_oo oooJfZX01=[Jo`04f]ZZ][JZ][JZKFeE0TQ8E@0792@0B4QEB4QE92AEB4P0 92AE92@000M8B5D02R@TEB@T02@T02@TEDQ8EB@T04Q802@TEDQ802@TE@=8 B5D4KFeE00=8B5E]KEE8B5D014Q8E@9]KED01dQ8EFe]EDQ8EDQ8EFe]EDQ8 EFe]E@03B4QE00=]KEE8B5E8B5D00TQ8E@03B4P0B4QEB4QE0098B5D016e] EDQ8EDQ8EFe]E@E8B5D02DQ802@T04PT02@TEDPT02@T04PTEB@T04PT0003 92@000m8900T901895DT9018900T901895DT9018900T9018900T9018900T 901895D00b@T0003B2AEB2@0B4QE00A8900014PTEB@T02@T04PT008T9000 3dPTEDPT02@T06e8EDQ806e8EFe806e8EI5]EMZAEMZfZ_nfEMZfZ_oJZ_nf ZP07omZZ00Gooj[ofZ[ooj[of_ooojX01_oJZP0SokJZf[IE]VeEKDQEB4P0 B2@0B2AEB4P0B2@0B4P0B2@0B4QEKDP0B4QEKDP0B4P0KDQEB4P0KDP0B4QE KB@0B4P0KDQEB2@0KDQEB4P0B2AEB4P0B4QEB2@092@0B2@092@0B2@092AE 008T90003DPT02@TEB@T04PT02@T02@TEDPT02@T02@TEB@T02@TEB@T02@T E@0592@000B2@0B2AE92@092AE 92@0B2AE92@0900092AE92@0900092AE92@090000R@T000792AE900092@0 92@092AE92@092AE008T90000b@TEB@002@TE@0292@000HT05DT95DT900T 95DT900T95D292@000@T000T95DT900T95D292@002]895DT901895DT900T 95DT900T05DT900T000T95DT900T95DT900T95DT900T95DT901895DT900T 95DT900T95DT900T95DT900T95DT901895DT901895DT900T95E895DT900T 95E8B5DT9018B5DT9018B5E895E8B00TB5D00TQ8E@0=B4P0B4QE92AEB4P0 B2AE94QEB4P0B4QE94QE92AEB4P0B4QEB6eE0098B5D014Q804Q8EDQ8EFe8 E@98B5D016e]EDQ8EFe]EDQ8E@9]KED00fe8EFfAEFe]ZP02KFeE00=8B5E] KEE]KED00Ve]E@0=KFfZKFeEKFeEKFeEKFfZKFeEKFfZKFeEB4QEKFeE92@0 92AEB4P00098B5D00dPT02A8EFe8E@06B4QE00A]KEFATJZf]Z[JfZX6f][o 00?JfZ[Jf_oJfZX00kJfZP03TI6ZB4QEKFeE009]KED01dQ8EB@TEDQ8EDQ8 02@TEDQ8EB@T0002B4QE00E]KEE8B5E8B5DT900T95D00R@T000592AE92@0 92@0B4QE92AE0098B5D01TQ804Q8EDQ8EFe]EDQ8EFe]E@=8B5D00fe]EDQ8 EDQ8E@02B4QE00E]KEE8B5E8B5E]KEE8B5D00Ve]E@03B4QEKFeEB4QE00Y8 B5D00fe]EDQ8EDQ8E@02KFeE0dQ8E@08B4P0B4QEB4QEB4QE92@0B4QE92@0 B2@01B@T000A92AEB2@092@092AEB2@092@0B2@092AEB2@092@0B2@092AE B2@092@0B2AE92@0B2@0008T90000b@002@TEDPT0002B2@000E895E89018 95DT901890000b@T0006B2AEB2@0B4P0B2@0B2AEB4P00Ve8E@0:KDP0KDQE TFd0]Y5EfY5Ef[JZokJZomYEomZZokJZ1ooJZP07oonZomZZoonZomZZoonZ omZZoonZ00?ofZX06mZfEKJAEI58EFe806dT06e8EDQ804PT04Q8EFdT04Q8 EFe804PT06e8EDQ806e8EDQ806e804Q8EFe804Q806e804Q8EFe804Q806e8 EDQ80003B2@000HT901895DT900T9018900T95D;92@000@T000T900T900T 000292@000/T95DT900T900T900T95DT000T901895E8B0189018B0000DPT E@000dQ8E@0HB2@0B4QE92@0B4QEB2@092AEB2@092AEB2AE92@0B2AE92AE 92@0B2AE92@0B2AE92@0B2AE92@0B2AE92@092AE92@092AE0R@T0003B2AE 92@0B2AE008T90000b@TEB@T02@TE@0292@000]895DT900T900T95DT900T 000T95DT901895DT900T95D00R@T000992AEB2@092@092AE92@092AE92@0 B2@092AE008T900034PTEB@T02@TEB@T04PT02@TEB@T04PTEFe]EI5]EI6A EI5]ZP?J]ZX00mZfEMZfZ]ZfZP02f[JZ00?JTEFATEFfKED00]ZAZP0=]Y5E ]VfZf[IEfY6Zf]ZZfY5E]VfZTDQETFeEKDQE]VeE]VfZ]VeE00:AB5D4KDQE 00]8900T95DT9018900T95DT000T95DT900T95DT900T95D00R@T000>92AE 92@092AE92@092AE92@092AE92@092AE900092@092AE92@092AE0R@T000: 92AE92@092@092@092AE92@0900092AE900092AE0R@T008T95D032@002@T EB@T02@TEB@T04PTEB@T04PTEB@T02@TEB@T02@TE@8T900022@TEB@T02@T 02@0EB@T02@TEB@T04PTE@8T900044PTEB@T04PTEB@T02@TEB@T02@TEB@T 02@TEDPT02A8EDPTEB@T04PTEDQ8EDPTE@=8B5D292@000I8B5DT95E8900T B5E895DTB002B4QE00=8B018B5E8B0001dQ8E@04KFeEB4QEKFeEB4QE0Ve] E@07KFfZKFeEKFeEKFfZKI5EKFfZTFeE00:ATJX01fe]EI6AZVe]EI6AZVe] EI6AZY6AE@02TI6Z00>ATEE]KJZATED014Q8E@0492@0B4QE92AEB6eE0dQ8 E@0392@0B4QEB4QE0098B5D014Q806e]EI6AZY6AZPNf]ZX2TI6Z00FATEE8 B5E]KEE8B5E8B0001TQ8E@0592@0B4QEB4QE92@092AE0098B5D026e]EDQ8 EDQ8EB@T02@TEDQ80000EB@T0098B5D01B@TEDQ802@TEDQ802@TE@02B4QE 0Ve]E@06B4QEKFeEB4QEKFeEB4QEKFeE0TQ8E@05KFeEKFfZB4QEB4QEKFeE 00=8B5D3KFeE0TQ8E@03KFeEB4QEKFeE009]KED00dQ8EFe]EDQ8E@03KFeE 0dQ8E@03KFeEB4QEB4QE0098B5D014Q804Q8EDPT02@TE@8T90000b@TEB@T 04PT000492@000Q8900T901895DT9018900T900T95E8900292@000E8900T 9018900T901895D01B@T0004B2AE92@0B2@092@00TPT000692AE92@0B2@0 B2@0B4P0B2AE0TPT0005B4P0KDQEKDP0KDQEKDP000:AKED01;I]EMZAEMZf Z_nfZP[ofZX2oonZ1OoJZP0Wf[JZfY5ETFeETDQEKDP0KDQEKDP0KDQEB4P0 B2AEB4P0B2AEB4P0B2@0B4QEB2@0KDP0B4P0KB@0B4QEKDP0B4P0KDQEB4P0 B2@0B4QEKDP0B4QEB2@0B2AEB4P0B4QEB2@092@0B2@092AE92@0B2@0901E 008T90000dPTEB@T04PTE@0292@000@T95E8900T900T95D292@00092AE92@0B4QE92@0B4QE92AE92@0000092@092AE 92@092AEB4QEB4P00R@TE@98B5D00dQ804Q8EDQ8E@04KFeE00=8B5E]KEE] KJX00fe]E@05B4QEKFeEKFeEB4QEKFeE00E8B5D00fe]EDQ8EDQ8E@04B4QE 0Ve]E@98B5D00fe]EDQ8EFe]E@05B4QE00M8B018B5E8B5E8B5E8B01895E8 90000R@T000592AE92@0B2@092@092AE008T900034PT02@T04PTEB@T04PT 02@T04PT02@TEDPT02@T04PT02@T009890000b@TEDPT02@TE@02B2@000fTJZfTEFAKED00Y5]E@0AB01]B5E]B5D00fe80006KDQEB4P0B4QEB2@0 KB@0B4QE0TPT000>B4P0B4QEB4P0KDQEB4P0KDP0B4P0KDQEKDP0B4P0B2AE B4P0B2@0B4P00TPT00@T90000b@TEB@T02@T000292@000@T95DT900T900T 95D492@00092AE900092@0901E92@092AE92@092AE900092AE900092@092AE9000 0R@T0003901E92@092AE008T90001b@002@TEB@T02@0EB@T02@002@TE@02 92@000DT05DT900T900T900T95D00R@T000392AE92@0901E008T90001b@T EB@T02@TEB@T02@TEB@T02@TE@0292@001HT95DT900T95DT900T95DT900T 95DT900T95DT900T95DT901895DT901895DT901895DT901895DT9018B5E8 95D2B4QE00TT9018B5DTB5E8900T95E8900T95DTB5E890000dQ8E@0392AE B4QEB4QE00=8B5D01Fe]EDQ8EFe]EFe]EDQ8E@02KFeE00M]KJZATEE]KJZA TEFAKJY]TEE]KJX00fe]E@03B4QEKFeEKFeE009]KED026e]ZY6AEFe]EFe] ZVe]EFe]ZVe]EFe]ZPM]KED3B4QE00fTJX02I6AEFe8EB@TEDPT02@TEB@T02@TEB@T02@0000292@0 00A TJY]KEFATJX00Ve]E@05KFfZKFeEKFfZKFeEKFfZ009]KED0296AZY6AEFe] ZY6AEFe]EI6AZVe]EFe]ZP9]KED3B4QE00LT9018B5E8B5E8B00T900T95DT 900014Q8E@03KFeEB4QEB4QE0098B5D01b@TEDQ804Q8EDQ8EB@TEDQ802@T E@02KFeE00U8B5DT95E8B00T95E8B5DT900T95E8B00T95D00dQ8E@8T9000 1DQ8EB@T02@T02@T02@TE@02B4QE0Ve]E@08B4QEKFeEB4QEKFeEKFfZKFeE KFfZB4QE1Fe]E@98B5D016e]EDQ8EDQ8EFe]ZP=]KED01DQ8EFe]EFe]ZTQ8 EFe]E@06B4QE00=8B018B5E8B5D014Q8E@03KFeEB4QEB4QE00I8B5D034Q8 04PTEDPT02@T04PTEDPT02@T04PT04PTEB@T04PT02@TE@DT90004DPT02@T 02@T02@TEB@T02@002@T04PT02@T04PTEB@T02@TEDPT02@T02@TEB@T04PT E@0392@000E8900T901895E89018B0000dPT000DB4QEB4P0B2@0B4P0KDQE B4P0KDP0B2@0B4P0B2AEB4P0KDQEKDP0B4QEB2@0B4P0B2AEB4P0B2@0B4QE 0dPT0004B2AEB4P0B2@0B4QE0TPT0008B4QEB2@0KDQEB4P0KB@0B4P0KDP0 KDQE0Ve80009KDQEKDP0B4QEB4P0B2@0KDP0B2AEB2@0B4P0009890001TQ8 EDPT02@TEDPT02@TEDPT00HT90001b@TEB@T02@T02@T02@TEB@T02@0000: 92@000M8900TB5E89018B5DT9018B01895D00dPT0006B2AEB4P0B2@0B2AE B4P0B2AE0DQ800000TQ8E@0JB2@0B4QE92AEB4QEB2AE94QEB2AEB2@094QE B2AEB4P0B2AE94P0B2@092AEB2AEB2@092AE92@092AE92@092AE92@0901E 92@092AE0R@T000=92AE92@092AE92@0901E92@092AE92@092AE900092AE 92@0901E00@T90001b@TEB@T02@TEB@T02@0EB@T02@TE@0292@000@T000T 95DT900T05D392@000@095DT900T0000900292@000DT95DT900T95DT900T 95D00R@T000=92AE92@0B2AE92@0B2AEB4P0KDQETI6Z][JZf[JZf]ZZom[o f]ZZ00;of_l00m[JZ_oJZ]ZfZP03f[JZ00Jf]Z[JTJZfTEFATJZAKEFATED2 ]Y6Z00bATJY]B5DT95E8900T95DT900T95DT900T000T95DT900T95D292@0 00DT000T95DT000T900T05D00R@T0017901E92@092AE92@092AE92@092AE 92@0901E92@002AE92@092AE92@0901E92@092AE92@0901E92@092AE92@0 900092@002@092AE900002@0901E92@092AE92@092AE92@092AE92@092AE 92@092AE92@092AE92@092AEB2@092AE92@092AE92@092AE92@092AE92@0 92AE92@092AE92@0B2AE92AE92@092AEB2@092AEB2@092AEB2@0B4QEB2AE 92@0B4QE94QEB2@00098B5D01DPT02A8EDQ8EDPTEB@T0002B4QE00ATJZf]Z[J]ZX01=[JZP04f[Kof]ZZf[JZ][JZ0]Zf ZP:fTJX04i5]EI5]Z[JAZ[JAZY6AEFe8EDPTEB@T02@002@T02@TEB@002@T 02@TEB@002@TEB@002@T0000E@0292@000@T95DT900T900T95D292@000/T 95DT000T95DT900T95DT000T900T95DT000T900T95D00R@T000492AE92@0 900092AE0R@T000592AE900002AE92@0901E008T900092AE92@09000B2@092AE92@0B2@092@092AE92@0 92AE92@0900092AE0b@T00039000B2AE92@00098900014Q8EDPT04PT04Q8 E@9890001fe8EDQ804PT04PT06e8EDPT06e8E@02B4P000M89018B5E8901] B018B5E89018B5D00dPT000Q92AEB4P0B4P0B2AEB4P0B4QEB2@0KDQEKDP0 B4P0KDQEKDP0KDQEKDP0TFeEB4P0KDQEB4P0KDP0B4QEB2@0B4QEB2@0B4QE B2@0B4P0B2@092@0B2@092@092AEB2@092AE008T90001R@002@T02@T02@T 02@TEB@000DT90001b@002@T02@T02@T02@TEB@T04PTE@02B4P000E895E8 B01895E89018B0000TPT0005B4QEB2@0B2@0B2AEB4P000989001B4P00DPT 0058B0000098B5D05TPTEBA804PTEDPTEBA8EDPT04Q8EDPTEDPT02A8EDPT 02@TEDPT04PTEB@T02@TEB@T04PTEB@T02@TEDPT02@TE@8T90005B@TEB@T 02@TEB@T02@002@TEB@T02@002@TEB@002@TEB@T02@TEB@002@TEB@0000T 02@TEB@T02@TEB@0000392@000DT95DT000T900T000T95D00R@T0007901E 92@092@092AE900092@09000008T90002@00EB@T02@T000002@T02@TEB@0 02@T02@TE@0292@000lT95DT900T95DT900T95DT900T95DT901895E89018 B5E]KEFfTJ[JfZ[Jf_l00m[JZP06f[JZ][JZTFeE]Y6ZTFeEKFeE0Ve8E@07 B4QEB2AE92@092@092AE92@092AE008T90000b@TEB@T02@T000292@000`T 95DT900T95DT900T000T95DT900T000T95DT000T900T95D292@000B4P0B2AEB4P0B2AE B4P0B2AE92@0B2AE92@0B2AEB2@094P0B2@0B2AE0b@T0003B2@092@092@0 00KFfZKFeE KFeEKFeETI6ZTI5EKFeETI6ZKFeETI6ZKFeEKFfZKFeEKFfZ0Ve]E@06KFfZ TI6ZKFeEKFfZKFeEKFfZ0Ve]E@06KFfZKFeEB4QEKFeEKFfZB4QE16e]E@04 KFfZKFeEKFeETI6Z0fe]E@06B4QEKFeEKFeEB4QEKFfZKFeE0TQ8E@06KFeE B4QEB4QEKFeEKFfZB4QE0fe]E@09KFfZB4QEKFeEKFeEB4QEKFeEKFfZKFeE B4QE009]KED014Q8EFe]EDQ8EFe]E@a8B5D00fe]EDQ8EDQ8E@05B4QE0Ve] E@06B4QEKFeEB4QEKFeEB4QEKFeE0TQ8E@03KFeEB4QEB4QE00A8B5D00fe] EDQ8EDQ8E@03B4QE00"], "Graphics", ImageSize->{483, 154.188}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, Background->RGBColor[0.924025, 0.891524, 0.771649]], Cell["\<\ In a letter to L\.b4Hospital in 1695 Leibniz raised the following question: \ \ \>", "Text"], Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgf]Z[Jf_nf]ZX00[JfZP07TI6Z KFeEKFeE92AE92@0B4QEB4P000D000001B@TEB@T02@TEB@T02@TE@020000 00f]ZZATJZf]ZX00[JfZP04TI5EB4QE B4QE92@00`00000<92@0000092AE000092AE92@0B4QE92@0001E92@00000 92@00R@TE@0392@092AE0000008T90001P0002@TEB@T02@T0000EB@T00D0 00002R@TEB@T000002@T000002@TE@0002@T0000EB@T00@000001B@T0000 E@00000002@TE@0=000000LT95D00018B5E8B00T95DT900T95D00R@T008T 95D292@00092@092AE92@092@092AE000092@092AEB4P092@092AE 92@092AE92@00TQ8E@03B4P0000092AE00f]ZX05=[JZ[JfZ][Jooooom[Jom[JZ][Jom[JZ][J om[JZY6AZVe]EDQ8EB@T02@TEI6AZ][JZ][Joi6AZR@T00T000000b@TE@00 0000000G00000092AE92@092AE92@0 92AE000092@0000092AE92@0001E000092@0B4QE0Y6AZP05B4QE92AE92@0 92AE000000A8B5D292@01DQ8E@05KFeEB4QEB4P092AEB4P000E8B5D03DQ8 02@TEB@T02@T02@TEB@T02@TEB@T000002@T000002@T0000000292@000LT 95DT900T900T95E]KED0000T90002P00000:92@0000092AEB4QEB4P092AE 92@092AE0000B4QE0Y6AZP09KFeE92AE92@0KFeE0000B4QEKFfZKFeEKFfZ 00>f]ZX03i6AZTQ8EDQ8EDQ8EB@T0;JfZ][Jom[JZY6AZTQ8EM[Jom[JZVe] ZP0002@T0002000000XT95Ff]ZZf]_m8B5D0000T9000000T9000001]KJX2 ][JZ00Kooonf]ZZf]ZZf]Z[JfZZf]ZX3TI6Z00E]KEDT900T902ATJY]KED0 0P00000792@0B4QEf]ZZf][o][JZTI6Z92@000P000000b@T00000000000H 000000ATJ[JfZZf]ZX0 0R@T008000004b@TEFe]EM[JZ[JfZVe]EB@TE@0002@T02@TEB@T06e]EKJf Z][Jom[JZ[JfZY6AZVe]EI6AZTQ8E@0292@0010T95E]KEDT95E8B5FATJZf ]ZY8B5D0000T95E8B5Ff]Z[Jf_nf]ZZATJX0000T9002000000DT90000000 0000000T90001000000492@00000000092@05000000392@092AE92@00080 000392@00Oooo`0000<0000T900005D00`00000592AE000092@0000092@0 0080000032@T02@TE@0002@TEB@T000002@T02@TE@0002@TEB@T02@TE@80 00001B@T0000EB@T02@T02@TE@04000000hT95FATJZATJZATJZATEE8B5DT 95DT9000000T95DT9000000T900T95D292@000ATJX00i6AEB@TE@00000392@000P0000T9000000T900T95E8B00T95DT 9002B4QE01M]KJY8B5D0000T902f]ZY8B5D00018B5Gooom8B5E]KEDT95E] KEGJf_nATJY8B5D0000T901]KEFATJZf]ZZATJXT90001000000792@00000 92@0001E000092@0B4QE008T90000b@TE@0000000002000000ATJX2KFeE 00Y8B5DT900T95E8B018B5DT95E8B00T95E8B018B5D292@000ATJY] KEE8B5D00TQ8E@03000092@0KFeE00:ATJX00dQ8E@0002@T0002000012@T 0004000092AE92@092AE0R@T000@92AE000092@0001E000092@0B4QEKFeE B4QE92@0KFeEf][ooonZf][oB4QEKFeE0R@T0004TI6Z][JZKFfZB4P00P00 000392@00000000000<000001B@TEB@T04Q8EDQ8EI6AZP02][JZ00>ATJY] KEE8B5D00dQ8E@03TI6ZB4QEB4QE00=8B5D012@TEB@T02@TEB@T00H00000 32@TE@00000002@TEDQ8EDQ802@TEB@T000002@T000002@T007oool0008T 90000`00EB@T00000004000000D005DT90000000000T90001P00000392@0 001E00000080000392@000@T95DT900T95E8B002B4QE00>ATJY]KEE]KED0 1DQ8E@03KFeETI5ETI6Z009]KED2B4QE00HT9018B5E8B5E8B5E]KEFATJX3 KFeE1dQ8E@03KFeEB4QEB4QE00=8B5D00dQ804Q8EDQ8E@03B4QE00ATJX00i6AEI6AZY6AZP02TI6Z0[JfZP>ATJX01Y6AEFe]ZVe]EFe] ZY6AEI6AZP9]KED5B4QE00M8B018B5E8B5E8B5E]KEE8B5E]KED01dQ8E@04 B4P092AE92@092@00TQ8E@0692@092AE92@092AE92@092AE0`00000492@0 000092AE92@00TQ8E@0392@0000092AE008T90002DQ8EFe]EKJfZ[JfZTQ8 EB@T02@TEDQ8EB@TE@0292@000<005E8B01]KED00[JfZP03TI5EB4QEKFeE 00:ATJX016e]EDQ8EDQ8EDQ8E@>ATJX292@000@0000T95DT900T95D20000 00<005DT900T90001000000892@0000092@092@092AE92@0TI6ZKFfZ0TQ8 E@06KFeE][JZf][of][ooooo][JZ0Ve]E@0:92@0000092@0KFfZf]ZZB4QE 92@0B4QE92@000001DQ8E@04B4P092@092AE92@00TQ8E@0792@000000000 92AEB4P0KFfZKFeE0098B5D00b@T000000000002000000ATEE]KEE8B5D00TQ8E@0492@0 B4QEB4QEB4P00dQ8E@9]KED01fe]ZVe]EDQ8EDQ8EDQ802@TE@00000292@0 00DT95DT900T95E8B018B5D00R@T000692AE000092@092AEB4QE92@00R@T E@06B4P092AEB4P092AE92@000000R@TE@0792@092AEKFeETI6ZKFeE92AE 92@000H000000b@T000002@TE@04B4QE00hT9018B5FATJY]KED0002ATEGJ f_oJfZ[Jf_oJfZY]KJZATJ[Jf_nATED3000000@T9018B5E8B5DT9002B4QE 0[JfZP0592@0TI6ZTI6ZTI6Z92@000:f]ZX01Y6AZ[JfZTQ8EB@T000006e] E@Coool03M[Jom[JZ][JZ][JokJfZP0002@T000002@T04Q8EFe]EFe]ZVe] E@02B4QE00@T9000000T900T95D292@00P00000492@00000000092AE0R@T 0006000092@092@092@0000092@01000000<92@000000000000092@00000 92AE92@092AE92@092AE92@00dQ8E@0492AEB4P092AE92AE0Oooo`0000X0 000T900T95DT9018B5E]KEFATJY]KEE8B5D0000292@01P00000692AE0000 92@0000092@000000R@T000792AE92@00000001E92@0000092AE00A TED0000T95D00dQ8E@06KFeETI6ZTI6ZKFeE92AE92@00TQ8E@0>92AE92@0 92@0000092AE92@00000001E92@092AE92@092AEB4P092AE0P00008T9000 2@0002@TEB@T02@T02@TEB@T04Q8EB@T02@TE@0292@000PT95E8B00T95E8 B5DT95E8B5DT95E8B5D1oooo00000b@TEB@T00000002000000@T900T95DT 9018B5D3TI6Z00A8B5DT95D0000T9003000000ATJX01i6AEDQ8EB@TEB@T04Q8EB@T0000 E@05000000HT9000000T900T95D0000T9002000000ATJX024Q8EB@TEB@T02@TEB@T02@TEB@T 0000008T95D2B4QE00DT95DT900T9000000T90000P00000692@092AE92@0 92AEB4QEB4P00TQ8E@0592@0B4QEB4QE92@0001E008T90001P00E@000000 02@T000002@TE@8000001R@TEDQ8EDQ8EB@T02@TEB@T00<000000b@T0000 02@T0007000000@T95E]KEE]KEE]KED2][JZ00cJfZ[Jf_oJf_oJf_oooonf ]ZZATJ[ooooJfZY]KED00018B5D2][JZ0R@T000D92AE92@0000092@0f][o TI6Z92@0B4QE][JZKFfZKFeE][JZTI6ZB4QE92@0B4QETI5EKFeE92AEB4QE 0_ooo`07f][ooonZ][JZB4QE000092AE00000098B5D03Ve]EDQ8E@0002@T EB@T06e]EI6AZ[JfZY6AZVe]EDQ8EDQ802@TEB@T00P000001B@TE@0002@T 0000EB@T0002000000`T900T95DT900T95DT900T95E8B00T95E8B5DT95E8 B00T95D292@000DT95DT9018B5E8B5DT95D00dQ8E@7oool0000392@00000 000000<000000b@TEB@T0000E@02B4QE0Y6AZP04KFeEB4QE000092@01P00 000792@0B4QEB4QE92@092AEB4QE92@00098B5D01B@T000002@T02@T02@T E@0300000R@T000392AE92@000000080000032@T000006e]EFe]EB@TE@00 02@T000004Q8EB@TEB@T0000008T900022@TEB@T000002@T02@TE@0002@T 02@TE@8T90002b@TEB@T04Q8EB@T02@TEDQ8EB@TEB@T02@TEB@T02@TE@02 92@00P00000692@0000092@092AE000092@00TQ8E@03KFeEB4QE00000080 000012@T000002@T02@TE@H0000012@T0000000002@T00=8B5D2KFeE0Y6A ZP0:f]ZZoooof][o][JZKFeE][JZTI6ZB4QE92@0B4QE0[JfZP0SKFfZB4QE B4QE92@0001E0000B4QE92@0KFfZf]ZZKFeE92@0B4QETI6ZB4QE92@0B4QE TI5EKFfZB4QE92@0B4QEf][o][JZTI6ZB4QE92AE000092@0000092@092AE 0000B4QEB4P0008000001b@TEDQ8EFe]EKJfZY6AZVe]EB@TE@02000000f]ZX0296AZ[JfZ[JfZY6A ZR@TEB@T000002@TE@@T9000100002@TE@0002@T00<000000b@T00000000 0005000000@005D00000000T9002B4QE0118B00T95DT900T900T95D0000T 95DT9000000T900005D0000T902ATJZf]Z[JfZX2TI6Z00lT9000000T900T 9018B5E]KEFATJY]KEE8B5DT900T95DT900T95D0000T90000`00000392AE 000092@000@000002B@T096AEFe]ZTQ8EB@TEDQ8EB@TEB@T0000E@0292@0 00A8B5FATJZATJZATED3B4QE00P0000T95DT95DT95DT9000000T90000002 92AE00A]KEE8B5D0000T95D40000000000 000000 92AE92@092AE000092AE92@0000092@0001E000092@0000092@01P00008T 9000100002@T00000000008T90000b@TEB@T02@TE@0292@000HT95D0000T 900005DT900T95D5000000dT95E]KEFATJY]KEDT95DT900T95DT9018B5FA TJZf]Z[JfZZf]ZX00Ve]E@07B4QE000000000000B4QETI6ZB4P000H00000 12@T04Q8EFe]EFe]E@E8B5D03B@T000002@TEB@T04Q8EFe]ZY6AZY6AEDQ8 E@0002@T02@TEB@T000292AE00TT9000000T900T95D00018B5D00018B5FA TED00TQ8E@0492@00000000000000R@T0004B4QEKFeEKFeEKFfZ0Ve]E@8T 9000100002@T0000EB@T00L0000012@T000002@TEB@T00A8B5D01DQ804Q8 EDQ8EDQ8EDQ8000292AE00E8B018B5E8B5E8B5E8B0000TQ8E@4T9001001E 0Oooo`000`00000?92AE92@092AE000092@00000KFeETI6ZB4QE000092@0 000092@092AEB4QE00A]KED01B@TEB@T02@TEB@T0000E@0292@000E8B5FA TJZf]Z[JfZZf]ZX00i6AZP05][JZTI6Z][JZKFeEB4QE008000000b@TEB@T 00000002000000PT95D00000000T95DT901]KEFf]ZZATJX4000000f]ZX2TI6Z00>ATEFATJY]KED00Y6AZP08 TI5ETI6ZB4QEB4QE000092@092AE92@00`000098B5D00fe]EI6AZ[JfZP02 ][JZ00NATJY]KEE8B5DT95D0000T900T95D01@00000692AE000000000000 92@000000TQ8E@>ATJX03[JfZY6AZY6AZR@TEDQ802@TEDQ8EDQ802@TEB@T 04Q8EB@TE@0002@T008000002000E@0002@T02@TEB@T02@TEB@T02@TE@ATJX036e]EFe]Z[JfZ[Jfoi6AZTQ8E@0002@T0000 04Q8EI6AZY6AE@:ATJX024Q8EB@T04Q8EFe]EDQ8EB@TEB@T00000098B5D2 000000@T900005D0000T9004000000ATJX2][JZ00BATJZATEE8B5E8B5D3KFeE 00A8B5E]KEE]KEE]KED3TI6Z00Bf]ZZATJZf]ZZf]ZX2TI6Z00Jf]Z[JfZ[J f_oJfZ[Jf_oJfZX2f][o00BATEE8B5DT900T9002B4QE01HT9000000T95DT 900T95E8B01]KEE]KJZATJZf]ZZATJZf]ZZf]_oJfZZf]ZY]KEE8B5D0000T 95DT900T95DT9003B4QE00E8B00T9000000T95DT90000TQ8E@0592@092AE 000092@092AE008T90001B@TEFe]EFe]Z][JZ[JfZP02TI6Z00Jf]ZZATJZA TEE]KEE]KJY]KED2B4QE00LT9000000T95DT900T95DT9018B5D00Y6AZP09 TI5EKFfZTI5ETI6Zf][of]ZZ][JZTI6ZB4QE00<000001DQ8EKJfZ[JfZ[Jf ZY6AZP03B4QE00=]KEE8B5D000000`00000392AEB4QE92@000@000001R@T 00000000000002@T00000098B5D014Q802@TEDQ8EDQ800=8B5D2KFeE00E] KJY8B5DT9000000T90001@00008T900022@TEB@T02@T02@T02@TEDQ802@T EDQ800=8B5D01fe]EDQ8EDQ8EB@T02@TEB@T02@TE@07B4QE0B@T007oool0 0080000012@T02@TEB@T02@TE@8000002R@T0000000002@TEDQ8EM[Jom[J ZY6AZP0002@T0080000012@TE@0002@T04Q8E@>f]ZX0296AZ[JfZ[JfZY6A ZTQ8EB@T04Q8EDQ80098B5D00b@T04Q8EDQ8E@02B4QE0fe]E@:ATJX2][JZ 00[Jf_oJfZ[Jf_oJfZ[Jf_oooooooj[Jf_oJfZZATJX2][JZ00A]KJY8B5FA TJY]KED2B4QE0kJfZP04oooof][of]ZZf][o0][JZP04][JZf]ZZ][JZB4QE 0P00000492@0B4QEB4QE92AE0P00000392@0B4QE92AE0080000042@T04Q8 EI6AZVe]EDQ8EB@T000002@TEB@T0000E@0002@T096AZ][Jom[JZY6AZP:f ]ZX2TI6Z00=]KEE8B5DT90000P00000392@0B4QE92@00080000012@TEI6A EI6AZY6AE@98B5D00i6AZ][JZ][Jo`02][JZ00>ATJY]KEDT90000P00000: B4QETI6Z][JZf]ZZ][JZKFfZ92@0B4QEKFeEB4QE1@00000492@0B4QEB4QE 92AE0R@T00H0000292AE0TQ8E@03KFeEB4QEB4QE0098B5D01Ve]EFe]ZY6A ZVe]EB@T02@TE@L000002R@T02@TEB@TEB@T02@TEB@T02@TEB@T04Q8EB@T E@M8B5D01b@T04Q8EB@TEDQ802@TEDQ8EDQ80004B4QE0Oooo`000R@T0008 92AE92@0000092@0000092@0000092AE0R@T00050000KFeEf]ZZf][oB4QE 008000001R@T00000000000002@T04Q8E@:ATJX2][JZ00>ATJY]KEE8B5D0 0dQ8E@0392AE92@00000008T900022@TEDQ8EDQ8EDQ8EFe]EFe]ZY6AEI6A ZP:f]ZX01=[Jom[JZ][Jooooo`CJf_l00m[JZ[JfZ[JfZP03][JZ00KJfZ[J f_oJf_oooj[Jf_oJfZX2f][o00cJfZ[Jf_nf]Z[Jf_nATJY]KEE8B5DT95DT 900T95DT900T95D392@00TQ8E@0892AE92@092@092AEB4QEKFeETI6ZKFeE 0TQ8E@03000092@0000000<0000016e]EKJfZ[JfZVe]E@:ATJX02Ve]EI6A ZVe]EB@TEB@T000002@T04Q8EI6AZR@TE@8T90001fe]EFe]ZVe]EFe]ZY6A Z][Jom[JZP02][JZ0Y6AZP07TI5EB4QE000092@0KFeETI6Zf]ZZ00;Jf_l0 1[JfZY6AEDQ8EFe]ZVe]EDQ8E@D0000292AE00I8B00T95E]KEE8B5DT95DT 9002000000A TJY8B5DT90000Y6AZP0;KFeE92@092@0000092AEKFeEKFfZTI5ETI6ZB4QE 92AE008T900012@TEB@T000002@T008000000b@TEDQ8EI6AZP02][JZ0Y6A ZP03f]ZZ][JZTI6Z00:ATJX2][JZ00Bf]_nATJY]KEE8B5D2KFeE00M8B5FA TJZf]ZZf]Z[JfZ[Jf_oJfZX00oooo`0;f]ZZoooof][of]ZZf][ooooof]ZZ ][KoTI6ZB4QE92@0008000002`00EB@T000002@T0000E@0002@T000002@T 000002@TE@02KFeE00DT95DT9000000T9018B5D01I6AZP:f]ZX0196AZY6A EDQ8EDQ8E@D000001B@T000002@T000002@T0002000000@T9000000T95DT 9002KFeE00Q8B5Ff]ZZf]ZZf]Z[Jf_nf]ZZATEE8B5D292@000HT95E8B5E8 B5DT900T95FATJX2oooo00GJf_oJfZ[Jf_oJf_nATED00TQ8E@T0000012@T 0000EB@T02@TE@=8B5D014Q804Q8E@0002@T00D0000022@TE@0002@TEB@T EDQ8EB@T0000EB@T00H000001R@T0000EB@T02@TEB@T02@TE@8T900012@T EB@T04Q8EDQ800E8B5D00fe]EDQ8EFe]E@04B4QE00@T900T95DT95E8B003 B4QE0Fe]E@7oool00003f]ZZf][of]ZZ00;Jf_l01Oooom[JokJfZTQ8EFe] E@02TI6Z00@T900T95D0000T9002B4QE00U]KEE8B5E]KEE8B5DT9018B5FA TJY]KEDT95D01`00000:92@0B4QEKFeE][JZf]ZZ][JZTI6ZKFeEf]ZZf][o 0[JfZP05TI6ZB4QEB4QETI5EKFeE0098B5D01I6AZ][JZ][Jooooom[Jo`06 oooo00CJf_nf]ZY]KEDT9002000000ATJX01Fe]EB@T02@T000002@T0002B4QE00000000@T95D0000T9018B5D2TI6Z01:f ]Z[JfZ[Jf_oooj[Jf_oJfZXT902ATJ[Jf_oJfZY]KEFATJ[JfZ[Jf_oooonf ]Z[Jf_oJfZX2oooo00?JfZZATJX000002000000592@0000092@092AEB4QE 00=]KED2][JZ0Y6AZP04TI5ETI6ZTI6ZTI5E0[JfZP05KFfZB4QE92@00000 92AE00=8B5D01B@T02@TEB@T04Q8EB@T0002000000@T95DT900000000002 92@000DT95DT9018B5DT95E8B0000dQ8E@07B4P0B4QEB4QE92AE92@092AE 92@00098B5D01B@T02@TEB@T02@T02@TE@0292@000@T95E8B00T95E8B5D1 oooo00000`0002@T0000000292AE0dQ8E@0392@0B4QEB4QE0098B5D01b@T 0000EB@T02@TEB@T04Q8EB@TE@0292@000lT95E8B5Ff]Z[JfZZATJY]KEE] KJZATEE]KEE8B5DT900T95D0000T900T95D00`00000592@00000001E0000 92@000`000000b@T000002@T0004000000@T90000000000T900292AE0Ve] E@06TI6ZTI5EKFeEB4QE92AE92@01000000:001E92@092AE92@0KFeETI6Z ][JZTI6ZKFeETI6Z0[JfZP03TI6ZKFeE92AE00/0000012@T0000000002@T 008000002TQ8EFe]EKJfZY6AZ[JfZ][Jooooom[Jooooom[Jo`=]KED2TI6Z 0oooo`03f][of]ZZ][JZ00;Jf_l01=[JZ][JokJfZR@T00`00002KFeE0Y6A ZP:f]ZX0196AZ[JfZY6AZ[JfZP:ATJX3][JZ00E]KEDT95D00000000T9000 0dQ8E@06B4P0B4QEB4QE92AE000092@01000000592@092AE92@092AEB4P0 00Q8B5D01dQ802@TEB@T02@TEDQ802@TEDQ8E@0292@000f]ZX0196AZ[JfZY6AZ[JfZP:ATJX2 ][JZ00E]KEE8B5D00000000T900014Q8E@0392@0B4QE92@000@000001R@T 0000E@0002@T02@TEB@T00U8B5D03R@T04Q8EB@T02@TEB@T02@TEDQ802@T EB@T02@TEB@T02@TEB@T02@TE@98B5D192AE0Oooo`000`00000492AEB4QE KFeEKFfZ0fe]E@07B4QEKFfZTI5EB4QE000092@0001E00ATJZf]ZZATJX00kJfZP05TI6Z][JZ][JZTI6ZB4QE0080 00000b@T04Q8EFe]E@02B4QE00ATJX0196AEI6AZ[JfZY6AZPFf]ZX00i6AZVe]EB@TE@02000000DT95E8 B5FATJY]KEDT95D00R@T000592AE92@00000000092@0008000000b@T02@T EB@T0005B4QE00=8B018B5DT95D00dQ8E@8T900012@TEB@T02@T02@TE@8T 900012@TEB@T02@TEB@T00ATJX0196AEI6AZVe]EDQ8E@8T9009000000ATJXT900000000P00000692@000000000000092@092AE0TQ8 E@A]KED00dQ8EFe]EI6AZP02TI6Z00JATEFf]ZZf]ZZf]ZZATJY8B5D292@0 0P00000<92AEKFeEKFfZB4P0000092@0B4QE92AE92@0000092@092AE0R@T 000692AE92@092AE92@092AEB4P00TQ8E@0492AE92@092AEB4P00TQ8E@0@ B4P092AE92@092AEB4P092AE92@092AEB4P092AEB4P092AE92@0B4QE92AE 92@00Oooo`0000<0000T900000000TQ8E@09KFeETI5ETI6ZTI5ETI6ZKFeE B4QE92AEB4QE009]KED00b@T000002@TE@0292@000@T95DT900T900T9002 B4QE00E]KEFATJZATJZf]ZZATJX00Ve]E@NATJX2KFeE0TQ8E@0592@092AE 92@0000092@000<0000012@T000000000000E@D000000b@T04Q8EDQ8E@02 KFeE00f]ZX3 TI6Z0kJfZP03TI6ZKFeEKFfZ00=8B5D01dQ804Q8EDQ8EB@TEDQ8EFe]EFe] ZP02B4QE00=8B018B5DT95D00dQ8E@03KFeEB4P092AE0098B5D2KFeE00>A TJZATEFATED00i6AZP06][JZTI6ZTI6ZB4QE92AE92@01`00000492AEB4QE ][JZTI6Z0kJfZP08TI6ZKFeEB4QE92@0000092AE000092AE3`000007001E 92@0TI6Z][JZKFfZKFeEf][o00?oool01=[Jooooom[Jom[Jo`;JfZX00i6A ZVe]EB@TE@0292@000=8B5E]KEDT90000TQ8E@06][JZoooof]ZZoooof]ZZ f][o0_ooo`03f]ZZ0000000000P000000b@TEDQ8EB@T0002B4QE0Ve]E@03 TI6ZKFfZTI5E00>ATJX00fe]EDQ8EB@TE@04000000A8B5E]KEE]KEDT95D5 000000lT900T95DT900T900T95E8B00T95DT9018B5E8B00T95DT900T95E8 B5DT90001DQ8E@08KFeEB4QEB4QEB4QEB4P092AEB4QEB4P00TQ8E@0392AE B4P0B4QE0098B5D192AE0Oooo`000R@T000392AEB4QEKFeE009]KED3B4QE 0Ve]E@03TI6ZTI5EKFeE009]KED2TI6Z00>f]Z[Jf_ooool00][JZP06][JZ TI6Z][JZf][o][JZTI6Z0Ve]E@98B5D022@T02@TEB@TEDQ8000002@T04Q8 EFe]E@E8B5D014Q802@TEFe]EFe]ZP98B5D00fe]EDQ8EI6AE@05TI6Z00Ff ]ZZATJZATJY]KEE8B5D00R@T00@000001R@T0000E@00000002@T04Q8E@:A TJX2][JZ0Y6AZP08KFeEB4QEB4QE92@0000092@0000092@03@00000<92@0 0000KFeE][JZKFeEB4QEf]ZZoooof][ooonZf][ooonZ0][Jo`05f]ZZ][JZ TI6ZKFeEB4QE008T900292AE0TQ8E@06KFeETI6Zf]ZZf][ooooof][o0_oo o`04f][oooooooooB4QE2000008T90000`0002@T04Q8E@03KFeE00=]KJZA TEFATJX00i6AZP03KFeEB4QE000000<0000012@T06e]EFe]EDQ8E@800000 0b@T0000EB@T0003000000lT900T95E8B5DT900T95DT9018B5DT95E8B00T 95E8B00T95E8B5DT95E8B00024Q8E@0;92@0B4QE92AEB4QE92@0B4QE92AE B4QEB4P092AE92@0007oool000060000B4QEB4QEB4QEKFeEB4QE0Ve]E@A8 B5D3TI6Z1;JfZP03f][of]ZZf][o00;Jf_l2][JZ00Q]KEE8B5E]KEE8B5DT 95E8B5FATEE]KED2000000f]ZX02=[JZ[JfZ[JfZY6AZY6AEDQ8EFe]EI6AZP9]KED016e]ZVe]EFe] EFe]E@98B5D022@T000002@T0000E@0002@T000002@TE@98B5D00b@TE@00 02@T000292AE00E8B00T95DT900T95DT90000P0000A8B5D01TQ802@TEDQ8 EB@T000002@T00L0000014Q804Q8EDQ8EFe]E@:ATJX02I6AEDQ8EDQ8EDQ8 EFe]EB@TEB@T000002@T000<000000lT95E]KEFATJZATJZATEFATJ[Jf_oo oooJfZ[ooooJf_oooooJf_oooonATJX00Ve]E@06TI6Zf][ooooof]ZZ][Ko B4QE0R@T00:f]ZX01_ooom[Jooooom[JZ_ooom[Jo`;oool00m[JokJfZVe] E@0900000dQ8E@09B4P092AEB4P092@092AEB4P0000092@092AE0098B5D2 000000ATJX00i6AEFe]ZVe]E@02KFeE00=8 B5E]KEE]KJX014Q8E@8T90001B@TEDQ8EB@T0000EB@T0002000000@T900T 95DT900005D3000000ATJX2KFeE00I8B5DT900T900T95DT900005D5000000ATEE]KEE8B5D06P000003B4QEB4P092AE0098B5D01B@T02@TEB@T 02@T02@TE@0292@01dQ8E@0592@092AEB4QEB4QE92@000H000000`00EB@T 0000000200000R@T000392AE92@092AE009]KED2B4QE0Ve]E@08KFfZKFeE B4QEB4QE92AEB4QE92AEB4P024Q8E@9]KED014Q8EFe]EDQ8EFe]E@E8B5D1 92@00Oooo`000`00000392@092AEB4P0009]KED2B4QE00m]KEE8B5DT95E8 B00T95DT9000000T9000000T95E8B5E]KEE8B5DT9018B5D00Ve]E@05KFfZ TI6Z][JZTI6ZTI5E00:ATJX00fe]EFe]ZY6AE@02TI6Z0[JfZP03KFeE92AE 92@0008000002b@TEDQ8EFe]EI6AZY6AEI6AZ[JfZ][JZ[JfZY6AZTQ8E@02 92@00P00000392@0TI6ZKFeE0098B5D00fe]EDQ8EB@T0003B4QE00A8B00T 95DT900T9002000000ATJX3][JZ00>ATJY8B5DT90000P00000392@092AETI6Z00=8B5D0 1Fe]EDQ8EB@T04Q8EFe]E@02B4QE00ATJX00fe]EB@TEB@T000J000000ATJX0000000001@00000392@00000000001H0000012@T02@TE@0002@T E@=8B5D292@00`00000392@092AEB4QE0098B5D292@000D0000T95E8B5DT 900T95D00TQ8E@0792@092AE92@092@092AEB4QE92AE008T9002000000DT 9018B5E8B5E8B5E]KED01DQ8E@9]KED7B4QE0Ve]E@04B4QEKFeEB4QEKFeE 0dQ8E@04KFeEB4QEKFeEB4QE16e]E@98B5D1oooo0002000000ATJX01Fe]EB@T02@TE@0002@T 0003B4QE00A]KEE]KJZATEFATJX3][JZ01VATJY]KEE8B5DT900T95DT900T 95DT900T95E8B00T95DT900T95DT9000000T900T95DT901]KEFATJY]KEE8 B5DT9000000T95D00R@T00<000003R@TE@00000002@T02@TEB@T04Q8EFe] Z][JZ][Jom[JZ[JfZVe]EDQ8E@>f]ZX0196AZR@TEB@T02@T0098B5D016e] EFe]ZVe]EFe]E@=8B5D2KFeE0i6AZP98B5D022@TEFe]EKJfZ[JfZY6AZTQ8 EB@TEB@T00l000003b@T0000E@0002@T04Q8EB@T02@TE@0002@T04Q8EB@T 000002@TEB@T00000003B4QE00ATJX01;JfZY6AZVe]EB@TE@8T90000b@TEDQ804Q8E@02 B4QE00=8B00T95DT90000P00000;92@0000092AEB4QEKFeEB4QE92@092AE 92@092AE92@000@000000b@T02@TEDQ80002B4QE00VATEFf]ZZATJZATEE] KEE]KJZATJZf]ZZATED00TQ8E@04000092@092AEB4QE1Fe]E@03TI5EKFeE TI6Z00>ATJX03[JfZ][Jom[JZY6AZY6AEFe]EI6AZ][Jom[JZ[JfZY6AZVe] EB@TEB@T014000001R@TE@0002@TEB@T02@TEB@T00=8B5D01B@T02@TEB@T 02@TEB@T0003B4QE0i6AZP06KFeEKFfZKFeEKFeEB4QE92AE0`00000492AE 92@0B4QEB4P024Q8E@09B4P0B4QEB4QEB4QEB4P0B4QE92AEB4QEB4P000A8 B5D016e]EFe]ZVe]EFe]E@98B5D01dQ804Q8EDQ8EDQ8EFe]EFe]ZVe]E@01 oooo0002000000LT95D00000000T900T95DT900T95D00TQ8E@0692AEB4P0 92AE92@0001E92@00`00000692@0000092@0001E92@092AE0R@T00030000 92@00000008T95D01DQ8EFe]EI6AEFe]ZY6AE@03KFeE0TQ8E@0392@092AE B4P000=8B5D292AE00=8B018B5FATJX00kJfZP04TI6ZKFeEB4QE92@01dQ8 E@0392@092AE92@000<000000b@T02@TEDQ8E@02B4QE00DT900T95DT9000 05DT90000P00000392@0B4QEB4QE00=8B5D00fe]ZVe]EDQ8E@02B4QE00BA TEFATJY8B5E8B5D292@000LT95DT9018B5E]KEFATEFATJY]KJX0196AZP>f ]ZX01M[JZ][Jom[JZ][JokJfZP02TI6Z00Nf]Z[JfZ[Jf_oJf_nf]ZY]KEE8 B5D00P000003001E0000000000`000000b@T00000000000292@00dQ8E@03 KFeEB4QEB4QE008T90001`0002@T02@TEDQ8EFe]EI6AZY6AE@04KFeE00a8 B5DT95DT9000000T9000000T9000000T95E8B5DT95DT9004B4QE00ATJX2][JZ 00Ff]_nf]Z[JfZZf]_oJfZX00][Jo`09oooof]ZZoooof][ooooooonZf][o f]ZZ][Ko00:f]ZX01m[JoooookJfZY6AZVe]EDQ8EB@T000;00000R@T0080 00001B@T02@TEB@T02@T02@TE@02B4QE00A8B00T95DT900T9002000001<0 05DT9018B5DT95DT900T95DT900T95DT900T95DT900005DT9000000T9000 000T95DT900T95D00R@T000392AE92@0B4QE0098B5D00dQ804Q8EDQ8E@02 B4QE00M]KEE8B5E8B5E8B5DT900T95E8B00024Q8E@03KFeEB4QEB4P000=8 B5D00fe]EDQ8EFe]E@01oooo0003000000LT900005DT9000000T9000000T 90001`00000592@00000000092@00000008T90003R@TEB@T02@T02@TEB@T 000002@T02@TEDQ8EFe]EI6AZVe]EFe]ZVe]E@98B5D00fe]EDQ8EDQ8E@04 B4QE0Ve]E@0;TI6ZTI5EKFfZB4QE92@0B4QEKFfZTI6Zf]ZZf][of]ZZ00:f ]ZX0196AZVe]EFe]ZVe]E@98B5D02B@T02@TEB@TE@0002@T000002@T0000 02@T0005000000DT900T95D0000T900T95D00R@T000792AE92@0B4QEB4QE KFeEB4QE92AE00<000000b@T06e]EFe]E@02TI6Z1;JfZP;JfZX01][Jom[J Z][Jom[JooooZ][Jo`Goool01=[Jom[JZ[JfZ[JfZP;Jf_l2f]ZZ00JATJY] KEE8B5DT9000000T900:000000`T95D0000T9000000T95DT9000000T95E8 B5E8B00T95E8B5D2000001XT900000000000000T95DT9000000T95DT900T 95DT900T95D0000T9000000005D0000T900T95E8B00T95E8B00T95E8B018 B5E8B005B4QE00=]KEE8B5E]KED00dQ8E@0392@0B4QE92AE00A8B5D00dQ8 04Q8EDQ8E@07B4QE00=]KEE]KJY]KED00Oooo`000P00000<92@000000000 92@0001E92@00000001E000092@0000092AE0P00000892@0001E000092@0 001E92@0000092AE0P000004001E0000000000000R@T0003B4QETI5EKFfZ 009]KED014Q8EFe]EFe]EFe]E@98B5D3KFeE0TQ8E@03KFeETI6ZTI6Z009] KED01b@TE@0004Q804Q8EKJfZ][Jom[JZP02f][o00JATJY]KEE]KEE]KEE8 B5DT95D492@000T005DT9000000T95DT900T95DT9000000T95D00P000004 92@0B4QE92AE92@01TQ8E@0792AE92@00000000092@092AEB4QE00>ATJX2 ][JZ00?JfZ[Jf_oJfZX00][Jo`06f]ZZf][ooonZf][ooooof]ZZ1_ooo`0< f]ZZf][of]ZZf][of]ZZf][o][JZTI6ZKFeEB4QE0000001E2P00000A92@0 B4QE92@0001E92@0000092@092AE92@092AEB4QE92AEB4P0001E92@00000 92@00080000012@TE@00000002@T008000000b@T00000000000200000b@T 000392AEB4QEB4QE00]8B5D016e]EDQ8EDQ8EFe]E@98B5D00b@T04Q8EDQ8 E@03B4QE00ATJX01;Jf ZVe]EDQ8EB@T0098B5D02Fe]EDQ8EDQ8EDQ8EDQ804Q8EKJfZY6AZ[JfZP02 f][o00>f]ZY]KEE8B5D00TQ8E@06B4P092@092@092AE92@0001E0P000005 92@092AEB4QEB4QEB4P000@000000b@T0000EDQ80003B4QE1@00000492@0 B4QEB4QETI5E0kJfZP08f][of]ZZf][ooooof][of]ZZf][ooonZ0][Jo`03 oonZf][ooooo00Coool03M[JZ_ooooooooooooooZ][Jom[JZ][Jom[JZ[Jf ZY6AZY6AEFe]ZP02B4QE00f]ZX00m[Jom[JZ[JfZP03B4QE00DT95E8B5E8 B5E8B5DT90000P00000792@092AE92@092AEB4P0B4RZB4QE00@0000012@T E@0002@T0000E@@000001b@TE@00000002@TEDQ8EFe]EI6AZP02][JZ00SJ f_oJfZ[Jf_oooooJfZ[ooooJf_ooool2f][o1_ooo`07f][ooooof][ooooo f][ooooof][o00;oool00m[Jom[JZY6AZP02TI6Z00JATEFATJY]KEE8B5DT 95DT9007000000TT95E8B5E8B5E]KEE8B5D00018B5E]KEE]KJX00TQ8E@04 KFeEKFfZKFeEKFeE0TQ8E@0392AE92@0000000P000000b@T02@TEDQ8E@03 B4QE00Y]KEE8B5E8B5E8B5DT900T95DT9018B5DT900T95D2B4QE00@T95E8 B5DT900T95D3B4QE00000000D0 05DT900T95DT9018B5D00Y6AZP08KFeEB4QEB4QE92AEB4P092AEB4QE92AE 0dQ8E@0392@0000092AE008T90000fe]EI6AZY6AZP02f][o00?JfZZf]_nA TJX01Ve]E@0>TI6Z][JZ][JZf][of]ZZTI6ZKFeE92AE92@092AE000092@0 001E92@01000000392AE92@00000008T90000`00E@000000000;000000DT 900T95E8B5FATEFATJX00[JfZP08f][of]ZZoooof][ooonZf][ooooof][o 0_ooo`08f][ooooooooooooof]ZZoooof][of]ZZ0][Jo`Bf]ZX00m[JZ[Jf Z[JfZP02TI6Z00FATEFATJZATEFATJZATED00Ve]E@04B4QE92@0000092@0 0`00000792@00000000092AE92@0B4QEKFeE0098B5D01b@T04Q8EFe]EDQ8 EFe]EDQ8EB@TE@0292@03000000392@0001EB4P00098B5D03fe]EDQ8EDQ8 EDQ804Q8EB@T02@TEB@T04Q8EB@TEDQ8EDQ802@TEDQ8EDQ80006B4QE00M8 B00T95DT900T95DT900T95DT900014Q8E@03KFeEB4QEKFeE0098B5D192@0 0Oooo`000P00000592@0000092@0000092@000H000001B@T000002@T0000 02@T000200000R@T000:B4QEKFeETI6ZKFeEB4QE92@092AE92@0001E92@0 0P00000592@092AE92@092AE92@000=8B5D2TI6Z00>f]Z[JfZZf]ZX00kJf ZP03TI6ZB4QEB4QE00:ATJX4][JZ00KJf_oJfZZf]ZY8B5E8B00T95D292@0 1`00000392@00000000001400002B4QE0Y6AZP0;][JZf]ZZf][ooooof][o oooof][ooooof][ooonZf][o00Goool00m[Jooooom[JZP02f][o00CJfZZf ]ZZATJZf]ZX3TI6Z00>ATEE]KJY]KED00Ve]E@07KFfZTI6ZTI5ETI6ZKFfZ B4QE92@0008000000b@T000000000006000000HT95E8B5E]KEE8B5DT95DT 9002B4QE00f]ZX00fe] EDQ8E@000004000000@T90000000000T95D2000000ATJY]KJY]KED0 0i6AZP07KFeEB4QEB4QE92@0B4QE92@092AE009]KED01Y6AZY6AEI6AZY6A EFe]ZTQ8E@8T9003000000PT9018B5E8B5E8B000000T95DT900T95D30000 00HT9000000T9000000T900005D292@00TQ8E@05KFfZTI5EKFfZKFeEB4QE 00<0000292@000f]ZX01i6AZVe]EDQ8EB@TEB@T04Q8EFe]E@02TI6Z00=8B5DT900T 95D00R@T000792AE92@0KFeE][JZTI6ZTI5EKFeE0098B5D00b@T04Q8EDQ8 E@02B4QE00ATJX0196A EB@TEB@T02@T00@000003B@T000004Q8EDQ8EDQ804Q8EFe]EDQ8EB@TEB@T 000002@T02@TE@0292@00TQ8E@03KFeEB4QEB4QE0098B5D00b@TEDQ804Q8 E@08B4QE00A8B018B5E8B5E8B003B4QE00/T9018B5DT900T95DT900T95DT 9000000T900T95DT90000Oooo`0000@0000T9000000T9002000000ATJZATEE]KED00Y6A ZP07TI5ETI6ZTI6ZTI6ZKFeEB4QE92AE008T900034Q8EI6AZY6AZ[JfZVe] EB@TE@0002@T0000EB@T02@TEDQ8E@>ATJX2KFeE00M8B5DT95E8B5E8B5E8 B00T95E8B5D00P00000892@00000000092@092AEB4QEKFeE92AE0P000003 92@0000092@000<00002B4QE0Y6AZP04TI5ETI6ZTI5EKFfZ0Ve]E@03TI6Z ][JZf]ZZ00;Jf_l02][JZ_ooom[Jooooom[JZ][Jooooom[Jooooom[Jo`?o ool00m[Jooooooooo`02f][o1oooo`06f][ooooof][of]ZZf][ooooo0[Jf ZP:ATJX0196AEI6AZVe]EFe]E@98B5D00fe]EI6AZY6AE@02KFeE00ATJX03;JfZY6AEDQ8EDQ8EB@T02@T EB@T000002@T0000E@0002@T00E8B5D292@000@005D0000T900T95D3B4QE 0Ve]E@=8B5D00dQ802@TEB@T0002B4QE00A]KEE8B5E8B5E]KED6B4QE00=8 B018B5E8B0000R@TE@0692@092AE92@092AE92@092AE0b@T007oool000@0 00001000EB@T00000000E@D000000b@T000000000006000000/T90000000 000T95DT9018B5E]KEFATJZf]ZZATJZf]UD00Y6AZP0@TI5EKFeEKFeE92AE 92@092AEB4QEKFeE][JZf]ZZf][oTI5EB4QE92@0000092@00P00000492@0 B4QETI6ZKFeE0dQ8E@8T90001TQ8EB@TEB@T02@T000002@TE@<000000b@T 04Q8EDQ8E@02KFeE00ATJX0196AEFe]ZTQ802@TE@80 00002B@T04Q8EDQ8EI6AZ[JfZ][JZ][Joi6AZY6AE@02B4QE00dT9000000T 900005D0000T900T95DT900T95DT900T95DT900T95D00b@T00Q8B5D01fe] EDQ8EDQ8EDQ804Q8EDQ804Q8E@04KFeE00=8B5E]KEE8B5D00TQ8E@0392@0 B4QEB4QE0098B5D01DQ804Q8EB@TEDQ8EB@T000292AE0R@T004T95D1oooo 00000b@T0000EB@T0003000000@005DT9000000005D>00000R@T0098B5D2 KFeE00]]KJZATEE]KJZATEE]KJY]KEE8B5DT95DT900T95E8B5D00Y6AZP04 TI5EKFeE92AE92@01000000592@00000B4QETI6ZTI5E00:ATJX2KFeE00I] KJY]KEE]KEFATJY]KEE8B5D292@000PT95D0000T900T95DT900T95E]KEE] KJX2][JZ0Y6AZP04KFeEB4QE92@092AE0P00000392@0B4QEKFeE00>ATJX2 ][JZ00?JfZ[Jf_ooool00][Jo`;oool02M[JZ_ooom[JooooZ_ooom[Joooo om[JZ_ooo`02f][o00?JfZ[oooooool01_ooo`0=f][ooooof][of][of]ZZ ][JZKFeE92AEKFeEB4QE92@092AE92@000@000000b@T02@TEI6AE@04TI6Z 00BATEE8B5D0000T9002000000dT95E8B5FATJ[JfZ[Jf_oJfZZf]ZZATJY8 B5DT900T95DT900000000R@T008000001b@T02@TE@0002@TEB@T000002@T 0004B4QE00E8B018B5E8B5E8B5E]KED01dQ8E@06KFeEB4QEKFeEKFeEB4QE KFeE0dQ8E@04B4P092AEB4QE92@014Q8E@04B4P092AEB4P092AE0R@T004T 95D192@00Oooo`0000H0000T9000000T9000000T9007000000<005D0000T 90001000000392@0001E000000<00002B4QE00A]KEE]KJZATEE]KJX2KFeE 0dQ8E@0392@0B4P0B4QE009]KED3B4QE00f]ZX0196AZY6AEI6AZY6AZP:f]ZX01Fe]EDQ8EB@TEB@T0000 000292@000@T95E8B018B5FATED5TI6Z00a]KEDT95DT900T95DT9000000T 9018B5E]KJZATEFATJZf]ZX2f][o00?JfZ[ooooJfZX00_ooo`05f][ooooo f][ooooof][o00;oool01m[Jooooom[Jooooom[JZ_ooom[Jo`02oooo00KJ fZ[ooooooooooonf]ZZATJX2KFeE00Zf]ZZATJY8B5DT95FATJ[JfZZf]ZZA TJY]KEFATJX292@00`000003B4QETI6Z][JZ00:f]ZX2TI6Z00=8B5DT900T 95D00P00008T90003i6AZ[JfZ[JfZ][Jom[JZY6AZVe]EB@TEB@T000002@T EB@T02@TEB@T02@TE@02000000LT900000000000000T95E8B5E]KED014Q8 E@03KFeEB4QEB4QE00=8B5D00fe]EDQ8EDQ8E@02B4QE0Ve]E@04B4QEKFeE B4QEKFeE14Q8E@0>B4P0B4QEB4QEB4QE92@0B4QE92AE92@0B4QE92AE92@0 92AE92@092AE0Oooo`0000ATJX2KFeE00=8 B5E]KEFATJX00Y6AZPA8B5D2000000dT900T95E]KEE]KEGJfZ[Jf_oJfZZf ]ZZATJY]KEE8B5E]KEE]KJX00Ve]E@08B4QE92AEKFeETI6Z][JZf][of]ZZ f][o0_ooo`03f][ooooooooo00Woool00m[Jooooom[Jo`02oooo00?Jf_oo oooJf_l00oooo`04oonZf][of]ZZf][o2?ooo`0?f]ZZoooof][oTI6ZB4QE TI5E][JZf][of]ZZf][of]ZZ][JZ][Ko][JZTI6Z0098B5D3000000f]Z[Jf_oJfZX0 0][Jo`08f]ZZf][of]ZZ][JZTI6ZTI5EB4QE92AE0P00000=92@0B4QE][JZ ][JZf]ZZ][Kof]ZZKFeEB4QE000092@092AE92@000=8B5D00b@T000002@T 000600000092@092AE92@092AEB4P092AEB4QE92@0B4QE92@092AE92@092AE92@0 0R@TE@7oool00005000092@00000000092@000H000000`00EB@T0000000; 000000000000XT9000000T900T95E8B5E8B000000T900T95DT9002B4QE 00=]KEFATJZf]ZX00kJfZP0:TI6ZKFfZKFeEKFeEB4QEKFeEB4QEKFeETI6Z f][o0[JfZP:ATJX00dQ8EB@T02@TE@02B4QE00Q]KJZATJZATJZATEDT95DT 9000000T9003000000^ATJ[JfZZf]Z[Jf_nf]ZZATEE8B5DT95E8B5E8B00T 90000P00000=B4QETI6Z][JZf][o][JZoooof]ZZoooof][ooooooonZoooo f][o00Goool00m[Jooooooooo`07oooo00?ooj[oooooool00_ooo`04oonZ f][ooooof][o1oooo`03f][ooooo][JZ0098B5D00kJfZ][Jom[Jo`02oooo 00WJf_oooooJf_oJfZ[Jf_oJfZZf]ZZATJXT95D00`00000:92@092AEB4QE B4QETI5ETI6Z][JZf][of]ZZf][o0Y6AZP07TI5EB4QEB4QEB4QE92AE0000 92AE008T9004000000@T95DT900T95E8B002B4QE00f ]ZX0396AZTQ8EB@T000002@T02@TE@0002@T06e]EI6AZ[JfZY6AZP>f]ZX0 0i6AZTQ8EB@TE@0392@000@T95E8B5E]KEFATJX2f][o00?ooooJf_ooool0 1oooo`03f][ooooooooo00Koool00oooZ][Jooooo`0Aoooo00Rf]ZY8B5D0 001]KEGJfZ[Jf_oooj[Jf_l2oooo00CJf_oooooJfZ[Jf_l2][JZ00JATJY8 B5D00000000T9018B5D3KFeE00@T95E8B5E8B5E8B5D2KFeE00m]KJZATJ[J f_oJfZZf]ZY]KEE8B5DT95DT900T95DT900T95DT900T95D000000R@T0009 92AE92@0B4QEB4P092AEB4QEB4P092AEB4P000A8B5D00dQ804Q8EDQ80003 B4QE00I8B00T95DT95DT900T95DT9003B4QE00PT9018B5DT95E8B018B5DT 95E8B018B5D1oooo0004000000LT900000000000000005D0000T90001@00 0003001E000092@000H0000292@000A8B5E]KEE8B5DT95D2000000A8B5FA TJY]KEDT95D2B4QE0fe]E@04TI5ETI6ZB4QE92@00TQ8E@05TI5ETI6ZTI6Z TI5ETI6Z00>f]ZX00i6AZVe]EDQ8E@02B4QE00A]KEE]KJZf]Z[Jf_l2][JZ 00A]KEDT95DT900T95D292@000@T95E8B5E]KEFATED3TI6Z00NATEE]KEDT 9000000T9018B5DT95D00R@T000492AEKFeEoooof]ZZ1oooo`04f][ooooo oooooonZ1?ooo`03f][ooooooooo00;Jf_l00oooom[JooooZP05oooo00?J f_ooooooool01_ooo`07f][of]ZZ][JZ92AE92@0TI6Zf][o00Goool02m[J om[JZ][Jom[JZ][JokJfZY6AZTQ8E@0002@T02@TE@02B4QE019]KEE8B5D0 000T900T95DT900T95E8B5E]KEFATJ[JfZ[Jf_oJfZZATJY]KJY8B00T900T 95D292@000PT95DT900T900T95D0000T900T95DT9002B4QE00=8B00T95E8 B5D034Q8E@8T90003R@TEB@T04Q8EB@TEDQ802@TEDQ8EDQ804Q8EB@TEDQ8 EB@T02@TEDQ8E@7oool000L000000b@T00000000000500000b@T00030000 92@0000000D0000012@TEDQ804Q8EB@T00<000001TQ8EI6AZTQ8EB@T04Q8 EDQ800=8B5D2TI6Z00E]KEE8B5E8B5E8B5E]KED00i6AZPBf]ZX02I6AZVe] EFe]EFe]EI6AZVe]EI6AZ[JfZ][JZP02][JZ015]KEDT95DT9018B5DT95DT 90000018B5DT95E8B5E]KEE8B5E]KJY8B5DT95D0000T95D00TQ8E@06TI5E KFfZ92@092AEB4QEf][o0_ooo`03f]ZZoooooooo00Ooool00m[Joooooooo o`02oooo00GJfZ[Jf_oJfZ[Jf_oJfZX00m[Jo`03oonZf][ooooo00Koool0 3=[JooooooooooooZ_ooom[JokJfZR@T06e]EKJfZ_ooom[Jo`;oool2f][o 00CJfZ[Jf_oJfZZf]_l2][JZ00NATJY8B0000000000T9018B5DT95D01P00 000592@00000KFeEKFeE][JZ00;Jf_l00m[JZ[JfZVe]ZP04B4QE00H0000T 9000000T900T95DT9006B4QE00=8B018B5E8B5D01TQ8E@0DKFeEB4QEB4P0 92AE92@092AEB4QE92@092AEB4P092AEB4QEB4P092AEB4QEB4P092AE92@0 92AEB4QE0Oooo`001@00000492@0001E000092@01@00000392AE00000000 008000000`00E@0000000002000000HT9000000T900T95DT900T95D30000 0TQ8E@0392@092AEB4QE0098B5D01Ve]EDQ8EFe]EFe]ZVe]EDQ8E@9]KED2 TI6Z00FATEFATJZf]ZZf]ZZf]_l00i6AZP05KFeEKFfZKFeETI6ZTI5E00>A TJX00i6AEDQ8EB@TE@0392@000L0000T95DT900T900T95DT900T95D00R@T 000<000092@0000092@092AEB4QE][JZB4QE92@092AEf]ZZf][o3Oooo`0> f]ZZoooof][of][of]ZZf][o][JZf][of]ZZf][of]ZZf][ooooof][o2_oo o`;Jf_l01Fe]EDQ8EKJfZ][JooooZP02oooo00OJf_oJfZ[Jf_nf]Z[JfZZf ]_oJfZX00[JfZP09TI6ZB4QE0000000092@092AE92@092AE92@000<00000 12@T000002@TEB@TE@98B5D0196AZ][JZ][Jom[JZPBf]ZX03TQ8E@0002@T EB@T02@TEB@T02@TEDQ804Q8EFe]EDQ8EFe]EDQ8EFe]E@=8B5D01DQ804Q8 EDQ8EDQ8EFe]E@04B4QE010T9018B5DT900T95E8B00T95E8B5DT900T95E8 B5DT900T95DT9000000T95DT9001oooo0004000000@T90000000000T9008 000000ATJX00kJfZY6A Z[JfZP03][JZ00>ATJZATEE8B5D00TQ8E@A]KED3B4QE00dT900T95D0000T 95DT900T95DT9000000T900T95DT900T95DT90000P00000<92@0000092AE 92@0TI5EB4QEB4P092AE][JZf]ZZoooof][o2Oooo`05f]ZZoooooooooooo f][o00:f]ZX01?ooom[JZ][Jom[JZP:f]ZX00m[JZ][Jooooo`0:oooo00cJ f_nf]ZY]KEFATJ[Jf_oooooJf_oJfZ[Jf_oJfZZf]Z[Jf_l2][JZ00>ATJY8 B5E]KED00Ve]E@04B4QE0000000092AE0TQ8E@04B4P0B4QE92@092AE0R@T 008000001b@T0000EB@T02@TEFe]EI6AZ][JZP03f][o00GJfZZf]ZZATJZA TJY]KED00TQ8E@03B4P0B4QEB4QE00=8B5D00fe]EDQ8EDQ8E@04B4QE00=] KEE8B5E]KED01DQ8E@0492@0B4QEB4QEB4P01TQ8E@0592@092AE92@092@0 B4QE007oool00007000092@0001E000092@0000092AE00<000000`00E@00 02@T000>000000KFeETI6ZTI5EKFfZKFeEB4QEKFeE92AE92@092AE 92@092AE92@092AE0R@T0005000092@092AE000092@000P000001B@T04Q8 EI6AZ[JfZ][JZP02f][o1Oooo`08f][o][JZTI6ZTI5ETI6Zf]ZZ][JZB4QE 0P00000692@0KFfZf]ZZoooof][o][JZ0TQ8E@03KFeE][JZoooo00Woool0 1I6AZTQ8EDQ8EFe]EKJfZP02f][o00bf]ZY8B5E8B5E]KEFATJ[Jf_oJfZZA TJXT900T95DT900T95D3000000=8B5E]KJZATJX00i6AZP0@KFeE92AE92@0 92@0000092AE92@0000092AE92@092AEB4QEB4P092AEB4QE92AE0TQ8E@04 B4P0B4QEB4QEKFeE0dQ8E@03B4P0B4QEB4QE00E8B5D00fe]EDQ8EFe]E@07 B4QE00ATJX2][JZ0Y6AZP03TI5ETI6Z][JZ00Bf]ZX01M[JZ][Jom[JZ[Jf ZY6AZP02B4QE00=]KEE]KJZATED00i6AZP09KFeEB4QE92@092@092AEB4P0 92AE92@092AE008T900012@TE@00000002@TE@H0000022@TE@00000002@T EDQ8EI6AZ][Jom[JZPCoool01m[Jooooom[JZY6AZTQ8EB@TEDQ80002TI6Z 0`00008T90002KJfZ][JokJfZY6AZTQ8EDQ806e]Z[JfZ][Jo`08oooo00WJ fZZATJY8B5DT902ATJZf]Z[Jf_nf]ZY8B5D010000003f]ZZf][oTI6Z00f]ZX00oooom[Jooooo`02f]ZZ00JATJZATEE8B5E8 B5E8B018B5D2KFeE00I8B5DT900T900T95E8B5E]KED2B4QE00M8B00T95DT 9000000T9018B5DT90002P00000692@00000B4QEKFfZ][JZf]ZZ0][Jo`07 f]ZZf][of]ZZf][of]ZZ][JZTI6Z00:f]ZX2TI6Z00E]KEFATJY]KEFATJY] KED00TQ8E@9]KED2TI6Z00CJfZ[Jf_oooooJf_l4oooo00?Jf_oJfZY]KED0 0TQ8E@05TI6Z][JZ][JZTI6ZKFeE0098B5D292@00Ve]E@06B4QE92AEB4QE B4QEKFeEB4QE0`000007B4QE][JZf][of]ZZf][ooooof]ZZ00;Jf_l00kJf ZVe]EDQ8E@02B4QE00U8B00T95DT900T95DT900005DT9000000T95D01DQ8 E@0:B4P0B4QEB4QE92@0B4QE92@0B4QE92AEB4QE92@014Q8E@08B4P0B4QE 92@0B4QE92AE92@092AE92@014Q8E@8T90001b@TEB@T02@TEDQ8EB@T02@T E@000001oooo0004000000f]ZX02m[J ooooom[JZ[JfokJfZY6AZVe]EFe]ZVe]EFe]ZY6AZP02][JZ00>f]_oJfZ[J f_l01?ooo`04f]ZZf][of]ZZKFfZ0TQ8E@05TI6Z][JZf][of][of]ZZ00:f ]ZX2TI6Z00>ATEE]KJZATED00Ve]E@03TI6ZKFfZB4QE00<000001B@T06e] Z[JfZ][JokJfZP02f][o0][JZP03f][oTI6ZKFeE00A8B5D04DQ802@TEB@T 02@T000002@T02@TEB@T04Q8EB@TEDQ802@TEDQ8EB@TEDQ804Q8EB@TE@02 92@000=8B5E8B00T95D02DQ8E@0392@092AE92@000A8B5D01TQ802@TEB@T 02@TEDQ802@TE@8T900100000Oooo`002P000003001E000092@000T00000 0b@T0000E@00000:00000R@T008T95D00dQ8EFe]EFe]E@02B4QE00E8B02A TEFATJZATJZATED00[JfZP04f]ZZf][of]ZZf][o0[JfZP9]KED4B4QE00@T 900T95D000000002B4QE00Y]KEFATJY8B5E8B5DT900T95DT900T95DT900T 95D292@00`00000392@00000000000@0000012@T0000EB@T04Q8E@:ATJX0 0kJfZ][Jom[JZP03f][o00OJfZ[Jf_oJfZ[Jf_nf]Z[JfZ[Jf_l00[JfZP04 TI6ZKFeEKFeETI6Z0][JZP03][Kof]ZZf]ZZ00;Jf_l00oooZ_ooooooo`02 oooo00?Jf_oJfZZATJX00fe]E@08TI6Z][JZf]ZZoooof][of]ZZf][o][JZ 0Y6AZP03TI5ETI6ZTI6Z009]KED02b@T00000000000002@T02@TEFe]EI6A ZVe]EI6AZ][JZP02f][o00?JfZY]KEE8B5D00Ve]E@07TI6ZKFeEB4QEB4QE 92@092AE92@0008000001R@TEB@T02@T02@TEDQ8EDQ80098B5D00b@TEDQ8 02@TE@04B4QE00ATJX6][JZ00>ATJY]KJY]KED00dQ8E@04KFeEB4QEB4QE92@0 0P000007B4QEKFeEKFeETI6ZB4QE92AE92@0008000002B@T000002@T02@T EB@T02@TE@0002@T02@TE@0392@01@00000492@092AEKFeETI6Z0[JfZP06 f]ZZf][of]ZZf][of]ZZoooo0][JZP;Jf_l2f]ZZ0[JfZP:ATJX2][JZ00GJ f_nf]ZZATJZATJZf]ZX00][Jo`?oool02M[Jom[JZ][JokJfZY6AZVe]EDQ8 EI6AEI6AZP02f][o00?JfZ[Jf_nf]ZX00[JfZP:ATJX0196AEI6AZVe]EDQ8 E@80000032@T0000000002@TEDQ804Q8EFe]EI6AZ[JfZ][JZ][Joi6AZP98 B5D2TI6Z00i]KEE]KJY]KEE8B5DT9000000005D0000T9000000T95DT900T 95E8B002B4QE00=8B00T95DT900014Q8E@04B4P0B4QEB4QE92@00TQ8E@05 B4P0B4QEB4QE92@092AE008T90003B@TEB@T04Q8EB@T02@TEB@T02@TEDQ8 02@TEDQ8EB@T02@TEB@T0001oooo0008000000ATJX04I6AEDQ8EDQ8EB@T02@TEDQ8 EFe]EI6AZVe]EI6AZ][JZ][Joi6AZY6AEFe]EDQ8EB@T0002B4QE015]KEE8 B5E8B5E8B5DT900T95DT9018B5FATJZATEFATJZATEE8B5DT900T95DT9000 05D01000000492@0000092AEB4QE0Ve]E@04KFfZKFeEKFfZB4P00`000005 92@092AEB4QEKFeETI6Z00>f]ZX5f][o00KooooJfZ[Jf_oJf_oJfZ[Jf_l2 f]ZZ00Zf]_oJfZZATJY8B5DT9000000T902ATJ[JfZ[Jf_l5oooo00?JfZZf ]ZY]KJX00TQ8E@06KFeETI6ZTI6Zf]ZZ][JZf]ZZ0kJfZP:ATJX00fe]EDQ8 EB@T000700000092AE92@092@092AE92@0 B4QE92AEB4P092AE92@092AEB4QE92@092AE0Oooo`001@00000392@00000 000000L000001B@T00000000000002@T0003000000@T90000000000T9007 00000R@T0004B4QE92@0KFeEKFfZ0Ve]E@98B5D012@T000002@T02@TE@98 B5D0296AEFe]EDQ8EB@T04Q8EFe]EDQ8EFe]E@98B5D012@TEB@T02@T0000 E@8T90000b@TEFe]EI6AZP03][JZ00BATJY8B5E8B5DT95D2B4QE0R@T0080 00002R@T04Q8EDQ8EB@TE@0006e]EKJfZ[Jfom[JZVe]E@<000000dQ8EB@T 02@TE@02B4QE0Y6AZP>f]ZX02M[Jom[JZ][Jom[Jom[JZ][Jom[JZ[JfZY6A ZP02KFeE0R@T008000000dQ804Q8EKJfZP02f][o0_ooo`0;f][ooooooooo f]ZZf][of]ZZTI6ZB4QE92AE92@092AE0098B5D2KFeE00BATJZATEE]KJZA TED2B4QE00ATJ[Jf_oJf_l00[JfZP05TI6ZB4QEKFeEB4QE92AE 008T9002000000HT9000000T900005DT900T95D5B4QE00M]KEE8B5DT9018 B5E8B018B5E8B0000TQ8E@0492@092AE92@092@00P00000592@092AE92@0 92AE92@000=8B5D01dQ802@TEDQ802@TEDQ8EDQ804Q8E@01oooo00050000 00ATJX02;JfZ][JZ][Jom[J ooooom[Jooooom[Jo`;oool02_ooZ][Jooooooooom[JZ_ooom[Joi6AZVe] EDQ8E@8T9002000000ATJX2B4QE00XT900T95E8B5FATJZATEFf]ZZATJZATEFATJZA TED2TI6Z00>ATEE]KEE8B5D00Ve]E@09TI6Z][JZf]ZZf][oTI6ZTI5ETI6Z ][JZTI6Z0098B5D02B@TEDQ8EFe]EM[JZ][Jooooom[Jom[JZ[JfZP02TI6Z 00E]KJZATEFATJZf]ZZATJX00[JfZP;Jf_l?oooo00CJf_oooooooooJf_l2 oooo0][Jo`05f]ZZoooof]ZZ][JZB4RZ00A8B5D016e]EKJfoi6AZVe]E@@0 000024Q806e]ZVe]EI6AZY6AEFe]EB@TEB@T00<000001R@TEDQ802@TEDQ8 04Q8EB@TE@8000001000E@00000002@T0080000012@TEB@T02@TEB@T0098 B5D3KFeE00=8B5DT95E8B00014Q8E@0=B4P0B4QE92AEB4P0B4QEB4P0B4QE B4P0B4QE92AE92@092AEB4P000=8B5D01R@TEDQ8EB@T02@TEB@T02@TE@7o ool000@0000012@TE@0002@T02@TE@D000000b@T00000000000>000000TT 9000000T95D0000T90000018B5E]KEFATJX00Ve]E@05B4QEKFeEB4QEB4QE 92@00098B5D036e]EDQ8EDQ8EDQ8EFe]EI6AZ[JfZ][JZ[JfZ][JokJfZ][J o`>f]ZX01Ve]EDQ8EDQ8EB@T04Q8EFe]E@:ATJX00kJfZY6AZY6AE@02TI6Z 0Ve]E@=8B5D00fe]EI6AZ][JZP02f][o00?JfZZATJZATJX00Y6AZP0:KFeE B4QE00000000B4QETI6Zf]ZZf][of]ZZoooo0][JZPFf]ZX01=[Jom[JZ][J om[JZP?oool01=[JZ_ooooooom[Jo`;oool04][Jooooooooooooom[JZ_oo om[JooooooooZ][JooooooooZ_ooom[JooooZ][Jom[JZ][Jo`;JfZX01;Jf ZY6AZY6AZY6AZP;JfZX02KJfZVe]EB@T0000EB@TEFe]EI6AZ][Jom[JZP02 f][o00Ff]ZY]KEDT95DT900000000R@T000392AEB4QEB4QE0098B5D00b@T 000002@T0003000000f]ZX01Y6AZY6AEI6AZVe]EDQ8EB@TE@9]KED2TI6Z00?J fZ[Jf_oJf_l06?ooo`04f][ooooooooooonZ1?ooo`07f]ZZoooooooof][o oooof][ooonZ00?Jf_l01;JfZY6AZR@T02@TE@80000024Q8EI6AZ[JfZY6A ZY6AEI6AZY6AEI6AZP:f]ZX0196AZY6AEFe]ZTQ8E@8T90001b@TEB@T04Q8 EB@TEDQ8000002@T0002000000HT95DT9000000T900T95E8B003B4QE00=8 B00T95E8B0000TQ8E@0;92@092AEB4QE92@092AEB4P092AE92@0B4QE92@0 92AE008T90003R@TEB@T02@TEB@T02@TEB@T04Q8EB@T04Q8EB@T02@TEB@T 04Q8EDQ8007oool000@000000`00EB@T00000006000000ATJX026e]EI6AZVe]EFe]ZVe]EDQ8EB@T02@TE@98B5D01Y6AZ[JfZ][J om[Jom[JZ][Jo`>f]ZX0396AZY6AEB@TEB@T000004Q8EFe]EI6AZVe]ZY6A Z[JfZ][JZQ_oool00m[Jooooom[Jo`04oooo0][Jo`05oonZf][ooooof][o oooo00;JfZX02[JfZY6AZTQ8EB@T0000EB@T02@TEFe]EI6AEDQ8E@BATJX0 4I6AEKJfZY6AZY6AEI6AZTQ8EB@T02@TEB@T02@TEB@T04Q8EB@T02@TEB@T 02@TEB@T0002000000f]ZX01Y6AZVe]EB@T02@TEFe]EI6AZP>f ]ZX01=[Jom[JZ][Jom[Jo`;JfZX03M[JokJfZ[JfZ[JfZY6AZY6AEFe]ZVe] EFe]ZVe]EFe]ZVe]EDQ8E@0292@000U8B5E]KEFf]Z[JfZ[Jf_oJfZ[Jf_oJ fZZATJX00kJfZP0;TI6Z92@092@092@0B4QETI6ZTI5EKFeETI6Z][JZf][o 01ooool02=[Jooooooooom[JooooZ][Jooooom[JZP;Jf_l01M[JZ][JokJf ZVe]EDQ8E@0292@000<00018B5E8B5D00TQ8E@07TI5ETI6ZTI6ZTI5EKFfZ TI6Z][JZ00:ATJX02Fe]EDQ8EB@T04Q8EB@T02@TEB@T02@TEB@T00050000 00lT9018B5DT95E8B5DT9018B5DT9018B5DT9018B018B5DT900T95E8B00T 95D00TQ8E@0FB4P0B4QE92@092AE92@0B4QE92@0B4QE92@0B4QE92AEB4QE 92@0B4QE92@092AE92@0B4QE92AEB4P092AEB4P00Oooo`001P00000392@0 0000000000X000003@00EB@T000002@TEB@T000002@T000002@T00000000 EB@T0000000392@000L0000T9000000T95E8B018B5E]KED01kJfZP=8B5D0 1Y6AEI6AZY6AZ[JfZY6AZ[JfZP;Jf_l01m[JZ][Jom[Jom[Jom[JZ[JfokJf ZP02TI6Z00>ATEE]KEE]KED00fe]E@98B5D01B@TEFe]EI6AZ[JfZ][Jo`02 oooo00?Jf_oJfZZATJX00Y6AZP:f]ZX01TQ8EB@TEDQ8EFe]EI6AZVe]E@:A TJX00kJfZ][JZ][Jo`0Poooo00Oooj[Jf_oJf_oJf_oJfZ[Jf_oJfZX00][J o`:f]ZX0296AZTQ8EB@TE@0004Q8EFe]EDQ8EB@T0098B5D2KFeE00=]KJY] KEFATJX00i6AZP98B5D01`0002@T04Q8EDQ8EB@TEDQ802@TE@0292@000DT 95DT900T95DT9018B5D00R@T000392AE92@0B4QE008T95D02TQ8EB@TEB@T 02@TEB@T02@TEDQ802@TEDQ8EB@TE@8T900292AE0118B00T95E8B5DT9018 B5DT9018B5DT900T95DT900T95E8B5DT9018B5DT95E8B5D1oooo000;0000 00f]ZY]KEE]KED00Ve]E@09TI6ZKFeEKFfZ TI6Zf]ZZf][ooooof][ooonZ01koool01=[Jooooom[Jom[JZP;Jf_l01kJf Z][JZ[JfZ[JfZY6AZY6AEDQ8E@0292@000I8B5FATJY]KEE8B5DT95E8B5D3 KFeE00>ATJZf]ZZf]ZX00[JfZP0QKFeEB4QE92AE000092AEB4QE92@0B4QE KFeEB4QE92@0000092AE92@092AE92@0000092AE92@0B4QE92@0B4QE92@0 B4QE92@0B4QE92@092AE92@092AEB4P092AEB4P0008T95D02B@T04Q8EB@T 02@TEB@T02@TEDQ804Q8EB@TE@0392@000HT95E8B00T95E8B00T95DT9001 oooo000:000000f]ZX01][JZY6AZ[Jf ZVe]EDQ8EFe]E@ATJX6][JZ00>ATJZf]ZZA TJX00Y6AZP04][JZTI6ZKFeEB4QE0Y6AZP0:f]ZZf][ooooof][ooonZf][o f]ZZoooof]ZZ][JZ0TQ8E@0592AEB4QEKFeEKFeEB4QE00=]KED2B4QE00=] KEFATJZf]ZX00][Joakoool01M[Jooooom[Jooooom[JZP02f][o0kJfZP:A TJX01DQ8EB@T02@T04Q8EI6AZP02][JZ00i]KJZATJ[JfZ[Jf_oooooJf_oJ fZZf]ZZATJY8B5FATJY8B5E8B02f]ZX2TI6Z0kJfZP04B4QE000000000000 0R@T000W92AE000092AE92@092AEB4P092AE92@092AE92@092AEB4P092AE 92@092AE92@092AE92@0B4QE92AEB4P092AE92@092AEB4P092AEB4P0B4QE 92@0B4QE92@0000092@092AE92@092AE92@092AE92@0007oool000T00000 12@T02@TEB@T02@T00L000000b@T000000000003000000ATJY]KEE]KED00fe]E@07 B4QEKFeETI6ZKFeETI6Z][JZf][o00Bf]ZX01i6AZVe]EFe]EKJfZ][Joooo om[JZP02f][o00SooooJf_oJf_nf]ZZATEE8B5DT9000000292AE00E8B5D0 000T900T95E]KED00dQ8E@06KFeE][JZ][JZf][ooooof][o7_ooo`04oonZ f][ooooof][o0][JZP0;][Ko][JZTI5EB4QE92@0001EB4QEKFeETI6Zf]ZZ ][JZ00:ATJX02M[JZ][Jooooom[JZ_ooom[Joi6AZ][JZ][Jo`02B4QE00KJ fZ[ooooooooJf_oooonATJX700000R@T000392AEB4QE92AE00f]ZX2 TI6Z00=]KEE8B5E8B5D00dQ8E@0A92@0B4QETI5EKFfZKFeEf][of]ZZf][o ][JZ][Ko][JZTI6ZKFeEB4QE][JZf]ZZoooo00;Jf_l02M[JZ][Jom[JZ[Jf ZY6AZTQ8EB@T000002@TE@0292@00P00000392@092AEB4QE00=8B5D01Fe] EI6AZ[JfZ][JZ][Jo`0Noooo00OJf_oooooooooooooJf_oJfZ[Jf_l00[Jf ZP06KFfZB4QE92@092@0B4QETI6Z0[JfZP04f][o][JZKFeEf][o0_ooo`0A f][ooooof]ZZ][JZf][o][JZB4QEKFeEf]ZZf][of]ZZf][of]ZZKFfZ92@0 000092AE00D000003B@TEB@T04Q8EB@T04Q8EB@T02@TEB@T02@TEDQ802@T EB@T02@TE@0292@000f]Z[Jf_oJf_l07?ooo`0=f][ooooooooof][of]ZZf][o f]ZZTI6ZB4QE92@092AE92@0KFeE00:f]ZX01=[Jom[JZ][Jom[JZP:f]ZX0 2M[Jom[JZ][JZ[JfZTQ8EB@T0000EB@T02@TE@02B4QE0Y6AZP08KFeEB4QE B4P092AEB4P0B4QE92AE92@00P00000492AE000092@092AE0TQ8E@07B4P0 B4QEB4QE92@092AE92@092AE008T90000b@TEB@T02@TE@02B4QE00f]ZX2TI6Z00=]KEDT95D000000R@T 000492AEB4QEKFeE][JZ0i6AZP0792AEB4QEB4QEB4QEB4P092AE00000092AE92@092AE92@092AE92@0B4QE92AE B4P092AEB4QE92@092AE92@00Oooo`0000D0000T9000000T900005D00P00 000692@00000000092@0000092@01P00000692@00000001E92@0000092@0 1000000592@0000092@0000092AE008T90000b@TEDQ804Q8E@02KFeE0dQ8 E@0<92@0B4QETI6Z][JZf][of]ZZf][ooooof][of]ZZf][of]ZZ0kJfZP0> 92AEB4P0TI6ZTI6Zf][o][JZTI6Z][JZf][ooooof]ZZoooof]ZZ][JZ0Ve] E@08B4QE92AEKFeETI6Z92AE92@092AE92@00P00000392@0000000000098 B5D01Ve]EFe]Z[JfZ][JokJfZ][JZP>f]ZX022@TEDQ8EFe]EI6AZTQ8EI6A Z[JfZ][JZQWoool01m[Jooooooooooooom[Jooooom[Jo`02f]ZZ00>f]ZXT 95D000000R@T0004B4QE][JZ][JZf]ZZ0][Jo`03oooof]ZZ][JZ00:ATJX0 0dQ8EFe]EDQ8E@0292@000L0000T95E8B5FATEFATJ[JfZ[Jf_l00][JZP0= KFeEB4QEB4QEKFfZB4QEB4P0001E92@092AE92@092AEB4P092AE0098B5D0 6b@T02@TEB@T000002@TEB@T04Q8EB@T02@TEB@T02@TEDQ8EDQ802@TEB@T 02@TEB@T000002@TEB@T02@TEB@T02@TEB@T02@TEDQ802@TE@0292@00@00 007oool0008000001B@TE@0002@T000002@T0002000000DT900005DT9000 000005D04000000:92@0001E92@092@092AE92@092AE92@092AE92@00TQ8 E@07B4P092AEB4QEB4QEKFeETI6Zf]ZZ00;Jf_l02m[JZ][Jom[Jom[JZ][J okJfZY6AZY6AEB@TEDQ8EI6AZP02f]ZZ00Bf]ZZATJ[JfZ[oool2f][o00?o oooJf_nATJX00TQ8E@8T900032@TEDQ8EB@T000002@TEB@T00000000EB@T 000002@TEFe]E@Ff]ZX00m[JZY6AZY6AZP02TI6Z00M8B00T900T95E]KEE8 B5FATJZf]ZX00][Jo`Koool00m[Jooooooooo`0Aoooo00oJf_oooooJfZ[J f_oJfZZf]ZY]KJY]KED0000T95DT900T95Ff]Z[Jf_oJfZX00][Jo`04f]ZZ f][of][oTI6Z0[JfZP03KFeEKFfZ92@0008000000`00EB@T02@TE@02KFeE 012f]Z[Jf_oJfZ[Jf_nf]ZY]KEE8B5E]KEE8B5DT95DT900T95D0000T900T 95DT9002B4QE00LT900T95DT9000000T900T95DT90000R@TE@09B4P092AE 92AEB4P092AE92@092AE92@092AE00f]ZZATJY]KED00Y6AZP0ATEE8B5E8B5D00TQ8E@09][JZf][of]ZZoooof][ooooof]ZZ oooof][o00;oool00m[Jom[JZVe]ZP0292@000T005D0000T9000000T9000 000T9000000T95D00Ve]E@06TI6Z][JZ][JZTI6ZB4QEKFeE14Q8E@0992@0 B4QEB4P092@0000092@0TI6Zf]ZZoooo00?Jf_l01=[JZ[JfZ][Jom[JZP;J f_l01][JZ][Jooooom[JZ_ooom[Jo`Soool02=[Jooooom[Jooooom[JZ_oo om[Jom[JZPBf]ZX2f][o00OJfZZf]ZZf]Z[Jf_oJfZ[ooooJf_l00oooo`0: f][of]ZZ][JZTI6ZB4QE92AETI5ETI6ZTI5EKFeE0dQ8E@0:B4P0B4QEKFeE ][JZf][o][JZKFeEB4QE92@000000TQ8E@07B4P00000000092AE000092@0 92AE008T90000b@TEB@T02@TE@0292@00R@TE@0>B4P0B4QEB4QEB4QE92@0 92AE92@092AE92@092AE92@092AEB4P092AE0R@T000592AE000092AE92@0 92AE008T9001oooo0004000000@T95D00000000T9003000000f]ZX04][Jom[JZ[JfZ[JfZVe]ZTQ8EFe]EDQ8EI6AZ[JfZ][J Z][Jooooom[JZ][Jom[JZ][Jom[JZP;Jf_l01][JZ[JfZVe]ZR@T000002@T 00@000002R@T0000EB@T02@TEI6AEI6AZ][JZ][Joi6AZVe]E@=8B5D03b@T 02@TEB@T04Q8EFe]ZY6AZTQ8EB@T04Q8EI6AZ_ooom[Jom[JZ][Jom[JZP02 ][JZ00JATJZf]Z[JfZZf]Z[Jf_oJfZX4f][o00GJfZ[ooooooooooooJf_l0 0_ooo`04f][ooonZf][of]ZZ0m[Jo`0=][JZTI6ZTI5ETI6Z][JZf][of]ZZ f][of]ZZf][o][JZf]ZZf][o00?oool00m[JooooZ_ooo`03][JZ00>ATJX0 001]KED00Y6AZPI8B5D02Ve]EKJfZ][Jom[JZVe]ZR@T02@TE@0002@T02@T E@<0000292@000@T95DT900T900T95D292@001`T95DT900T95DT95E8B018 B5DT95E8B5E8B00T95E8B5DT900T95DT900T95DT9018B5DT95E8B00T95DT 9000000T900T95DT900T95DT90000001oooo0005000000PT9000000005DT 9000000T9000000T9003000000f]ZZf][of]ZZf]ZZ][JZKFeEB4QE92@092AEKFeE][JZf]ZZ][Ko f]ZZ0][Jo`05oooof][o][JZ][JZf][o00Coool02=[Joi6AEI6AZ[JfZ][J Z][JokJfZY6AE@98B5D00dQ804Q8EDQ8E@02B4QE00E]KEFATJ[JfZ[Jf_nA TED00Ve]E@0692AE92@092AE000092@092AE0R@T000792AE92@0000092@0 92AE92@092AE008T900012@TEB@T02@T02@TE@98B5D02TQ804Q8EB@T02@T EB@T02@TEB@T02@TEB@T02@TE@A TEE]KJY8B5D01@00000992AE92@092AE92@092AE92@092AE92@092AE008T 90001B@TE@0002@T02@TEDQ80003B4QE00HT95E8B5DT900T95DT900T95D2 92@000XT95D0000T95D0000T95D0000T900005DT900T95D1oooo00050000 00PT90000000000T9000000005D0000T9002000000ATJX024Q8EB@T04Q8EDQ8EKJfZ][Jom[JZ[Jfo`;JfZX00fe] ZTQ8EB@TE@03B4QE00=]KEE8B5E8B5D014Q8E@0392@092AE92@000=8B5D0 0fe]EI6AZY6AZP07][JZ00RATJY]KEFATJY]KJZATJZf]Z[Jf_oJfZX2][JZ 00?Jf_oJfZ[Jf_l00_ooo`;JfZX00m[Jooooooooo`03oooo00_JfZZf]ZZf ]Z[Jf_oJfZZATJY]KEE8B5E]KEE8B5E8B0000dQ8E@=]KED3B4QE00LT9000 000T900T9000000T95E8B0000R@TE@06B4P092AE92@092@092AEB4P00R@T E@8000002b@T02@TEDQ8EB@TEDQ8EDQ804Q8EDQ802@TEB@T02@TE@0292@0 00H005DT900T900T9000000T9002000000A TJX2][JZ00FATJY]KEE8B5E8B5E]KED01;JfZP0?f]ZZf][of][of]ZZf][o f]ZZf][oTI6Z92@092AEB4QE92AE92@0000092@000D000002B@TEDQ8EI6A Z][Jooooom[JZ[Jfom[JZ[JfZP02TI6Z00RATEE]KEE8B5E8B5FATJ[JfZ[J f_oJfZX2][JZ00?Jf_nf]ZZATED00TQ8E@ATJZf]ZZATJX00kJfZP03f][of]ZZf][o00:f]ZX01=[JZ_oooooo ooooo`?Jf_l01oooom[Jooooooooom[JZ_oookJfZP02TI6Z00GJfZ[Jf_nf ]ZZATJY]KED014Q8E@05TI5EKFeEB4QEB4QEKFeE00=8B5D00b@T000002@T E@02000000XT900T95DT9018B5DT900T95DT900T95DT900T95D292@000L0 000T900T95DT900T95E8B00T95D00TQ8E@8T95D01dQ802@TEB@T0000EB@T 000002@TE@02000000HT95D0000T9000000T900005D1oooo0003000000LT 90000000000T900T95D0000T90000P00000492AE0000000000000R@T0080 00001B@T000002@T000002@T0003000000lT900000000000000T900005DT 9000000T95E8B5DT900T95DT900T95E8B5D00Ve]E@0:KFfZTI5EKFfZKFeE KFfZKFeEB4QEB4P0B4QEKFfZ0[JfZP0:TI6Z][JZ][JZ][JZf]ZZf][o][JZ f]ZZ][Kof]ZZ1;JfZP:ATJX036e]EB@TEDQ802@TEB@T000002@T04Q8EI6A EM[Jom[JZ[Jfo`>f]ZX2TI6Z00A]KEE8B5E8B5FATED3][JZ0i6AZP04f]ZZ ][Ko][JZKFeE0TQ8E@07KFeEB4QEB4QEKFeETI5EB4QE92AE00=8B5D01DQ8 02@TEB@T02@TEB@T0003B4QE00LT900T95DT900T95FATJZATEFATJX00[Jf ZP04f]ZZf][of]ZZf][o0kJfZP03f][ooooooooo00;oool01KJfZ][Jom[J Z_ooom[Jo`02oooo00?Jf_nATJZATED00[JfZP06f][of]ZZTI6ZTI5EKFfZ KFeE0TQ8E@:ATJX01fe]EDQ8EFe]EB@TEB@T04Q8EB@TE@04000000dT95DT 9018B5DT900T95DT900T95DT900T95DT900T95DT900T95D00R@T000992AE B4P092AEB4P092AEB4P092AEB4P092AE00ATJX01;JfZY6AZ[Jf ZY6AZPBf]ZX01M[JZ][Jom[JZ][Jom[JZP02f][o00CJfZY]KJY]KEE]KED2 B4QE00D00018B5FATJ[Jf_oJfZX01;JfZP06TI6ZTI5EB4QEB4QEKFeETI6Z 0kJfZP:ATJX016e]EM[JZ][JokJfZPFATJX01[JfZY6AZY6AZTQ8EB@T02@T E@8T900012@TEDQ8EB@T02@T0098B5D00fe]EFe]ZVe]E@02B4QE00U8B01] KEFATJZf]ZZATJ[JfZ[Jf_oJfZZf]_l00[JfZP07f]ZZf][of][ooonZoooo f][of]ZZ00:f]ZX01[Jfom[JZ_ooooooom[JooooZP:ATJX2][JZ00CJf_oJ fZ[Jf_nf]ZX2TI6Z00=8B5E]KEFATJX00[JfZP06TI6ZKFeEB4QE92@092AE B4P00`00008T90002B@TEB@T02@TEB@T02@TEB@T02@TEB@T02@TE@0392@0 0R@TE@0B92@092AE92@092AEB4P092AEB4QE92@092AE92@092AE000092@0 001E000092@0000092@00P00000392@000000000007oool0000;000092@0 000092@0001E92@092AE000092@0001E92@00080000012@T0000E@0002@T 00D000000b@TE@0000000002000000f]ZX0 196AZVe]EDQ8EFe]E@=8B5D01R@TEFe]EKJfZ][Jom[JZ_ooo`;Jf_l00kJf Z][JZ[JfZP02TI6Z00>ATEFATJZATJX00TQ8E@0492AEKFeE][Kof]ZZ1;Jf ZP0;TI6ZKFeEB4QEKFeETI6Z][JZf][of]ZZ][KoTI6Z][JZ00:ATJX05KJf Z][JZ][Jom[Jom[JZ][Jofe]EDQ8EDQ804Q8EB@T02@TEDQ802@TEB@T02@T EDQ8EFe]EDQ8EB@T04Q8E@02TI6Z00CJfZ[Jf_oJfZZf]_l2][JZ0][JZP04 f][ooonZf][of][o0_ooo`06f][ooooooooof][o][JZTI6Z0Ve]E@:f]ZX0 0m[Jom[JZ][Jo`02oooo00Vf]ZZATJ[JfZZf]Z[Jf_oJfZ[Jf_nf]ZZATED0 0TQ8E@03KFeETI6ZTI6Z00:ATJX4B4QE0R@T0005000092AE92@092@092AE 008T9000100002@TEB@T02@TE@8T90003R@TEDQ802@TEDQ8EB@T02@TEB@T 04Q8EB@T02@TEB@T02@TEB@T02@TE@8T90002B@TE@0002@T000002@T0000 02@T000002@T000300000Oooo`0000H0000T900005DT900005DT90050000 00ATEFA TJZf]ZX01;JfZP0f]ZX2TI6Z1kJfZP?Jf_l01?ooom[Jom[Jom[Jo`;JfZX02M[Joooo Z][JoooookJfZVe]EDQ8EFe]EI6AZP02][JZ00CJf_oJfZ[Jf_oJf_l2TI6Z 00Bf]ZZATJ[JfZ[oool2TI6Z0TQ8E@07B4P0B4QETI6ZTI6ZTI5EKFfZTI5E 00E8B5D00b@T000002@T000292AE00DT900005DT9000000T95D00R@T000> 001E92@092AE92AEB4P092AE92@0B4QE92@092AE92@092AE92@092AE0R@T 000992AE000092@0001E92@0001E92@0000092AE0080000192AE0@00007o ool0008000002B@T0000000002@T02@TE@0002@T000002@T0002000000<0 05DT900000000`00000692@00000000092@00000001E1@00000892@00000 0000000092@0001E92@0B4QE0fe]E@:ATJX016e]EDQ8EDQ8EDQ80098B5D2 TI6Z00Bf]Z[Jf_oJfZ[Jf_l2][JZ00=]KEFATJY]KED00TQ8E@0392@0B4QE TI6Z00:f]ZX0196AZVe]EDQ8EFe]E@A8B5D02B@T096AEI6AZTQ8EB@T02@T EDQ806e]ZY6AE@04TI6Z00A]KEE]KJY8B5FATED2][JZ00CJfZZf]ZZf]ZZf ]ZX2TI6Z00Ff]Z[Jf_oooooooooJf_l00[JfZP03TI6ZKFeETI6Z0098B5D0 1Fe]EI6AZ[JfZ][JZ][Jo`04oooo00?Jf_oJfZ[Jf_l00Y6AZP>f]ZX00m[J om[JZ_ooo`02oooo00?JfZZf]ZZf]ZX01=[Jo`05f]ZZKFeEKFeEKFfZKFeE 00:ATJX01kJfZ][JZ][Jom[JZ][Jofe]EI6AZP02][JZ0][Jo`0?TI5EB4QE KFeEB4QE92AE92@0B4QEKFeETI6ZKFeEB4QE92@092AE92@000000098B5D0 0b@T02@TEB@TE@0492@000ATEDT95DT90000TQ8E@0592@0B4QE B4QEKFeEB4QE00:ATJX01DQ8000002@TEB@T04Q8E@03TI6Z0kJfZP06TI5E B4QEKFfZ][JZf]ZZf][o0kJfZP:ATJX01I6AEI6AZ][JZ_ooom[JZP02][JZ 0Y6AZP9]KED2TI6Z00^f]Z[JfZ[Jf_oJfZ[Jf_oJfZ[ooooJf_oJfZ[Jf_oJ fZX00kJfZP07f][of]ZZf]ZZf][ooooof][of]ZZ00:f]ZX01M[Jooooom[J Z_oookJfZP02B4QE00BATJ[JfZZATJZATJX2][JZ00Jf]_oJfZZf]ZZf]ZY8 B5E]KED2][JZ0][Jo`0f]ZZATJZATJX00TQ8E@03 TI6Z][JZ][JZ00:f]ZX0296AZ][JokJfZ][JZ[Jfom[JZ[Jfoi6AZP9]KED0 0dQ8EB@TEDQ8E@02B4QE0[JfZP0>f][ooooof][of]ZZf][oTI6ZTI5E][JZ f]ZZf][ooonZf][ooooof][o0][JZP08][JZf][of]ZZKFeEB4QEKFeETI6Z ][JZ196AZP>f]ZX01M[JokJfZ][Jooooom[Jo`02oooo00?Jf_oooj[oool0 0_ooo`;Jf_l01oooom[Jom[Jom[JZ][Jom[JZ][Jo`02TI6Z00FATEE]KEFA TJZf]Z[Jf_l00kJfZP0f]ZX01KJfom[JZ][JokJfZ][Jo`03][JZ00Y]KEE8 B5E8B5FATJZf]Z[JfZ[Jf_oJfZ[Jf_oJfZX2f][o00KJfZZf]_nf]ZZATJY] KEE8B5D392@0010T95E8B5E8B00T95E8B5Ff]Z[JfZZf]ZZATJY]KEE]KJZA TJ[ooooJfZ[ooooJf_l3oooo00OJf_oJfZZATJZATJY]KEE8B5E]KED014Q8 E@04KFeETI5EKFfZTI6Z0][JZP;Jf_l2oooo0][Jo`04oooof][ooonZf][o 1;JfZP03f]ZZ][JZ][JZ00:f]ZX01][JokJfZ[JfZ][JZ][Jom[JZP;Jf_l0 1;JfZVe]EDQ8EFe]E@98B5D01B@TEDQ8EKJfZ[JfZ][JZP02TI6Z00RATEFA TJZATEE]KEE]KJY]KEE8B5D00003B4QE0P00000?92@0000092@092@00000 92@0001E92@0000092@0001E000092@0000092@0008000000b@TE@0002@T E@0292@000T0000T95D00000000T95D0000T900T95DT90001`00000392@0 001E000000<00001oooo000400000R@T000792AE000092AE000092@00000 92@000H000001R@T0000000000000000EB@T00H000000b@T000002@T0002 000000<005DT900000001000000792@0000092AE000092@092AEB4QE00:A TJX2][JZ00KJfZ[Jf_oJfZ[Jf_oJfZZf]_l2][JZ00U]KJY8B018B5E8B5Ff ]Z[Jf_oJfZ[Jf_oJfZX00][Jo`07f]ZZ][JZ][JZTI6ZTI5EKFeEKFfZ0098 B5D012@T04Q8EB@TEDQ8E@8T90004Fe]Z[JfZ[JfZY6AEDQ8EFe]EI6AZ[Jf Z][Jooooom[JooooZ][JokJfZ[Jfom[JZY6AZP04][JZ00FATJY8B5DT9000 000T95D00TQ8E@05KFeE][JZf][ooooof]ZZ00;Jf_l00m[JZ][Jom[JZP02 f][o1;JfZP07TI6Z][JZ][JZ][JZf][o][JZf]ZZ00;Jf_l03M[JZ][Jom[J Z_ooom[JZ][JokJfZY6AZVe]EB@T02@TEB@T04Q8E@03TI6Z00>ATEE]KJZA TED00Y6AZP05KFeETI6ZKFeEKFeE00000098B5D024Q8000002@T0000EB@T 0000E@0002@TE@8T9000100002@TE@0002@T00<000000b@T0000EB@T0003 92@000HT95DT900T95D0000T9000000292@000f]ZX00kJfokJfZY6A ZP05][JZ00GJfZ[Jf_oJf_oJfZ[oool01M[Jo`0@f]ZZTI6ZKFeE92AE0000 92@0B4QETI5ETI6ZTI5ETI6ZKFeETI6ZKFfZTI6ZTI5E0Ve]E@98B5D00fe] EDQ8EB@TE@02000000f]ZX00m[J Z[JfokJfZP02][JZ00FATJY8B5E8B00T95E8B5D00Y6AZP;JfZX2f][o013J fZ[Jf_oJfZZf]ZZATJZf]ZZATJY]KEE8B5E8B00T95DT9018B5E]KJY]KEE] KJX2TI6Z00>ATEFATJZATJX00[JfZP;Jf_l01M[JZ][Jom[JZ][JZY6AZP04 ][JZ0Y6AZP:f]ZX0496AZVe]EDQ8EB@TEB@T02@TEFe]EKJfZ][Jooooom[J ooooom[JZ][Jom[JZ[Jfo`Ff]ZX3TI6Z0kJfZP04f][of]ZZf][ooooo0[Jf ZP03f]ZZf][of]ZZ00:ATJX00fe]EB@T02@T0002B4QE1Y6AZP0f][ooooof][of]ZZf][of]ZZ][JZf]ZZ TI6ZKFeEB4QE92@0001E00000TQ8E@05KFeETI6ZTI5EKFeETI6Z009]KED0 0i6AZ[JfZ][Jo`02f]ZZ0][Jo`03TI6ZKFeEB4QE00:ATJX2][JZ0Y6AZP04 ][JZTI6Z][JZTI5E0dQ8E@0492@0KFeETI6Z][JZ0oooo`;Jf_l00m[JZ[Jf ZY6AZP04][JZ0Y6AZP>f]ZX00m[JokJfZ][JZP02f][o00OooooJfZ[ooooJ f_nf]ZZATJY]KED00TQ8E@0592AEB4QEKFeETI6ZTI5E00>f]ZX0196AZ[Jf ZY6AZ[JfZP:ATJX014Q8EI6AEDQ8EB@TE@<0000022@T000002@T02@TEB@T 02@TEB@T02@TE@8T9000100002@T000002@T00@000003B@TE@0000000000 02@T000002@TEB@T0000EB@T02@TE@0002@TE@08000000<005DT90000000 0P00007oool000<000002R@T0000000002@T0000E@0002@T000002@T0000 008T90003@0002@T000000000000E@0002@T0000EB@T000002@TE@0002@T 0002000000@T9000000005DT9002000000f]ZZATJZATJX00Ve]E@=8B5D0296A Z[JfZ][Jom[Jom[JZ][JokJfZ][JZPJf]ZX2TI6Z0[JfZP06f][of]ZZf][o f][o][JZf]ZZ0m[Jo`0:f]ZZ][JZTI6ZKFeEB4QEB4P0B4QEKFeEKFfZKFeE 0Y6AZP03][JZf]ZZ][JZ00:ATJX01m[JZY6AZY6AZTQ8EFe]EDQ8EDQ80004 000000/T900T95DT900T95DT900T95DT900T95D0000T900T95D00P000009 92@000000000000092@0000092@0000092AE008000001B@T000002@T0000 02@T0009000000f]ZX00i6AZVe]EDQ8E@03B4QE00>ATEE]KJY8B5D00dQ8 E@04B4P0KFeETI6Z][JZ0][Jo`08f]ZZf][oTI6ZKFeEB4QE0000B4QETI6Z 0Ve]E@0?TI6ZTI5ETI6ZTI6ZTI5EKFfZTI5EKFeEB4QEKFeETI6Z][JZf][o f]ZZf][o00Bf]ZX2TI6Z0kJfZP03TI6Z][JZ][JZ00:f]ZX01][JokJfZ][J Z[JfZ[Jfom[JZPFf]ZX00fe]ZTQ8EDQ8E@02KFeE00fATJZATEFATJZATJZf ]Z[JfZ[Jf_nf]ZZATEFATJY8B5DT900T95D00TQ8E@0392AE0000000000<0 000012@T02@TEB@T02@TE@8T90003P0002@TE@0002@T000002@TEB@T0000 EB@T000002@T00000000EB@T0080000022@T000002@TE@0002@T0000E@00 02@T00P000001000E@0000000000007oool000@0000022@TE@00000002@T 00000000EB@T0000008T90003`0002@T000002@TE@0002@T000002@T0000 EB@T0000EB@T02@TE@0002@T0002000000LT90000000000T9000000005DT 90002P00000392@092AE92@000E8B5D00i6AZ[JfZ[JfZP03][JZ0i6AZP98 B5D01b@T0000000002@T096AZ[JfZ][JZP02f][o00CJfZZf]_oJfZZf]ZX2 TI6Z00I]KEE8B5E8B5E]KEFATJY]KED3B4QE00PT900T95E8B5E]KEFf]Z[J f_oJfZ[Jf_l2][JZ0Ve]E@04B4QEKFeEKFeEKFeE0i6AZP06TI5EKFfZTI5E TI6ZKFeEKFfZ0Ve]E@05KFfZTI5Ef]ZZ][JZ][Ko00>f]ZX2TI6Z00Y]KEFA TJZATJZATJZATEFATJZf]ZZATJ[JfZ[Jf_l2f]ZZ00?Jf_oJfZ[Jf_l00[Jf ZP=8B5D016e]EDQ8EDQ8EFe]E@>ATJX01i6AEI6AZY6AZY6AZ][JZ[JfZY6A ZP02B4QE00@T90000000000T9005000000`T95DT900T95DT900T95DT9000 05DT9000000T9000000T95D292@000<0000T900T95D00P00000892@00000 000092@0001E92@0000092@01@00000392@00000000000@0000012@T0000 00000000007oool00004000092@0000092@00P00000;92AE000092@00000 92@0000092AE000092AE000092AE008T90003P00EB@T0000000002@T0000 02@T000002@T000002@T0000E@0002@T00<000000b@T0000000000080000 00@T900T95DT900T95D4B4QE00E]KEFATJ[JfZZf]Z[Jf_l00[JfZP:ATJX0 0i6AEDQ8EDQ8E@03B4QE00>ATJY]KEFATJX01;JfZP03f]ZZf][of]ZZ00:f ]ZX3TI6Z00NATEFATJY]KEE]KEE8B5E]KEDT95D00R@T000f]ZX02Y6AZTQ8EB@T06e]EI6AZVe] EB@TEDQ8EB@T02@TE@A8B5D00fe]EI6AZY6AZP02TI6Z00fATEFATJZATJZf ]ZY]KJY8B5E8B000000T9000000T9000000T90000`00000492AE92@00000 92AE1000000A92@0000092AE92@092AE92@0001E92@0000092AE000092@0 000092AE92@0001E92@000h000000b@T000000000001oooo000;000000f]ZX3TI6Z00A]KEE]KJY]KEFf]ZX2f][o0[JfZP04f][o f]ZZf][ooooo0][Jo`?JfZX00kJfZY6AZVe]E@02B4QE00XT95DT900T95E8 B00T95DT901]KEFf]Z[Jf_oJfZX3][JZ00bATJZf]Z[Jf_oJfZ[Jf_oooj[J f_oJfZ[Jf_oJfZ[Jf_nf]ZX2TI6Z0[JfZP:ATJX3][JZ01>ATJY]KEE]KEE] KEFATJ[JfZ[Jf_oJfZ[Jf_oJfZZf]_nf]ZZATJZATEFATJY]KED005DT900T 95D00TQ8E@03B4P0KFeEB4QE00A8B5D02DQ804Q8EDQ8EI6AEFe]ZY6AEI6A ZVe]EFe]ZP02KFeE0TQ8E@0392@0001E00000080000042@TE@0002@T0000 02@T000002@TEB@T00000000EB@T000002@TE@0002@T0000008T90050000 00LT95D0000T9000000T9000000T90000P00000392AE0000000000/00001 oooo0009000000@T90000000000T9002000000`T90000000000T9000000T 95D0000T900005DT9000000T9009000000ATJX0196AEFe]ZVe]EFe]ZP:A TJX01m[JZ_ooooooooooom[JZ][JokJfZP02TI6Z00U]KEDT900T900T9000 05DT900T95E]KEFATJX00fe]E@E8B5D02Fe]EI6AZ[JfZVe]EI6AEFe]EI6A ZVe]EB@TE@0392@000L0000T90000000000T9000000005D00R@T00030000 92@0000000@000000b@T0000EB@T0002000000DT9000000T9000000T9000 0P00000592AE92@092@0001E92@000l00001oooo000;000000f]ZX0296AZY6A EI6AZY6AZVe]EI6AZVe]EFe]ZP=]KED064Q8EDQ8000002@T04Q8EI6AEM[J om[JZY6AZVe]E@0002@T02@TEDQ8EB@T0000EB@T04Q8EFe]EB@TEB@T02@T EB@T02@TE@8T900012@TEB@T000002@T00D000000b@T0000EB@T00050000 00DT95D0000T9000000005D00`00000392AE000092@0008000001000EB@T 000002@T00`00001oooo0005000000f]ZX01=[Jom[JZ][Jom[JZPBf]ZX0396AZY6AEKJfZ[Jfom[JZ][J om[JZ][Jom[JZ][Jom[JZ[JfZP:ATJX00i6AEFe]ZY6AZP03][JZ00fATJY] KEE8B5Ff]Z[Jf_oooooJf_oooooJf_oJfZZf]ZZATJY]KED00R@T00:ATJX3 ][JZ00OJfZ[Jf_oJfZ[Jf_oJfZ[Jf_nf]ZX00Ve]E@09B4QE92@0B4QEB4QE KFeE][JZTI6Zf]ZZf][o00:f]ZX01Y6AZTQ8EDQ8EFe]EFe]ZVe]E@A8B5D0 4fe]EDQ8EDQ8EDQ8EFe]EKJfZ][Jom[JZ[JfZY6AZR@TEB@T02@TEDQ8EB@T 02@TEB@T02@TEB@T0003000000ATJX2][JZ00gJfZ[Jf_oJf_oJfZ[Jf_oJfZZf]_nf]ZZATEE]KJZATEFA TJZf]ZX00][Jo`06f]ZZoooof]ZZf][of]ZZ][JZ0i6AZPFf]ZX2KFeE00^f ]Z[Jf_oooj[Jf_oooooJfZ[Jf_oJfZY8B5D0000T95D014Q8E@0=KFeETI6Z ][JZ][JZf][of]ZZ][Ko][JZTI5EB4QE92AE92@092AE0098B5D01Fe]EDQ8 EI6AZTQ8EI6AE@02KFeE0dQ8E@9]KED01TQ8EB@T04Q8EDQ8EFe]EFe]ZP98 B5D00fe]EI6AZ][JZP02f][o00?JfZY]KJXT90000P00000392AE000092@0 00<000003b@T000002@TE@0002@T0000EB@T000002@T000002@T000002@T E@0002@T0006000000HT9000000T9000000T900T95D4000000f]ZX0296AZ[Jf Z[JfZ[JfZY6AZ[JfZ][JokJfZP;Jf_l01?ooom[Jom[JZ][Jo`:f]ZX01i6A Z[JfZ[JfZ][JZ[JfokJfZ][JZP03f][o00GJfZ[Jf_oJfZZf]ZZATJX00dQ8 E@0692@00000000092AE92@092AE0R@T000392AE92@092AE008T90006b@T EDQ804Q8EFe]ZY6AEI6AZVe]EDQ8EB@TEFe]EI6AZ[JfZY6AEDQ8EB@TEB@T 04Q8EI6AZ][Jom[JZ[JfZVe]E@0002@T02@TEB@T02@TE@02B4QE00LT9018 B5E8B5E]KJY8B5DT900T95D00P00000@92@0001E000092@0000092@00000 92@092AE92@0000092@0000092@0000092@01@00000892@0000092@0001E 000092@0000092AE1`00000792@0000092AE000092@0001E92@000800000 2P00E@000000000002@T000002@T000002@TE@00007oool0008000000b@T 000002@TE@02000000HT95D0000T900005D0000T9002000000DT9000000T 95D0000T90000P00000392@000000000008000000b@T0000000000020000 00`T9000000T900T900005DT9000000T9000000T9000000T9002000000@T 95D0000T9000000292@000D0000T900005DT900T95D01DQ8E@0492@092AE B4QEKFeE1KJfZP07f]ZZ][Ko][JZ][JZTI6Z][JZTI6Z00Nf]ZX00m[JZ][J om[JZP03][JZ00^ATJZf]ZZf]ZZf]Z[Jf_nf]Z[JfZ[Jf_oJfZ[Jf_oJfZX0 0][Jo`:f]ZX0296AZVe]EFe]EB@TEB@T000002@T02@TE@ATEFATJZATJX00Y6AZP07TI5ETI6Z f]ZZ][JZTI6ZB4QE92@00098B5D02;JfZ][JokJfZY6AZTQ8E@0002@T0000 E@8T90001b@TEB@T02@T04Q8EI6AEFe]EDQ8E@030000018T900000000000 000005DT900T95DT900T95DT9000000T95D0000T900005DT9000000T95D3 000000f]ZZATJZf]ZX00kJfZP07f][of]ZZf][of]ZZf][of]ZZf][o 00:f]ZX03Y6AZVe]EI6AZTQ8EB@T02@TEB@T000002@TEB@T02@TEB@T0000 02@T00=8B5D01R@TEDQ804Q8EFe]EFe]ZY6AZP>f]ZX2f][o00Nf]ZZATJY8 B5E8B5DT9018B5FATJX00Ve]E@09][JZTI6ZTI6Z000092@0000092@092AE 92@000800002B4QE00E]KEE8B5DT900T900T95D00P00000592@000000000 92@00000008T90001@00EB@T000002@T0000000292@000@0000T9000000T 95D2000000PT9000000T900T9000000T95D0000T95D2000000PT90000000 05DT9000000T9000000T9008000000@T90000000000T900300000B@T007o ool00080000012@TE@00000002@T008000000b@T000002@TE@05000000@0 05D0000T900005D7000000/T90000000000T9000000005DT9000000T9000 000T90000P00000892AE000092@0001E92@0000092@0001E0R@T00080000 92@00000001E000092@092AE92@00dQ8E@04KFeEKFfZKFeEKFfZ0Ve]E@07 B4QEKFeEB4QEB4QETI5E][JZTI6Z008T95D01dQ8EFe]EFe]EI6AZ[JfZY6A Z[JfZP02TI6Z00>ATEFATJZATED00[JfZP:ATJX4][JZ00KJf_oJfZ[Jf_oJ f_nf]Z[Jf_l3][JZ00>ATJZATEFATJX00Ve]E@08B4QEB4P092AE92@092AE 92@092AE92@00TQ8E@03KFeEB4QEB4QE0098B5D016e]EI6AZY6AEFe]ZPE] KED02DQ8EB@TEDQ802@TEDQ8EB@TEDQ802@TEDQ8E@02KFeE0`00000692AE 000092@0001E000092@00R@TE@0392@0000092AE00@000003R@T00000000 02@TEB@T02@TEB@T000002@T0000EB@T02@TE@0002@TE@@0000012@TE@00 02@T0000E@<000001R@T000002@T02@T000002@T0080000012@TEB@T02@T 02@TE@@000000b@T000000000006000000ATJX00kJfZY6A ZTQ8E@02B4QE0R@T000792AE000092@092AEB4QEKFeEB4QE00=]KED01Ve] ZY6AEI6AZY6AZY6AEFe]ZP=8B5D00b@T04Q8EDQ80002B4QE0R@T000592AE B4QE92@092AE92@000@000001B@T000002@T02@T02@TE@0292@01P000003 92AE000092AE008T900082@TEB@T02@TE@0002@T000002@T000002@T0000 02@T000002@T000002@T000002@T000002@T000002@T00000000EB@T0000 EB@T0000EB@T000002@T0000EB@T00H000000`00EB@T0000000600000@00 E@4T9001oooo00001`0002@TE@0002@T0000E@0002@T0002000000ATJY]KEFATJX0 1;JfZP03][Kof]ZZ][Ko00>f]ZX0396AZVe]EDQ8EDQ8EB@T02@TEB@T0000 02@T02@TEDQ804Q8E@=]KED00i6AZY6AEI6AZP02TI6Z00NATEFATJY8B5E8 B000000T95DT90000R@TE@0:B4P0B4QEB4QEB4QE92AEB4P092AE0000B4QE 92@00`00000792AE00000000000092@0001E92@00080000012@T000002@T 0000008T9000100002@TEB@T0000008T90002000EB@T000002@T0000EB@T 00000000E@<000001000E@0002@T0000E@<0000022@T000002@T000002@T 000002@T0000E@8T9004000000LT9000000T9000000T900005DT90000`00 00ATJY]KEE]KED00Y6AZPBf]ZX01=[Jom[JZ][JokJfZP:A TJX01I6AEI6AZVe]EDQ8EB@TE@0200000092@00000001E92@0000092@0000092@0001E92@092AE92@0001E 92@00P00000492@00000000092@00P00000792AE92@092AE92@0000092@0 0000008T900192AE0B@T007oool000030000001E92@000<000001b@T0000 000002@T02@TE@0002@T0002000000f]ZZA TJZATJX00fe]E@04TI6ZTI5ETI6ZTI6Z1kJfZP:ATJX00fe]EDQ8EB@TE@02 92@00P00000692@00000001E000092AE92@00dQ8E@07KFeEB4QEB4QEB4QE 92@0B4QE92@00098B5D2KFeE00=]KJY]KEE]KED00Ve]E@03B4QEKFeEB4QE 0098B5D00b@T02@TEB@T0002000000DT900000000000000T900010000003 92AE00000000008T90001P00EB@T02@T02@T02@TEB@T00<000001R@T0000 02@TEB@T000002@T008000008R@TE@00000002@T000002@T0000EB@T0000 02@T000002@T000002@T000002@TEB@T000002@TEB@T0000EB@T000002@T 000002@T02@TEB@T000002@TEB@T02@TEB@T02@TE@7oool000ATJX2][JZ0Y6AZP04TI5ETI6ZKFeEKFfZ 0Ve]E@98B5D292@000H005D00000000T95D0000T9002000000@T900T95DT 9000000292@00R@TE@0592@092AE000092@092AE00=8B5D02fe]EI6AZY6A ZY6AEFe]ZVe]EDQ8EFe]EDQ8EB@T02@TE@02000000PT900000000000000T 900005D0000T9002000000hT9000000T900T95DT900005DT9000000T900T 95D0000T95D0000T9003000000DT900005DT900005DT90000`00000392@0 000092AE008T900012@TE@00000002@TE@8000005B@TE@0002@T0000EB@T 000002@T000002@T0000EB@T000002@TE@0002@TE@0002@T000002@T0000 EB@T0001oooo00001DQ8EB@T02@TEB@T0000E@0200000R@T0008000092AE 000092@0000092@0001E92@01@00000492@0000092AE92@00P00000592@0 000092@0000092@000<000001b@T000002@T000002@T000002@T00020000 00@T9000000T95DT9002000000@T95D0000T95DT9003000000DT95DT900T 900T900000000R@T0008000092@0000092@0000092AE000092@00R@TE@8T 90000b@TEB@T02@TE@03B4QE00DT9000000T95DT900T95D00R@T00070000 KFeEKFfZTI5EKFfZTI5ETI6Z00:f]ZX2TI6Z00=]KEE8B5E8B5D00TQ8E@05 92@0B4QE92AE92@092AE008T9000100002@T000002@T008000001R@T02@T EB@T02@T02@TE@00008T95D292@000H0000T900005DT900T95E8B002B4QE 00>ATEFATJZATJX00Ve]E@=8B5D292@000<0000T95D000000`00000392@0 000092@000<0000012@TE@0002@T000000 000092AE92@092AE92@092AE000092AE92@092AE92@0B4QE92@092AE0R@T 008000001R@TE@0002@T000002@T0000E@"], "Graphics", ImageSize->{155, 178.438}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, Background->RGBColor[0.924025, 0.891524, 0.771649]], Cell[TextData[{ "Can the meaning of derivatives with integral order ", Cell[BoxData[ \(TraditionalForm\`\(\(d\^n\) \(y(x)\)\)\/\(d\ x\^n\)\)]], " be generalized to derivatives with non-integral order; so that in general \ ", Cell[BoxData[ \(TraditionalForm\`n\)]], " is a complex number?" }], "MathCaption", CellTags->"Leibnit's Question"], Cell["\<\ The story goes that L\.b4Hospital was somewhat curious about that question \ and replied with another question to Leibniz. \ \>", "Text"], Cell[TextData[{ "What if ", Cell[BoxData[ \(TraditionalForm\`n\ = \ 1\/2\)]], "?" }], "MathCaption"], Cell[TextData[{ " In a letter dated September 30, 1695 Leibniz replied: ", StyleBox["Il y a de l'apparence qu'on tirera un jour des consequences bien \ utiles de ces paradoxes, car il n'y a gueres de paradoxes sans \ utilit\[EAcute]. ", FontSlant->"Italic"], "The translation reads: ", StyleBox["It seems that useful consequences shall be drawn from these \ paradoxes one day, as there are no paradoxes that do not prove useful.", FontSlant->"Italic", FontColor->RGBColor[0, 0.250004, 0.500008]], StyleBox[" ", FontSlant->"Italic"] }], "Text"], Cell["\<\ The question raised by Leibniz how to generalize derivatives has been an \ ongoing topic for the past 300 years. Many mathematicians such as Liouville, \ Riemann, and Weyl made major contributions to the theory of fractional \ calculus. \ \>", "Text"], Cell[TextData[{ "To show you what Leibniz and L\.b4Hospital were discussing, we examine the \ set of power functions. In this case a fractional derivative is useful and \ can be expressed again by power functions. For example let us examine the ", StyleBox["n", FontSlant->"Italic"], "th derivative of ", Cell[BoxData[ \(TraditionalForm\`x\^m\)]], ". We know that the general expression for the ", StyleBox["n", FontSlant->"Italic"], "th derivative of ", Cell[BoxData[ \(TraditionalForm\`x\^m\)]], " is given by" }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(\(d\^n\) x\^m\)\/\(d\ x\^n\) = \ \(\(m!\)\/\(\((m - n)\)!\)\) \(\(x\^\(m - n\)\)\(.\)\)\)]]], "NumberedEquation"], Cell[TextData[{ "We also know that the factorial is connected with Euler's \ \[CapitalGamma]-function by ", Cell[BoxData[ FormBox[ StyleBox[\(n != \[CapitalGamma](n + 1)\), FontColor->RGBColor[0, 0, 1]], TraditionalForm]]], ". Replacing the factorials in (1.1.1) with \[CapitalGamma]-functions, we \ can write" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(d\^n\) x\^m\)\/\(d\ x\^n\) = \ \(\(\ \[CapitalGamma](m + 1)\)\/\(\[CapitalGamma](m - n + 1)\)\) x\^\(m - n\)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "This representation is equivalent to equation (1.1.1). However, equation \ (1.1.2) contains the potential of a generalization. We know that the \ \[CapitalGamma]-function is defined for continuous arguments over the complex \ domain of numbers. If we change the integer value of ", Cell[BoxData[ \(TraditionalForm\`n\)]], " to a number ", Cell[BoxData[ \(TraditionalForm\`q \[Element] \ \[DoubleStruckCapitalC]\)]], ", we are able to generalize an integer differentiation to a non-integer \ one. We are even able to define a complex differentiation. Replacing ", Cell[BoxData[ \(TraditionalForm\`n\)]], " by ", Cell[BoxData[ \(TraditionalForm\`q\)]], " in (1.1.2) results into the relation" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(d\^q\) x\^m\)\/\(d\ x\^q\) = \ \(\(\ \[CapitalGamma](m + 1)\)\/\(\[CapitalGamma](m - q + 1)\)\) x\^\(m - q\)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "From a mathematical point of view, equation (1.1.3) has a well defined \ meaning. However, this meaning is restricted to the special class of power \ functions ", Cell[BoxData[ \(TraditionalForm\`x\^m\)]], ". Of course, a fractional differentiation is unknown to ", StyleBox["Mathematica", FontSlant->"Italic"], ". Applying the standard differentiation to the power function we get the \ result" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_{x, 1/2}\ x\^2\)], "Input"], Cell[BoxData[ \(D::"dvar" \(\(:\)\(\ \)\) "Multiple derivative specifier \!\({x, 1\/2}\) does not have the form \ {variable, n} where n is a nonnegative machine integer."\)], "Message"], Cell[BoxData[ \(\[PartialD]\_{x, 1\/2}x\^2\)], "Output"] }, Open ]], Cell[TextData[{ "The message and the output shows that ", StyleBox["Mathematica", FontSlant->"Italic"], " is not capable to deal with fractional derivatives. The developers of ", StyleBox["Mathematica", FontSlant->"Italic"], " designed the system in such a way that the user can extend the \ definition of derivatives. The extension of the derivative D[] will be our \ next task. Telling ", StyleBox["Mathematica", FontSlant->"Italic"], " that a fractional derivative of powers is a useful mathematical operator \ allows us to define" }], "Text"], Cell[BoxData[ \(\(Unprotect[D];\)\)], "Input"], Cell[BoxData[ \(D[x_\^m_. , {x_, q_}] := \(Gamma[m + 1]\/Gamma[m - q + 1]\) x\^\(m - q\) /; Head[q] == Real\ || \ Head[q] == Rational || Head[q] == Complex\)], "Input"], Cell[BoxData[ \(\(Protect[D];\)\)], "Input"], Cell["\<\ The definition of the fractional derivative of powers is based on equation \ (1.1.3) and restricts the order of differentiations either to a rational, a \ real or a complex number. Even the negative derivative for a rational number \ can now be calculated by\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_{x, \(-\(1\/2\)\)}\ x\)], "Input"], Cell[BoxData[ \(\(4\ x\^\(3/2\)\)\/\(3\ \@\[Pi]\)\)], "Output"] }, Open ]], Cell[TextData[{ "If we set the order of differentiation ", Cell[BoxData[ \(TraditionalForm\`q\)]], " to a real number, we find" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_{x, 2.1}\ x\^2\)], "Input"], Cell[BoxData[ \(1.8715574418257452`\/x\^0.10000000000000009`\)], "Output"] }, Open ]], Cell["\<\ Even if we use complex numbers as differentiation order, we find a result\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_{x, 11.5 + I}\ x\^4\)], "Input"], Cell[BoxData[ \(\((\(\(57152.07443885453`\)\(\[InvisibleSpace]\)\) - 143371.10944062413`\ \[ImaginaryI])\)\ x\^\(\(-7.5`\) - \ \[ImaginaryI]\)\)], "Output"] }, Open ]], Cell[TextData[{ "These types of formulas for rational ", Cell[BoxData[ \(TraditionalForm\`q\)]], "'s were first discussed by ", ButtonBox["Lacroix ", ButtonData:>"Lacroix-1819", ButtonStyle->"Hyperlink"], "in 1819 [", ButtonBox["1", ButtonData:>"Lacroix-1819", ButtonStyle->"Hyperlink"], "]. In retrospect, formula (1.1.3) is the first analytical answer to \ Leibniz's question on fractional derivatives. " }], "Text"], Cell[TextData[{ "The story on fractional calculus was continued with contributions from \ Fourier, Abel, Liouville, Riemann and Weyl. For an historical survey the \ books by ", ButtonBox["Oldham and Spanier", ButtonData:>"Oldham-1974", ButtonStyle->"Hyperlink"], " [", ButtonBox["2", ButtonData:>"Oldham-1974", ButtonStyle->"Hyperlink"], "] or ", ButtonBox["Miller and Ross", ButtonData:>"Miller-1993", ButtonStyle->"Hyperlink"], " [", ButtonBox["3", ButtonData:>"Miller-1993", ButtonStyle->"Hyperlink"], "] give a broad overview. Mainly two calculi developed over the years known \ as Riemann-Liouville and Weyl calculus. Main contributions were made by ", ButtonBox["Riemann", ButtonData:>"Riemann-1892", ButtonStyle->"Hyperlink"], " [", ButtonBox["4", ButtonData:>"Riemann-1892", ButtonStyle->"Hyperlink"], "] and ", ButtonBox["Liouville", ButtonData:>"Liouville-1832a", ButtonStyle->"Hyperlink"], " [", ButtonBox["5", ButtonData:>"Liouville-1832a", ButtonStyle->"Hyperlink"], "] and by ", ButtonBox["Weyl", ButtonData:>"Weyl-1917", ButtonStyle->"Hyperlink"], " [", ButtonBox["6", ButtonData:>"Weyl-1917", ButtonStyle->"Hyperlink"], "]. Both calculi Riemann-Liouville (RL) and the Weyl (W) calculus are \ connected. In fact Weyl's calculus is a subset of the Riemann-Liouville \ calculus. In section two, we will define the RL calculus. There we will also \ outline the connection between the W and RL calculus. In section three the \ application of the two calculi to physical problems shows the usefulness of \ these methods. The two physical models we are going to discuss are anomalous \ relaxation and anomalous diffusion in disordered systems. Section four is \ devoted to a final discussion." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], " The Riemann Liouville and Weyl Calculus" }], "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"The Riemann Liouville and Weyl Calculus"], Cell["\<\ The main two fractional calculi are the Riemann Liouville (RL) and the Weyl \ (W) calculus. Both calculi are based on an integral with a power kernel. The \ following sections discuss the theoretical background of the calculi and \ present some examples on how different functions are treated by the RL or W \ calculus.\ \>", "Text"], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], ".", CounterBox["Subsection"], " ", "Riemann Liouville", " Calculus" }], "Subsection", CellTags->"Riemann and Liouville Calculus"], Cell["\<\ In the previous section, we introduced the fractional derivative based on the \ relation between factorials and the \[CapitalGamma]-function. In this \ section, we will define an operator to calculate fractional derivatives. This \ operator is based on works by Riemann and Liouville (RL). Paradoxically, the \ basis of this fractional differential operator is not a derivative but an \ integral. However, we can understand an integration as a differentiation with \ negative exponents. For example the negative first-order derivative is \ defined by \ \>", "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(d\^\(-1\)\/\(d\ x\^\(-1\)\)\) \(f( x)\)\ := \ \[Integral]\_0\%x\( f(t)\) \[DifferentialD]t\)]], "." }], "NumberedEquation", TextJustification->1], Cell["The negative second-order derivative is", "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(d\^\(-2\)\/\(d\ x\^\(-2\)\)\) \(f( x)\)\ := \ \[Integral]\_0\%x\(\[Integral]\_0\%t\( f( s)\) \[DifferentialD]s \[DifferentialD]t\)\)]], " \[Ellipsis]" }], "NumberedEquation", TextJustification->1], Cell[TextData[{ "The negative order of differentiation means nothing more than an \ integration. Higher orders of differentiations are calculated by nesting the \ integrals on the right hand side. We abbreviate this kind of recursion by the \ symbol ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(0, \ x\)\%\(-n\)\)]], " where ", Cell[BoxData[ \(TraditionalForm\`n\)]], " is a positive integer and denotes the number of nested integrals. \ Equation (1.2.1) is simplified with this notation to" }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(0, \ x\)\%\(-1\)\) \(f( x)\)\ = \ \ \[Integral]\_0\%x\( f(t)\) \[DifferentialD]t\)]], "." }], "NumberedEquation", TextJustification->1], Cell[TextData[{ "The symbol ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(0, \ x\)\%\(-n\)\)]], " contains the complete information for the calculation of the negative \ differential in a nut shell. The lower two indices denote the lower and upper \ boundary of the integral. The superscript represents the order of \ differentiation. A week generalization of the above notation is an arbitrary \ lower boundary ", Cell[BoxData[ \(TraditionalForm\`a\)]], " satisfying ", Cell[BoxData[ \(TraditionalForm\`a < x\)]], "; meaning" }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(a, \ x\)\%\(-1\)\) \(f( x)\)\ = \ \ \[Integral]\_a\%x\( f(t)\) \[DifferentialD]t\)]], "." }], "NumberedEquation", TextJustification->1], Cell[TextData[{ "If we consider the ", StyleBox["n", FontSlant->"Italic"], "th negative derivative ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%\(-n\)\)]], " of an arbitrary function ", Cell[BoxData[ \(TraditionalForm\`f(x)\)]], ", we write" }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(a, \ x\)\%\(-n\)\) \(f( x)\)\ = \ \[Integral]\_a\%x\(\[Integral]\_a\%\(x\_\(n - 1\)\)\(f( x\_0)\) \[DifferentialD]x\_\(n - 1\) \[Ellipsis] \ \[DifferentialD]x\_0\)\)]], "." }], "NumberedEquation", TextJustification->1], Cell["Remembering Cauchy's integral formula ", "Text", TextJustification->1, CellTags->"Cauchy's integral formula"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(d\^n\/\(d\ x\^n\)\) \(f( x)\) = \ \(\(n!\)\/\(2 \[Pi]\ i\)\) \(\[Integral]\_C\(\((\[Zeta] \ - z)\)\^\(\(-n\) - 1\)\) \(f(\[Zeta])\)\ \[DifferentialD]\[Zeta]\)\)]], "," }], "NumberedEquation", TextJustification->1], Cell["we can reduce relation (1.2.5) to", "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(a, \ x\)\%\(-n\)\) \(f( x)\)\ = \ \(1\/\(\((n - 1)\)!\)\) \(\[Integral]\_a\%x\(\((x - x\_0)\)\^\(n - 1\)\) \(f(x\_0)\) \[DifferentialD]x\_0\)\)]], "." }], "NumberedEquation", TextJustification->1], Cell["\<\ Using the well known relation between the \[CapitalGamma]-function and the \ factorial, we can generalize the result to an arbitrary order of fractional \ differentiation. Thus the general formula follows as\ \>", "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(a, \ x\)\%\(-q\)\) \(f( x)\)\ = \ \(1\/\(\[CapitalGamma]( q)\)\) \(\[Integral]\_a\%x\(\((x - x\_0)\)\^\(q - 1\)\) \(f( x\_0)\) \[DifferentialD]x\_0\ \ \ \ \ \ \ \ \ and\ \ \ \ \ \ \(Re(q)\)\) > 0\)]], "." }], "NumberedEquation", TextJustification->1, CellTags->"Riemann fractional integral"], Cell[TextData[{ "This kind of operator is denoted as the Riemann (R) version of the \ fractional integral by ", ButtonBox["Miller and Ross [1993]", ButtonData:>"Miller-1993", ButtonStyle->"Hyperlink"], ". The Liouville (L) version of this operator follows if we replace the \ lower boundary ", Cell[BoxData[ \(TraditionalForm\`a\)]], " of the integral by -\[Infinity]; i.e. ", Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalD]\_\(\(-\[Infinity]\), \ x\)\%\(-q\)\) \(f(x)\)\(\ \)\)\)]], " is called the Liouville fractional integral. A sufficient condition for \ this integral to converge is ", Cell[BoxData[ \(TraditionalForm\`f(\(-x\)) = o(x\^\(\(-q\) - \[Epsilon]\))\)]], " for ", Cell[BoxData[ \(TraditionalForm\`\[Epsilon] > 0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`x \[Rule] \[Infinity]\)]], ". The special case where ", Cell[BoxData[ \(TraditionalForm\`a = 0\)]] }], "Text", TextJustification->1, CellTags->"Liouville fractional integral"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(0, \ x\)\%\(-q\)\) \(f( x)\)\ = \ \(1\/\(\[CapitalGamma]( q)\)\) \(\[Integral]\_0\%x\(\((x - x\_0)\)\^\(q - 1\)\) \(f( x\_0)\) \[DifferentialD]x\_0\ \ \ \ \ \ \ \ \ \ \ \ \ \(Re( q)\)\) > 0\)]]], "NumberedEquation", CellFrame->True, TextJustification->1, Background->RGBColor[0.929702, 0.753918, 0.0664073], CellTags->"Riemann-Liouville fractional integral"], Cell[TextData[{ "is known as Riemann-Liouville (RL) fractional integral. A sufficient \ condition for the RL integral to converge is given by ", Cell[BoxData[ \(TraditionalForm\`f(1\/x) = O(x\^\(1 - \[Epsilon]\))\)]], " for ", Cell[BoxData[ \(TraditionalForm\`\[Epsilon] > 0\)]], ". Functions satisfying this relation are called functions of \ Riemann-Liouville type. For example, the functions ", Cell[BoxData[ \(TraditionalForm\`x\^\[Alpha]\)]], " with ", Cell[BoxData[ \(TraditionalForm\`\[Alpha] > \(-1\)\)]], " belongs to this class of functions. We recognize that the different \ definitions of Riemann-Liouville fractional integrals differ only in the \ lower boundary of the integral. " }], "Text", TextJustification->1], Cell[TextData[{ "So far we have introduced the notation of the fractional integral. A \ fractional derivative is connected with a fractional integral by introducing \ a positive order of differentiation in the operator ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%\(-q\)\)]], ". This shift in the order can be obtained by incorporating an ordinary \ differentiation followed by a fractional integration. We thus define a \ fractional differentiation of order ", Cell[BoxData[ \(TraditionalForm\`s\)]], " by" }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(a, \ x\)\%s\) \(f( x)\) := \ \((d\^n\/\(d\ x\^n\))\) \(\[ScriptCapitalD]\_\(a, \ x\)\%\(-\((n - s)\)\)\) \(f(x)\)\)]], " with ", Cell[BoxData[ \(TraditionalForm\`n\ \[Element] \[DoubleStruckCapitalN], \ s > 0, \ and\ \ n - s\ > 0\)]], "." }], "NumberedEquation", CellFrame->True, TextJustification->1, Background->RGBColor[0.929702, 0.753918, 0.0664073], CellTags->"eq-3.2.10"], Cell[TextData[{ "In this Riemann notation the fractional derivative depends on a lower \ boundary ", Cell[BoxData[ \(TraditionalForm\`a\)]], " of the integral. This dependence disappears if we restrict our discussion \ to the RL operator with ", Cell[BoxData[ \(TraditionalForm\`a = 0\)]], "." }], "Text", TextJustification->1], Cell[TextData[{ "Up to the present point, we have presented the essentials of the theory of \ RL integrals. If we intend to use computer algebra (CA) in connection with RL \ operators, we need to implement the RL operators in ", StyleBox["Mathematica", FontSlant->"Italic"], ". Thus the next step is to create a ", StyleBox["Mathematica", FontSlant->"Italic"], " function carrying out the calculation. We call this function \ RiemannLiouville[]. Since the RL integral is applied to functions depending \ on one independent variable, say ", Cell[BoxData[ \(TraditionalForm\`x\)]], ", we need to supply this information to the function. Another quantity \ which must be given by the user is the order of differentiation ", Cell[BoxData[ \(TraditionalForm\`q\)]], ". In addition to these two input variables, we need information on the \ lower boundary of the integration interval. Thus, in addition to the function \ to which we apply the RL integral our function RiemannLiouville[] needs three \ input quantities. The lower boundary is superfluous when treating an RL \ integral. The following definition of the Riemann-Liouville fractional \ integral incorporates the theoretical considerations discussed above " }], "Text"], Cell[BoxData[{ \(\(Remove[ RiemannLiouville];\)\n (*\(\(--\(-\ main\)\)\ \(function\ --\)\)\(-\)\ *) \), "\n", \(RiemannLiouville[f_, {x_, order_, a_: 0}] := Block[{n, int, y}, \n\t\tIf[NumericQ[order] && Simplify[order > 0], n = Floor[order]; \ q = \ order - n]; \n\t\tint\ = \ Integrate[\(\((x - y)\)\^\(\(-q\) - 1\)\) \((f /. x \[Rule] y)\), {y, a, x}, GenerateConditions \[Rule] False]; \n\t\tD[ int\ /\ Gamma[\(-q\)], {x, n}]\ /; \ FreeQ[int, y]\n\t\t]\)}], "Input"], Cell[TextData[{ "At this stage, we know how functions are treated by an RL integral. Before \ applying RiemannLiouville[] to a mathematical problem or use it in physical \ models, we introduce some general properties of the fractional derivative. \ These properties are important for manual as well as for CA calculations in \ ", StyleBox["Mathematica", FontSlant->"Italic"], ". They also serve to extend the properties of the RiemannLiouville[] \ function. All of these mathematical properties and more are implemented in \ the package ", StyleBox["FractionalCalculus", FontSlant->"Italic"], " to make the application of RiemannLiouville[] efficient and flexible." }], "Text", TextJustification->1], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], ".", CounterBox["Subsection"], ".", CounterBox["Subsubsection"], " Properties of Riemann-Liouville Operators" }], "Subsubsection", CellTags->"Properties of Riemann-Liouville Operators"], Cell["\<\ The main properties needed in an implementation of RL operators are linearity \ and the composition rule. These two properties are basic properties besides \ the Leibniz rule of differentiation and the chain rule. Let us discuss these \ properties in more detail. In the implementation of the mathematical \ properties linearity and the composition of derivatives are of importance. \ The other two relations are of minor practical importance.\ \>", "Text", TextJustification->1], Cell[TextData[{ "2", ".", CounterBox["Section"], ".", CounterBox["Subsection"], ".", CounterBox["Subsubsection"], " Linearity" }], "Rule", CellTags->"Linearity"], Cell["\<\ Linearity is one of the basic properties of an RL operator. This property \ guarantees that the superposition of a RL operator applied to different \ functions is the same as the application of the RL operator to the \ superposition of functions. Linearity of a RL operator means\ \>", "Text", TextJustification->1], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%s\ \((\[Alpha]\ \(f( x)\) + \ \[Beta]\ \(g( x)\))\)\ = \ \ \[Alpha]\ \(\[ScriptCapitalD]\_\(a, \ x\)\%s\) \(f( x)\) + \ \[Beta]\ \(\[ScriptCapitalD]\_\(a, \ x\)\%s\) \(g( x)\)\)]]], "NumberedEquation", TextJustification->1], Cell[TextData[{ "with ", Cell[BoxData[ \(TraditionalForm\`\[Alpha]\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\)]], " being real constants. Relation (1.2.11) is implemented in the ", StyleBox["FractionalCalculus", FontSlant->"Italic"], " package by two functions. The first definition removes common constants \ from the argument of the input function." }], "Text", TextJustification->1], Cell[BoxData[ \(\(RiemannLiouville[c_\ f_, {x_, order_, a_: 0}] := c\ RiemannLiouville[f, {x, order, a}]\ /; \ FreeQ[c, x];\)\)], "Input"], Cell["\<\ The second extension of RiemannLiouville[] represents a superposition of two \ functions. This property is implemented as\ \>", "Text"], Cell[BoxData[ \(RiemannLiouville[f_\ + \ g_, {x_, order_, a_: 0}] := RiemannLiouville[f, {x, order, a}]\ + \ RiemannLiouville[g, {x, order, a}]\)], "Input"], Cell[TextData[{ "Both ", StyleBox["Mathematica", FontSlant->"Italic"], " definitions combined are equivalent with relation (1.2.11). Linearity of \ the RL operator means that the operator ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%s\)]], " may be distributed through the terms of a finite sum; i.e." }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%s\ \(\[Sum]\_\(i = \ 0\)\%n\( f\_i\)( x)\)\ = \ \[Sum]\_\(i = 0\)\%n \[ScriptCapitalD]\_\(a, \ \ x\)\%s\ \(\(f\_i\)(x)\)\)]], "." }], "NumberedEquation"], Cell["\<\ Another important relation is the composition rule of fractional \ differentiation. \ \>", "Text", TextJustification->1], Cell[TextData[{ "2", ".", CounterBox["Section"], ".", CounterBox["Subsection"], ".", CounterBox["Subsubsection"], " Composition Rule" }], "Rule", CellTags->"Composition Rule"], Cell[TextData[{ "In case of RL integrals for ", Cell[BoxData[ \(TraditionalForm\`\[Mu], \ \(\(\[Nu]\)\(>\)\(0\)\(\ \)\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`f(x)\)]], " RL integrable the relation" }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Mu]\)\ \(\ \[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)\) \(f( x)\)\ = \ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\((\[Mu] + \[Nu])\)\)\) \(f(x)\)\)]]], "NumberedEquation",\ TextJustification->1], Cell["holds.", "Text"], Cell["\<\ The composition rule combining two fractional derivatives of different order \ is\ \>", "Text", TextJustification->1], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%s\ \ \(\[ScriptCapitalD]\_\(a, \ x\)\%p\) \(f( x)\)\ = \ \(\[ScriptCapitalD]\_\(a, \ x\)\%\(s + p\)\) \(f( x)\)\)]]], "NumberedEquation", TextJustification->1], Cell[TextData[{ "with ", Cell[BoxData[ \(TraditionalForm\`p < 0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`f(x)\)]], " finite at ", Cell[BoxData[ \(TraditionalForm\`x = a\)]], ". This property serves to extend the definition of RiemannLiouville[] to" }], "Text", TextJustification->1], Cell[BoxData[ \(RiemannLiouville[\ RiemannLiouville[f_, {x_, order1_, a_: 0}], {x_, order2_, a_: 0}] := RiemannLiouville[ f, {x, order1 + order2, a}]\ /; \(\(order1\)\(<\)\(0\)\(\t\)\)\)], "Input", TextJustification->1], Cell[TextData[{ "In case of ", Cell[BoxData[ \(TraditionalForm\`p > 0\)]], " the following relation holds" }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%s\ \ \(\[ScriptCapitalD]\_\(a, \ x\)\%p\) \(f( x)\)\ = \ \(\[ScriptCapitalD]\_\(a, \ x\)\%\(s + p\)\) \(f( x)\) - \(\[ScriptCapitalD]\_\(a, \ x\)\%\(s + p\)\)( f(x) - \[ScriptCapitalD]\_\(a, \ x\)\%\(-p\)\ \ \[ScriptCapitalD]\_\(a, \ x\)\%p\ \(f(x)\))\)]]], "NumberedEquation"], Cell["where the last term in (1.2.14) is ", "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%\(-p\)\ \ \[ScriptCapitalD]\_\(a, \ x\)\%p\ \(f(x)\) = f(x)\ - \[Sum]\_\(k = 1\)\%m\( c\_k\) x\^\(p - k\)\)]]], "NumberedEquation"], Cell[TextData[{ "with ", Cell[BoxData[ \(TraditionalForm\`0 < p \[LessEqual] m < p + 1\)]], ". The constants ", Cell[BoxData[ \(TraditionalForm\`c\_k\)]], " in (1.2.15) are constants of integration. In case of the RL integral ", Cell[BoxData[ \(TraditionalForm\`\((a = 0)\)\)]], " these constants are given by" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`c\_k = \ \(1\/\(\[CapitalGamma]( p - \[ScriptCapitalD]k + 1)\)\) \[ScriptCapitalD]\_\(0, \ x\)\%\(p - k\)\ \ \(f( x)\)\( | \_\(x = 0\)\)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "The difference of ", Cell[BoxData[ \(TraditionalForm\`p > 0\)]], " or ", Cell[BoxData[ \(TraditionalForm\`p < 0\)]], " can be demonstrated by the example" }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%1\ \ \(\[ScriptCapitalD]\_\(a, \ x\)\%\(-1\)\) \(f(x)\)\ = \ f(x)\)]]], "NumberedEquation"], Cell[TextData[{ "for ", Cell[BoxData[ \(TraditionalForm\`p < 0\)]], " and" }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, \ x\)\%\(-1\)\ \(\ \[ScriptCapitalD]\_\(a, \ x\)\%1\) \(f(x)\)\ = \ f(x) + c\)]]], "NumberedEquation"], Cell[TextData[{ "with ", Cell[BoxData[ \(TraditionalForm\`c\)]], " a constant. This example also demonstrates the general property that RL \ integrals do not commute." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["", "Subsubsection", CellDingbat->None], Cell[TextData[{ "The presented code in ", StyleBox["Mathematica", FontSlant->"Italic"], " shows that it is sufficient for an implementation to use the definition \ of the RL operator given in equation (1.2.9)-(1.2.12). The code given above \ is the basis of a more sophisticated implementation in the package ", StyleBox["FractionalCalculus", FontSlant->"Italic"], ". This package contains additional definitions concerning special \ properties of the RL operator. However, the mathematical formulas and the ", StyleBox["Mathematica", FontSlant->"Italic"], " code above show that the RL operator in mathematical and ", StyleBox["Mathematica", FontSlant->"Italic"], " notation are quite similar. To make this similarity into an identity, we \ designed a special ", StyleBox["Mathematica ", FontSlant->"Italic"], "symbol identical with the RL operator symbol. " }], "Text", TextJustification->1], Cell[TextData[{ "The package ", StyleBox["FractionalCalculus", FontSlant->"Italic"], " supports symbolic short hand notation. The symbol ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(\[Placeholder], \ \ \[Placeholder]\)\%\[Placeholder][\[Placeholder]]\)]], " is connected with the RiemannLiouville[] function. The template is \ designed in such a way that it is identical with the mathematical notation \ given above. However, this notation differs a little bit from the standard \ notation used in the literature. Since in ", StyleBox["Mathematica", FontSlant->"Italic"], " it is saver to handle the lower indices of the operator ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, x\)\%\(-q\)\)]], " on the right side of the symbol \[ScriptCapitalD], we changed the \ notation used by ", ButtonBox["Davis [1936]", ButtonData:>"Davis-1936", ButtonStyle->"Hyperlink"], ". The RiemannLiouville[] function and the template ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(a, x\)\%\(-q\)\)]], " allow us to carry out different calculations. The following examples show \ how the RiemannLiouville[] function is used and what kind of calculations are \ supported by this function." }], "Text", TextJustification->1] }, Open ]], Cell[CellGroupData[{ Cell["2.2.2 Examples", "Subsubsection", CellTags->"Examples of the Riemann-Liouville Operator"], Cell[TextData[{ "An example frequently discussed in the literature, ", ButtonBox["Oldham and Spanier [1974] ", ButtonData:>"Oldham-1974", ButtonStyle->"Hyperlink"], "and ", ButtonBox["Miller and Ross [1993]", ButtonData:>"Miller-1993", ButtonStyle->"Hyperlink"], ", is the differentiation of a constant. From our experience in calculus, \ we know that an ordinary integer differentiation of a constant vanishes. \ Applying the RL operator of order ", Cell[BoxData[ \(TraditionalForm\`q = 1/2\)]], " to a numeric constant, say ", Cell[BoxData[ \(TraditionalForm\`c = 1\)]], ", we get" }], "Text", TextJustification->1], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(1/2\)[1]\)], "Input"], Cell[BoxData[ \(1\/\(\@\[Pi]\ \@x\)\)], "Output"] }, Open ]], Cell["\<\ This result compared to our knowledge of ordinary calculus is surprising. \ Contrary to an ordinary differentiation the result of a fractional \ differentiation does not vanish. The same result follows from applying the \ RiemannLiouville[] function to a constant. The difference is that we do not \ need to specify the lower boundary. The RiemannLiouville[] function assumes \ by default that the lower boundary is zero. However, we can change this \ boundary value by providing a third input variable in the second argument of \ RiemannLiouville[]. Let us demonstrate this by first calling \ RiemannLiouville[] with two arguments at the second input position\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(RiemannLiouville[1, {x, 1/2}]\)], "Input"], Cell[BoxData[ \(1\/\(\@\[Pi]\ \@x\)\)], "Output"] }, Open ]], Cell["\<\ then, we calculate the same with a third argument in the second input \ position\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(RiemannLiouville[1, {x, 1/2, 0}]\)], "Input"], Cell[BoxData[ \(1\/\(\@\[Pi]\ \@x\)\)], "Output"] }, Open ]], Cell["\<\ The result is the same. However, we have the freedom to choose the lower \ boundary as demonstrated by the second call of RiemannLiouville[].\ \>", "Text"], Cell[TextData[{ "The results obtained may contradict our general understanding that the \ differentiation of a constant vanishes. Contrary to the ordinary calculus in \ fractional calculus it is not true that the differentiation of a constant \ vanishes. This behavior is obvious if we recall the definition of a \ fractional derivative by an integration in ", ButtonBox["(3.2.9)", ButtonData:>"Riemann-Liouville fractional integral", ButtonStyle->"Hyperlink"], ". This non-vanishing of an RL operator applied to a constant is even true \ if we allow a general order of differentiation. Before we can apply the RL \ operator to the constant, we have to tell the package ", StyleBox["FractionalCalculus ", FontSlant->"Italic"], "that we restrict the order of differentiation to positive values; meaning \ ", Cell[BoxData[ \(TraditionalForm\`\[Nu] > 0\)]], ". This assumption is introduced into the package ", StyleBox["FractionalCalculus", FontSlant->"Italic"], " by means of the function Assume[]. This function allows us to specify \ conditions under which the integrals are calculated.", StyleBox[" ", FontSlant->"Italic"], "For our example we set" }], "Text", TextJustification->1], Cell[CellGroupData[{ Cell[BoxData[ \(Assume[\[Nu] > 0]\)], "Input"], Cell[BoxData[ \({{{\[Nu] > 0}, {Im[\[Nu]] \[Rule] 0, Re[\[Nu]] \[Rule] \[Nu]}}}\)], "Output"] }, Open ]], Cell[TextData[{ "This assumption tells the RL operator that ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\)]], " is a positive real number. The calculation of the RL integral in the \ general form gives" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\[Nu][K\ ]\)], "Input"], Cell[BoxData[ FractionBox[\(K\ x\^\(-\[Nu]\)\), RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - \[Nu]\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`K\)]], " is a positive constant. The expression shows that for positive ", Cell[BoxData[ \(TraditionalForm\`\[Nu] < 1\)]], " the RL operator provides a non vanishing result containing Euler's \ \[CapitalGamma] function." }], "Text"], Cell[TextData[{ "The calculations above contain some messages in between the input and \ output. These printouts inform you about conditions under which the \ calculation was carried out. The output of this information is controlled by \ the option ", StyleBox["ShowConditions", FontSlant->"Italic"], " of RiemannLiouville[]. The total number of options of the RL function \ are" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Options[RiemannLiouville]\)], "Input"], Cell[BoxData[ \({ShowConditions \[Rule] True, UniqueSymbols \[Rule] False}\)], "Output"] }, Open ]], Cell["\<\ To suppress the information on solution conditions, we set the option \ ShowConditions to False.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(SetOptions[RiemannLiouville, ShowConditions \[Rule] False]\)], "Input"], Cell[BoxData[ \({ShowConditions \[Rule] False, UniqueSymbols \[Rule] False}\)], "Output"] }, Open ]], Cell[TextData[{ "Now RiemannLiouville[] does not display any information about the \ calculation. An example for a RL integration demonstrates this. The example \ uses a power function ", Cell[BoxData[ \(TraditionalForm\`x\^\[Mu]\)]], " to which we apply the RL operator. Let us assume that the fractional \ order of integration is any positive number greater than zero and let ", Cell[BoxData[ \(TraditionalForm\`\[Mu]\)]], " be a real number. The application of the RL operator to this function \ gives " }], "Text", TextJustification->1], Cell[BoxData[ \(\(Assume[\[Nu] > 0];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[x\^\[Mu]]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(x\^\(\[Mu] + \[Nu]\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 + \[Mu]\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 + \[Mu] + \[Nu]\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "The result is again a power function containing both parameters ", Cell[BoxData[ \(TraditionalForm\`\[Mu]\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\)]], " as exponents. The behavior of projecting a function into the same class \ of function is not typical for the RL operator. The application to other \ classes of functions like exponentials, sines and cosines demonstrates that \ we get higher transcendental functions. An example for this behavior is the \ function ", Cell[BoxData[ \(TraditionalForm\`\[ExponentialE]\^\(\[Alpha]\ x\)\)]], " with ", Cell[BoxData[ \(TraditionalForm\`\[Alpha] > 0\)]], ". The application of the RL integral delivers" }], "Text", CellTags->"hier gehts weiter"], Cell[BoxData[ \(\(Assume[\[Alpha] > 0];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[\[ExponentialE]\^\(\[Alpha]\ \ x\)]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(\[ExponentialE]\^\(x\ \[Alpha]\)\), " ", \(\[Alpha]\^\(-\[Nu]\)\), " ", RowBox[{"(", RowBox[{ RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "\[Nu]", "]"}], "-", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\[Nu], x\ \[Alpha]\), "]"}]}], ")"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "\[Nu]", "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "which represents the Mittag-Leffler function in ", StyleBox["Mathematica", FontSlant->"Italic"], " notation. The Mittag-Leffler function ", Cell[BoxData[ \(TraditionalForm\`\(E\_\(\[Nu], \[Alpha]\)\)(x)\)]], " is defined by" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(E\_\(\[Nu], \[Alpha]\)\)( x)\ = \ \(\[ExponentialE]\^\(\[Alpha]\ x\)\/\[Alpha]\^\[Nu]\) \((1 \ - \(\[Gamma](\[Nu], \[Alpha]\ x)\)\/\(\[CapitalGamma](\[Nu])\))\)\)]], "." }], "NumberedEquation"], Cell["\<\ Other examples demonstrating the same behavior are trigonometric functions \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[Sin[\[Omega]\ x]]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(x\^\(1 + \[Nu]\)\), " ", "\[Omega]", " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({1}\)}, {\({1 + \[Nu]\/2, 3\/2 + \[Nu]\/2}\)} }], " ", ";", " ", \(\(-\(1\/4\)\)\ x\^2\ \[Omega]\^2\)}], " ", "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(2 + \[Nu]\), "]"}]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[Cos[\[Omega]\ x]]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(x\^\[Nu]\), " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({1}\)}, {\({1\/2 + \[Nu]\/2, 1 + \[Nu]\/2}\)} }], " ", ";", " ", \(\(-\(1\/4\)\)\ x\^2\ \[Omega]\^2\)}], " ", "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 + \[Nu]\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "Both results are connected with hypergeometric functions ", Cell[BoxData[ \(TraditionalForm\`F\_\(p, q\)\)]], ". Next we consider some slightly more complicated functions." }], "Text"], Cell[TextData[{ "Even if we look at special functions like the Bessel functions, we can \ calculate the RL integral. The following example takes a Bessel ", Cell[BoxData[ \(TraditionalForm\`J\)]], " as argument in the RL integral." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[BesselJ[n, x]] // FunctionExpand\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(2\^\(-n\)\), " ", \(x\^\(n + \[Nu]\)\), " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({1\/2 + n\/2, 1 + n\/2}\)}, {\({1 + n, 1\/2 + n\/2 + \[Nu]\/2, 1 + n\/2 + \[Nu]\/2}\)} }], " ", ";", " ", \(-\(x\^2\/4\)\)}], " ", "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 + n + \[Nu]\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "The result of this calculation is a hypergeometric function of general ", Cell[BoxData[ \(TraditionalForm\`F\_\(p, q\)\)]], " type multiplied by a power. Combining a Bessel function with a power we \ find" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[\(x\^\[Mu]\) BesselJ[n, x]] // FunctionExpand\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{\(2\^\(-n\)\), " ", \(x\^\(n + \[Mu] + \[Nu]\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 + n + \[Mu]\), "]"}], " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({1\/2 + n\/2 + \[Mu]\/2, 1 + n\/2 + \[Mu]\/2}\)}, {\({1 + n, 1\/2 + n\/2 + \[Mu]\/2 + \[Nu]\/2, 1 + n\/2 + \[Mu]\/2 + \[Nu]\/2}\)} }], " ", ";", " ", \(-\(x\^2\/4\)\)}], " ", "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 + n\), "]"}], " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 + n + \[Mu] + \[Nu]\), "]"}]}], ")"}]}]], "Output"] }, Open ]], Cell[TextData[{ "Again we find a hypergeometric function ", Cell[BoxData[ \(TraditionalForm\`F\_\(q, p\)\)]], " multiplied by an extended power. " }], "Text"], Cell["\<\ So far we have demonstrated basic properties of Riemann-Liouville fractional \ integrals. In the following we will show how a fractional differentiation \ affects functions. As we know fractional differentiation is denoted in \ fractional calculus by a positive differentiation order. This kind of \ calculation is also carried out by the RiemannLiouville[] function. As an \ example let us discuss the fractional differentiation of a constant.\ \>", "Text", TextJustification->1], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(1/2\)[1]\)], "Input"], Cell[BoxData[ \(1\/\(\@\[Pi]\ \@x\)\)], "Output"] }, Open ]], Cell[TextData[{ "The result is a function depending on ", Cell[BoxData[ \(TraditionalForm\`x\^\(\(-1\)/2\)\)]], ". Compared with a fractional integration" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(\(-1\)/2\)[1]\)], "Input"], Cell[BoxData[ \(\(2\ \@x\)\/\@\[Pi]\)], "Output"] }, Open ]], Cell[TextData[{ "we observe that the change of sign in the order of the RL operator results \ into a change of sign in the power of ", Cell[BoxData[ \(TraditionalForm\`x\)]], "." }], "Text"], Cell["\<\ The fractional differentiation of an exponential gives\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\[Nu][\[ExponentialE]\^\(\[Alpha]\ \ x\)]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(\[Alpha]\^\[Nu]\), " ", RowBox[{"(", RowBox[{\(\((x\ \[Alpha])\)\^\(-\[Nu]\)\), "+", RowBox[{\(\[ExponentialE]\^\(x\ \[Alpha]\)\), " ", RowBox[{"(", RowBox[{ RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - \[Nu]\), "]"}], "-", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - \[Nu], x\ \[Alpha]\), "]"}]}], ")"}]}]}], ")"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - \[Nu]\), "]"}]]], "Output"] }, Open ]], Cell["\<\ while the fractional integration of the exponential results into\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[\[ExponentialE]\^\(\[Alpha]\ \ x\)]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(\[ExponentialE]\^\(x\ \[Alpha]\)\), " ", \(\[Alpha]\^\(-\[Nu]\)\), " ", RowBox[{"(", RowBox[{ RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "\[Nu]", "]"}], "-", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\[Nu], x\ \[Alpha]\), "]"}]}], ")"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "\[Nu]", "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "The two results share the difference of complete and incomplete \ \[CapitalGamma] functions but differ in the dependence of ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\)]], ". The general observation is that a fractional differentiation differs \ from a fractional integration. This difference can be of minor or of major \ order. An example demonstrating this is the logarithm. The fractional \ differentiation is" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\[Nu][Log[x]]\)], "Input"], Cell[BoxData[ RowBox[{"-", FractionBox[\(x\^\(-\[Nu]\)\ \((EulerGamma + \[Pi]\ Cot[\[Pi]\ \[Nu]] - Log[x] + PolyGamma[0, \[Nu]])\)\), RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - \[Nu]\), "]"}]]}]], "Output"] }, Open ]], Cell[TextData[{ "Comparing this with the ", ButtonBox["fractional integration of the logarithm", ButtonData:>"Log-integrated", ButtonStyle->"Hyperlink"], ", we observe only minor changes." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[Log[x]] // FunctionExpand\)], "Input"], Cell[BoxData[ RowBox[{"-", FractionBox[\(x\^\[Nu]\ \((1 + EulerGamma\ \[Nu] - \[Nu]\ Log[x] + \[Nu]\ PolyGamma[ 0, \[Nu]])\)\), RowBox[{\(\[Nu]\^2\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "\[Nu]", "]"}]}]]}]], "Output"] }, Open ]], Cell[" This is true with other functions like the sine.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\[Nu][Sin[\[Omega]\ x]]\)], "Input"], Cell[BoxData[ RowBox[{"-", RowBox[{ FractionBox["1", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(5 - \[Nu]\), "]"}]], RowBox[{"(", RowBox[{\(x\^\(1 - \[Nu]\)\), " ", "\[Omega]", " ", RowBox[{"(", RowBox[{ RowBox[{\((\(-4\) + \[Nu])\), " ", \((\(-3\) + \[Nu])\), " ", \((\(-2\) + \[Nu])\), " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({1}\)}, {\({3\/2 - \[Nu]\/2, 2 - \[Nu]\/2}\)} }], " ", ";", " ", \(\(-\(1\/4\)\)\ x\^2\ \[Omega]\^2\)}], " ", "]"}]}], "+", RowBox[{"2", " ", \(x\^2\), " ", \(\[Omega]\^2\), " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({2}\)}, {\({5\/2 - \[Nu]\/2, 3 - \[Nu]\/2}\)} }], " ", ";", " ", \(\(-\(1\/4\)\)\ x\^2\ \[Omega]\^2\)}], " ", "]"}]}]}], ")"}]}], ")"}]}]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(-\[Nu]\)[Sin[\[Omega]\ x]]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(x\^\(1 + \[Nu]\)\), " ", "\[Omega]", " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({1}\)}, {\({1 + \[Nu]\/2, 3\/2 + \[Nu]\/2}\)} }], " ", ";", " ", \(\(-\(1\/4\)\)\ x\^2\ \[Omega]\^2\)}], " ", "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(2 + \[Nu]\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "The results contain hypergeometric functions ", Cell[BoxData[ \(TraditionalForm\`F\_\(p, q\)\)]], ". The example demonstrates that the fractional differentiation of a \ special function will result into special functions. This behavior is also \ true for Whittaker's ", Cell[BoxData[ \(TraditionalForm\`M\)]], " function" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{\(\[ScriptCapitalD]\_\(0, \ x\)\%\[Nu]\), "[", RowBox[{ SubscriptBox[ StyleBox["M", FontSlant->"Italic"], \(0, 0\)], "[", "x", "]"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ FractionBox["1", RowBox[{"64", " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(9\/2 - \[Nu]\), "]"}]}]], RowBox[{"(", RowBox[{\(\@\[Pi]\), " ", \(x\^\(1\/2 - \[Nu]\)\), " ", RowBox[{"(", RowBox[{ RowBox[{\(-4\), " ", \((\(-7\) + 2\ \[Nu])\), " ", \((\(-5\) + 2\ \[Nu])\), " ", \((\(-3\) + 2\ \[Nu])\), " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({3\/4, 5\/4}\)}, {\({1, 5\/4 - \[Nu]\/2, 7\/4 - \[Nu]\/2}\)} }], " ", ";", " ", \(x\^2\/16\)}], " ", "]"}]}], "+", RowBox[{"15", " ", \(x\^2\), " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({7\/4, 9\/4}\)}, {\({2, 9\/4 - \[Nu]\/2, 11\/4 - \[Nu]\/2}\)} }], " ", ";", " ", \(x\^2\/16\)}], " ", "]"}]}]}], ")"}]}], ")"}]}]], "Output"] }, Open ]], Cell["\<\ The fractional differentiation of a hypergeometric function is\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{\(\[ScriptCapitalD]\_\(0, \ x\)\%\[Nu]\), "[", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(1, 1\)], "[", \(\[Alpha], \[Beta], x\), "]"}], "]"}], "//", "FunctionExpand"}]], "Input"], Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{\(x\^\(-\[Nu]\)\), " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({1, \[Alpha]}\)}, {\({\[Beta], 2 - \[Nu]}\)} }], " ", ";", " ", "x"}], " ", "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(2 - \[Nu]\), "]"}]], "-", FractionBox[ RowBox[{\(x\^\(-\[Nu]\)\), " ", "\[Nu]", " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({1, \[Alpha]}\)}, {\({\[Beta], 2 - \[Nu]}\)} }], " ", ";", " ", "x"}], " ", "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(2 - \[Nu]\), "]"}]], "+", FractionBox[ RowBox[{\(x\^\(1 - \[Nu]\)\), " ", "\[Alpha]", " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(p, q\)], "[", RowBox[{GridBox[{ {\({2, 1 + \[Alpha]}\)}, {\({1 + \[Beta], 3 - \[Nu]}\)} }], " ", ";", " ", "x"}], " ", "]"}]}], RowBox[{"\[Beta]", " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(3 - \[Nu]\), "]"}]}]]}]], "Output"] }, Open ]], Cell[TextData[{ "A semi fractional derivative of ", Cell[BoxData[ \(TraditionalForm\`1/\@x\)]], " is given by" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\(1/2\)[1\/\@x]\)], "Input"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell["\<\ Surprisingly this differentiation vanishes. The reason why this result occurs \ is obvious from the more general derivative\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\[Nu][1\/\@x]\)], "Input"], Cell[BoxData[ FractionBox[\(\@\[Pi]\ x\^\(\(-\(1\/2\)\) - \[Nu]\)\), RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1\/2 - \[Nu]\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "We see that if ", Cell[BoxData[ \(TraditionalForm\`\[Nu] = 1/2\)]], " the \[CapitalGamma] function approaches infinity and thus the overall \ behavior is reduced to zero. Another example demonstrating the calculation of \ a fractional derivative is given by the square root of ", Cell[BoxData[ \(TraditionalForm\`x\)]], " multiplied by an exponential" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalD]\_\(0, \ x\)\%\[Nu][\(\@x\) Exp[\(-\[Alpha]\)\ x]] // FunctionExpand\)], "Input"], Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{\(\@\[Pi]\), " ", \(x\^\(1\/2 - \[Nu]\)\), " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(1, 1\)], "[", \(3\/2, \((5\/2 - \[Nu])\), \((\(-x\)\ \[Alpha])\)\), "]"}]}], RowBox[{"2", " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(3\/2 - \[Nu]\), "]"}]}]], "-", FractionBox[ RowBox[{ "3", " ", \(\@\[Pi]\), " ", \(x\^\(3\/2 - \[Nu]\)\), " ", "\[Alpha]", " ", RowBox[{ SubscriptBox[ StyleBox["F", FontSlant->"Italic"], \(1, 1\)], "[", \(5\/2, \((7\/2 - \[Nu])\), \((\(-x\)\ \[Alpha])\)\), "]"}]}], RowBox[{"4", " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(7\/2 - \[Nu]\), "]"}]}]]}]], "Output"] }, Open ]], Cell[TextData[{ "The above examples serve to demonstrate that the RiemannLiouville[] \ function is designed in such a way that a large class of functions is \ accessible via integration and differentiation. Other properties like the \ behavior of the RL operator under Laplace and Mellin transforms are \ incorporated in the package ", StyleBox["FractionalCalculus", FontSlant->"Italic"], "." }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], ".", CounterBox["Subsection"], " Weyl's Calculus" }], "Subsection", CellTags->"Weyl Calculus"], Cell[TextData[{ "Another fractional operator was defined by Weyl. Weyl defined the \ fractional derivative in a similar way as the Riemann-Liouville operator. In \ 1917 ", ButtonBox["Weyl", ButtonData:>"Weyl-1917", ButtonStyle->"Hyperlink"], " defined two integral operators of order ", Cell[BoxData[ \(TraditionalForm\`q\)]], ". We use them as Weyl operators. The first definition is " }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&+\)\_\(t, \ \ \[Infinity]\)\%\(-q\)\) \(f( t)\)\ = \ \(1\/\(\[CapitalGamma]( q)\)\) \(\[Integral]\_t\%\[Infinity]\(\((\[Zeta] - t)\)\^\(q - 1\)\) \(f(\[Zeta])\) \[DifferentialD]\[Zeta]\)\)]], " with ", Cell[BoxData[ \(TraditionalForm\`Re(q) > 0, \ t > 0\)]], "." }], "NumberedEquation", TextJustification->1, CellTags->"Weyl-Plus operator"], Cell["The second definition reads", "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&-\)\_\(t, \ \ \(-\[Infinity]\)\)\%\(-q\)\) \(f( t)\)\ = \ \(1\/\(\[CapitalGamma]( q)\)\) \(\[Integral]\_\(-\[Infinity]\)\%t\(\((t - \ \[Zeta])\)\^\(q - 1\)\) \(f(\[Zeta])\) \[DifferentialD]\[Zeta]\)\)]], "\twith ", Cell[BoxData[ \(TraditionalForm\`Re(q) > 0, \ t > 0\)]], "." }], "NumberedEquation", CellTags->"Weyl-Minus operator"], Cell[TextData[{ "Weyl assumed in his definition that ", Cell[BoxData[ \(TraditionalForm\`f(t)\)]], " is a periodic function with mean zero over one period. Today the two \ definitions (1.2.21) and (1.2.21) are used without any condition on ", Cell[BoxData[ \(TraditionalForm\`f\)]], ". The only restriction is that ", Cell[BoxData[ \(TraditionalForm\`Re(q) > 0\)]], ". Both definitions ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalW]\&+\)\_\(t, \ \[Infinity]\)\%\(-q\ \)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalW]\&-\)\_\(t, \ \ \(-\[Infinity]\)\)\%\(-q\)\)]], " are related to the Riemann-Liouville operator. The first relation \ (1.2.21) is connected with the LR operator by" }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&+\)\_\(t, \ \ \[Infinity]\)\%\(-q\)\) \(f( t)\) = \ \(\((\(-1\))\)\^q\) \(\[ScriptCapitalD]\_\(\[Infinity], \ \ t\)\%\(-q\)\) \(f(t)\)\)]], "." }], "NumberedEquation", CellTags->"eq-4.2.3"], Cell["The second definition is related to the RL integral by", "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&-\)\_\(t, \ \ \(-\[Infinity]\)\)\%\(-q\)\) \(f( t)\)\ = \ \ \(\[ScriptCapitalD]\_\(\(-\[Infinity]\), \ t\)\%\(-q\)\) \(f(t)\)\)]], "." }], "NumberedEquation", TextJustification->1, CellTags->"eq-4.2.4"], Cell[TextData[{ "Relation ", ButtonBox["(1.2.24)", ButtonData:>"eq-4.2.4", ButtonStyle->"Hyperlink"], " shows that ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalW]\&-\)\_\(t, \ \(-\[Infinity]\)\)\%\(-q\)\)]], " is nothing more than the Liouville operator introduced in section ", ButtonBox["(2.1)", ButtonData:>{"RiemannLiouvilleCalculus.nb", "Liouville fractional integral"}, ButtonStyle->"Hyperlink"], ". Since we already defined the RL operator in ", StyleBox["Mathematica", FontSlant->"Italic"], ", we can use this definition to generate the Weyl operators. The \ difference between the Weyl definition and the Liouville definition is a \ change of the limits in the integral and the factor ", Cell[BoxData[ \(TraditionalForm\`\((\(-1\))\)\^\(-q\)\)]], ". Knowing this behavior we can define the Weyl operators just by" }], "Text", TextJustification->1], Cell[BoxData[ \(WeylPlus[f_, {t_, q_}] := RiemannLiouville[\(\((\(-1\))\)\^q\) f, {t, q, \[Infinity]}]\)], "Input",\ TextJustification->1], Cell["and", "Text"], Cell[BoxData[ \(WeylMinus[f_, {t_, q_}] := RiemannLiouville[f, {t, q, \(-\[Infinity]\)}]\)], "Input"], Cell["\<\ We realize that the second Weyl operator (1.2.22) is identical to the \ Liouville operator.\ \>", "Text"], Cell[TextData[{ "So far we have defined the Weyl operators as fractional integrals. A \ fractional derivative is connected with a fractional integral by a positive \ order of differentiation in the operators ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalW]\&-\)\_\(t, \ \ \(-\[Infinity]\)\)\%\(-q\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalW]\&+\)\_\(t, \ \[Infinity]\)\%\(-q\ \)\)]], ". The shift to positive orders, say ", Cell[BoxData[ \(TraditionalForm\`p > 0\)]], ", can be achieved by introducing an ordinary differentiation followed by a \ fractional integration. We thus define a fractional Weyl differentiation by" }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&-\)\_\(t, \ \ \(-\[Infinity]\)\)\%p\) \(f( t)\) := \ \(\((\(-1\))\)\^n\) \((d\^n\/dt\^n)\) \((\(\(\ \[ScriptCapitalW]\&-\)\_\(t, \ \(-\[Infinity]\)\)\%\(-q\)\) \(f(t)\))\)\)]], " with ", Cell[BoxData[ \(TraditionalForm\`\(\(\ \)\(\(s > 0\)\(,\)\)\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`q = n - p > 0\)]] }], "NumberedEquation", TextJustification->1], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`n\)]], " is the smallest integer greater than ", Cell[BoxData[ \(TraditionalForm\`p\)]], ". Now if p is a nonnegative integer, we assert that" }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&-\)\_\(t, \ \ \(-\[Infinity]\)\)\%p\) \(f( t)\) := \ \(\((\(-1\))\)\^n\) \((d\^n\/dt\^n)\) \(\(\ \[ScriptCapitalW]\&-\)\_\(t, \ \(-\[Infinity]\)\)\%\(-q\)\) \(f(t)\)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "For the second Weyl operator ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalW]\&+\)\_\(t, \ \[Infinity]\)\%\(-q\ \)\)]], ", we find the relation" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&+\)\_\(t, \ \ \[Infinity]\)\%p\) \(f( t)\)\ = \ \(\(\((\(-1\))\)\^n\) \((d\^n\/dt\^n)\) \((\(\(\ \[ScriptCapitalW]\&+\)\_\(t, \ \[Infinity]\)\%\(-q\)\) \(f( t)\))\)\(\ \)\)\)]], " with ", Cell[BoxData[ \(TraditionalForm\`\(\(\ \)\(q = n - p > 0\)\)\)]], "." }], "NumberedEquation"], Cell["\<\ In close analogy to the RL operator, the Weyl operators and their derivatives \ have some algebraic properties in addition to their definitions.\ \>", "Text"], Cell[CellGroupData[{ Cell[TextData[{ "2", ".", CounterBox["Section"], ".1 Properties of the Weyl Operator" }], "Subsubsection", CellTags->"Properties of the Weyl Operator"], Cell["\<\ The Weyl operators satisfy linearity, composition rule, Leibniz's rule, and \ the chain rule.\ \>", "Text"], Cell[TextData[{ "2", ".", CounterBox["Section"], ".1.", CounterBox["Subsubsection"], " Linearity" }], "Rule", CellTags->"Linearity"], Cell["\<\ Linearity is an essential property of the Weyl operators. In mathematical \ terms we write\ \>", "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&\[PlusMinus]\)\_t\%\(-q\)\)(\ \[Alpha]\ \(f(t)\) + \[Beta]\ \(g( t)\))\ = \ \[Alpha]\ \(\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\ \[PlusMinus]\)\_t\%\(-q\)\) \(f( t)\)\ + \ \[Beta]\ \(\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\ \[PlusMinus]\)\_t\%\(-q\)\) \(g(t)\)\)]]], "NumberedEquation"], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`\[Alpha]\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\)]], " are real constants. We combine both operators (1.2.21) and (1.2.22) with \ a common symbol denoted by ", Cell[BoxData[ \(TraditionalForm\`\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\ \%\(-q\)\)]], " and suppress the infinite boundary. The linearity consists of two \ operations: first the extraction of common factors independent of ", Cell[BoxData[ \(TraditionalForm\`t\)]], " and second the superposition of the single terms. In terms of ", StyleBox["Mathematica", FontSlant->"Italic"], " we define these two operations by" }], "Text"], Cell[BoxData[ \(\(WeylPlus[c_\ f_, {x_, order_}] := c\ WeylPlus[f, {x, order}]\ /; \ FreeQ[c, x];\)\)], "Input"], Cell["and", "Text"], Cell[BoxData[ \(WeylPlus[f_\ + \ g_, {x_, order_}] := WeylPlus[f, {x, order}]\ + \ WeylPlus[g, {x, order}]\)], "Input"], Cell["\<\ The same is necessary for the second operator in order to establish the \ property of linearity.\ \>", "Text"], Cell[BoxData[ \(\(WeylMinus[c_\ f_, {x_, order_}] := c\ WeylMinus[f, {x, order}]\ /; \ FreeQ[c, x];\)\)], "Input"], Cell["and", "Text"], Cell[BoxData[ \(WeylMinus[f_\ + \ g_, {x_, order_}] := WeylMinus[f, {x, order}]\ + \ WeylMinus[g, {x, order}]\)], "Input"], Cell[TextData[{ "Both rules for each function WeylePlus[] and WeylMinus[] combined in ", StyleBox["Mathematica", FontSlant->"Italic"], " are equivalent with relation (1.2.28). Linearity of the Weyl operators \ means that they may be distributed through the terms of a finite sum; i.e." }], "Text", TextJustification->1], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\(\[ScriptCapitalW]\)\(\ \)\)\&\[PlusMinus]\)\_t\ \%\(-q\)\ \(\[Sum]\_\(i = 0\)\%n\( f\_i\)( t)\)\ = \ \[Sum]\_\(i = 0\)\%n\(\(\(\ \ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\%\(-q\)\ \(\(f\_i\)(t)\)\)]], "." }], "NumberedEquation"], Cell["\<\ Another important relation is the composition rule of Weyl operators. \ \>", "Text", TextJustification->1], Cell[TextData[{ "2", ".", CounterBox["Section"], ".1.", CounterBox["Subsubsection"], " Composition Rule" }], "Rule", CellTags->"Composition Rule"], Cell["\<\ In this subsection let us assume that the exponent in a fractional Weyl \ operator is positive. The composition rule combining two Weyl operators of \ different order is given by\ \>", "Text", TextJustification->1], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\%\ \(-s\)\ \(\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\%\(-p\)\) \(f( t)\)\ = \ \(\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\%\ \(-\((s + p)\)\)\) \(f(t)\)\)]]], "NumberedEquation", TextJustification->1], Cell[TextData[{ "with ", Cell[BoxData[ \(TraditionalForm\`s > 0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`p > 0\)]], ". This relation defines a property simplifying the calculation of two \ nested Weyl operators. The following lines contain the definition of this \ property in ", StyleBox["Mathematica", FontSlant->"Italic"], " notation. " }], "Text", TextJustification->1], Cell[BoxData[ \(WeylPlus[\ WeylPlus[f_, {x_, order1_}], {x_, order2_}] := \(\(WeylPlus[ f, {x, order1 + order2, a}]\)\(\ \)\(/;\)\((order1 < 0 && order2 < 0)\)\(\t\)\)\)], "Input", TextJustification->1], Cell["The same definition holds for the second Weyl operator", "Text"], Cell[BoxData[ \(WeylMinus[\ WeylMinus[f_, {x_, order1_}], {x_, order2_}] := \(\(WeylMinus[ f, {x, order1 + order2, a}]\)\(\ \)\(/;\)\((order1 < 0 && order2 < 0)\)\(\t\)\)\)], "Input", TextJustification->1], Cell["If we choose one of the orders equal to zero, we get", "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\ \%\(-0\)\ \(\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\%\(-p\)\) \ \(f(t)\)\ = \ \(\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\%\(-p\)\ \) \(f(t)\)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "Now ", Cell[BoxData[ \(TraditionalForm\`\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\ \%\(-p\)\)]], " is a well defined operator, but no meaning has yet been assigned to ", Cell[BoxData[ \(TraditionalForm\`\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\ \%0\)]], ". We shall define ", Cell[BoxData[ \(TraditionalForm\`\(\(\(\ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\ \%0\)]], " as the identity operator by" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\(\(\ \ \)\(\[ScriptCapitalW]\)\)\&\[PlusMinus]\)\_t\%0\) \(f(t)\)\ = \ \ f(t)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "In terms of ", StyleBox["Mathematica", FontSlant->"Italic"], " we have the relation" }], "Text"], Cell[BoxData[ \(\(\(\ \)\(\(WeylPlus[f_, {x_, 0}]\)\(:=\)\(f\)\(\ \)\)\)\)], "Input"], Cell["and", "Text"], Cell[BoxData[ \(\(\(\ \)\(\(WeylMinus[f_, {x_, 0}]\)\(:=\)\(f\)\(\ \)\)\)\)], "Input"], Cell["\<\ With this definitions the essential properties of the Weyl operators are \ defined.\ \>", "Text"], Cell[TextData[{ "In close analogy to the Riemann-Liouville derivative, we can formulate the \ law of exponents for Weyl fractional derivatives. Suppose that ", Cell[BoxData[ \(TraditionalForm\`p > 0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`s > 0\)]], " are positive numbers. Then the following relation holds" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&\[PlusMinus]\)\_t\%s\)(\(\(\ \[ScriptCapitalW]\&\[PlusMinus]\)\_t\%p\) \(f( t)\))\ = \ \(\(\[ScriptCapitalW]\&\[PlusMinus]\)\_t\%\(s + p\)\) \(f(t)\)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "Relation (1.2.33) is simpler than the corresponding rule for the \ Riemann-Liouville derivative. Equation (1.2.33) has its ", StyleBox["Mathematica", FontSlant->"Italic"], " equivalent in" }], "Text"], Cell[BoxData[ \(WeylPlus[\ WeylPlus[f_, {x_, order1_}], {x_, order2_}] := \(\(WeylPlus[ f, {x, order1 + order2, a}]\)\(\ \)\(/;\)\((order1 > 0 && order2 > 0)\)\(\t\)\)\)], "Input", TextJustification->1], Cell[TextData[{ "and the corresponding relation for ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalW]\&-\)\_t\%s\)]] }], "Text"], Cell[BoxData[ \(WeylMinus[\ WeylMinus[f_, {x_, order1_}], {x_, order2_}] := WeylMinus[ f, {x, order1 + order2, a}]\ /; \((order1 > 0 && order2 > 0)\)\)], "Input"], Cell[TextData[{ "Combining relation (4.2.9) and (4.2.12), we can write for any ", Cell[BoxData[ \(TraditionalForm\`p\)]] }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(\[ScriptCapitalW]\&\[PlusMinus]\)\_t\%\(-p\)\)(\(\ \(\[ScriptCapitalW]\&\[PlusMinus]\)\_t\%p\) \(f(t)\)) = \ \(f( t)\ = \ \(\(\[ScriptCapitalW]\&\[PlusMinus]\)\_t\%p\)(\(\(\ \[ScriptCapitalW]\&\[PlusMinus]\)\_t\%\(-p\)\) \(f(t)\))\)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "This identity is valid for any ", Cell[BoxData[ \(TraditionalForm\`p\)]], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "2", ".", CounterBox["Section"], ".3 Examples" }], "Subsubsection", CellTags->"Examples"], Cell[TextData[{ "In this section we present some examples of Weyl's fractional integrals. \ The first example deals with the ", StyleBox["q", FontSlant->"Italic"], "th differentiation of an exponential. Before we carry out the calculation \ we turn off the messages of the WeylMinus[] and WeylPlus[] functions." }], "Text", TextJustification->1], Cell[CellGroupData[{ Cell[BoxData[{ \(SetOptions[WeylMinus, ShowConditions \[Rule] False]\), "\n", \(\(SetOptions[WeylPlus, ShowConditions \[Rule] False];\)\)}], "Input"], Cell[BoxData[ \({ShowConditions \[Rule] False, UniqueSymbols \[Rule] False}\)], "Output"] }, Open ]], Cell[TextData[{ "The first example demonstrates the application of WeylMinus[] to ", Cell[BoxData[ \(TraditionalForm\`\[ExponentialE]\^\(\(-\[Alpha]\)\ t\)\)]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Assume[q > 0]\)], "Input"], Cell[BoxData[ \({{{q > 0}, {Im[q] \[Rule] 0, Re[q] \[Rule] q}}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&-\)\_t\%q[\[ExponentialE]\^\(\(-\[Alpha]\)\ \ t\)]\)], "Input"], Cell[BoxData[ \(\[ExponentialE]\^\(\(-t\)\ \[Alpha]\)\ \((\(-\[Alpha]\))\)\^q\)], \ "Output"] }, Open ]], Cell[TextData[{ "The result is an exponential containing the differentiation order ", Cell[BoxData[ \(TraditionalForm\`q\)]], " in a factor. The application of WeylPlus[] to the same function gives us" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&+\)\_t\%q[\[ExponentialE]\^\(\(-\[Alpha]\)\ t\)] // Simplify\)], "Input"], Cell[BoxData[ \(\[ExponentialE]\^\(\(-t\)\ \[Alpha]\)\ \[Alpha]\^q\)], "Output"] }, Open ]], Cell[TextData[{ "Both results differ from each other by the factor ", Cell[BoxData[ \(TraditionalForm\`\((\(-1\))\)\^q\)]], ". The second example deals with a general polynomial of ", StyleBox["p", FontSlant->"Italic"], "th order. " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&-\)\_t\%q[\((t + a)\)\^p] // FunctionExpand\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(\((\(-\(1\/a\)\))\)\^q\), " ", \(a\^p\), " ", \(\((\(-\(1\/t\)\))\)\^\(-q\)\), " ", \(\((\(-t\))\)\^\(-q\)\), " ", \(\((\(a + t\)\/a)\)\^\(p - q\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\(-p\) + q\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(-p\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "The second Weyl operator ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalW]\&+\)\_\[Placeholder]\%\ \[Placeholder][\[Placeholder]]\)]], " applied to this polynomial results to" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&+\)\_t\%q[\((t + a)\)\^p] // Simplify\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(\((1\/a)\)\^q\), " ", \(a\^p\), " ", \(\((\(a + t\)\/a)\)\^\(p - q\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\(-p\) + q\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(-p\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "Changing the sign of the order ", Cell[BoxData[ \(TraditionalForm\`q\)]], " for each of the functions used in the calculations above, we find" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&-\)\_t\%\(-q\)[\((t + a)\)\^p] // Simplify\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(\((\(-\(1\/a\)\))\)\^p\), " ", \(a\^p\), " ", \(\((\(-\(1\/t\)\))\)\^\(-p\)\), " ", \(\((\(-t\))\)\^q\), " ", \(\((\(a + t\)\/t)\)\^\(p + q\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\(-p\) - q\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(-p\), "]"}]]], "Output"] }, Open ]], Cell["and", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&+\)\_t\%\(-q\)[\((t + a)\)\^p]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(\((1\/a)\)\^p\), " ", \(a\^p\), " ", \(t\^\(p + q\)\), " ", \(\((\(a + t\)\/t)\)\^\(p + q\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\(-p\) - q\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(-p\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "The Weyl fractional derivative is again a polynomial of order ", Cell[BoxData[ \(TraditionalForm\`p + q\)]], ". So far we used arbitrary orders ", Cell[BoxData[ \(TraditionalForm\`q\)]], " in the Weyl operator. A special Weyl derivative of order ", Cell[BoxData[ \(TraditionalForm\`\(-1\)/2\)]], " of the power ", Cell[BoxData[ \(TraditionalForm\`t\^\[Mu]\)]], " gives the result " }], "Text", TextJustification->1], Cell[BoxData[ \(\(Assume[\[Mu] > 0];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&+\)\_t\%\(\(-1\)/2\)[t\^\[Mu]] // Simplify\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(t\^\(1\/2 + \[Mu]\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\(-\(1\/2\)\) - \[Mu]\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(-\[Mu]\), "]"}]]], "Output"] }, Open ]], Cell["and", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&-\)\_t\%\(\(-1\)/2\)[t\^\[Mu]] // Simplify\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(\((\(-1\))\)\^\[Mu]\), " ", \(\((\(-\(1\/t\)\))\)\^\(-\[Mu]\)\), " ", \(\@\(-t\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\(-\(1\/2\)\) - \[Mu]\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(-\[Mu]\), "]"}]]], "Output"] }, Open ]], Cell[TextData[{ "The general Weyl derivative of \[Nu]th order of ", Cell[BoxData[ \(TraditionalForm\`x\^\(-\[Mu]\)\)]], " gives us again a power relation of order -\[Mu]-\[Nu]." }], "Text", TextJustification->1], Cell[BoxData[ \(\(Assume[\[Nu] > 0];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&+\)\_x\%\[Nu][x\^\(-\[Mu]\)]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(x\^\(\(-\[Mu]\) - \[Nu]\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\[Mu] + \[Nu]\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "\[Mu]", "]"}]]], "Output"] }, Open ]], Cell["\<\ The fractional integral of Weyl for the same function results in a power \ behavior with -\[Mu]+\[Nu]\ \>", "Text", TextJustification->1], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ScriptCapitalW]\&+\)\_x\%\(-\[Nu]\)[x\^\(-\[Mu]\)]\)], "Input"], Cell[BoxData[ FractionBox[ RowBox[{\(x\^\(\(-\[Mu]\) + \[Nu]\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\[Mu] - \[Nu]\), "]"}]}], RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "\[Mu]", "]"}]]], "Output"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], " Applications" }], "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}], Cell["\<\ This section contains two applications of fractional calculus. The first \ application generalizes the Debye relaxation phenomena of damped systems. The \ second example introduces diffusion processes incorporating memory effects in \ the time domain. Both examples are known as anomalous relaxation and \ anomalous diffusion.\ \>", "Text"], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], ".", CounterBox["Subsection"], " Anomalous Relaxation" }], "Subsection", CellTags->"Anomalous Relaxation"], Cell["\<\ This example is concerned with linear anomalous relaxation dynamics. The \ standard (Maxwell-Debye) relaxation process, for example, is modeled by the \ initial value problem\ \>", "Text"], Cell[TextData[{ Cell[BoxData[ FormBox[ RowBox[{"\[Tau]", " ", FormBox[\(\[PartialD]\_t\( \[Phi](t)\)\ = \ \(-\(\[Phi](t)\)\)\), "TraditionalForm"]}], TraditionalForm]]], ", with ", Cell[BoxData[ \(TraditionalForm\`t > 0\)]], ", and ", Cell[BoxData[ \(TraditionalForm\`\[Phi](0) = \[Phi]\_0\)]] }], "NumberedEquation", CellTags->"eq-3"], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`\[Phi]\_0\)]], " is a constant and ", Cell[BoxData[ \(TraditionalForm\`\[Tau]\)]], " denotes the relaxation time. The solution is given by an exponential" }], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ RowBox[{\(\[Phi](t)\), " ", "=", RowBox[{ StyleBox["{", "Text"], GridBox[{ {\(\(\[Phi]\_0\) \[ExponentialE]\^\(\(-t\)/\[Tau]\)\ \ \ \ \ if\ \ t \[GreaterEqual] \ 0\)}, {\(0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ t < 0. \)} }], " "}]}], TraditionalForm]]]], "NumberedEquation", CellTags->"eq-4"], Cell[TextData[{ "The initial value problem (", ButtonBox["1.3.1", ButtonData:>"eq-3", ButtonStyle->"Hyperlink"], ") reads in an integral representation" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Phi]( t)\ - \[Phi]\_0\ = \ \(\(-\[Tau]\^\(-1\)\) \ \(\[Integral]\_0\%t\( \[Phi]( t')\)\ \[DifferentialD]t'\)\ = \(\(:\)\(\ \ \)\(\(-\[Tau]\^\(-1\)\)\ \(\(d\^\(-1\)\) \ \(\[Phi](t)\)\)\/dt\^\(-1\)\)\)\)\)]], "." }], "NumberedEquation", CellTags->"eq-5"], Cell[TextData[{ "The integral equation (", ButtonBox["1.3.3", ButtonData:>"eq-5", ButtonStyle->"Hyperlink"], ") incorporates the initial value ", Cell[BoxData[ \(TraditionalForm\`\[Phi]\_0\)]], " right from the beginning. This representation of a relaxation process \ contains the total information on the process in a nut shell. Relaxation \ processes deviating from the classical Maxwell-Debye behavior are referred to \ as Non-Debye, non-exponential or anomalous relaxation processes. Anomalous \ relaxation processes have been observed in dielectrics, in \ diffusion-controlled relaxations, in liquid crystals, polymer melts, \ amorphous polymers, rubber, biopolymers, and other disordered systems [", ButtonBox["20", ButtonData:>"Podlubny-1999", ButtonStyle->"Hyperlink"], "]. Typical Non-Debye relaxation processes are described empirically either \ by a Kohlrausch-Williams-Watts (KWW) decay" }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[Phi]( t)\ = \ \(\[Phi]\_0\) \[ExponentialE]\^\(-\((t/\[Tau])\)\^\[Alpha]\)\ \)]]], "NumberedEquation", CellTags->"eq-6"], Cell[TextData[{ "with ", Cell[BoxData[ \(TraditionalForm\`0 < \[Alpha] < 1\)]], ", or by an asymptotic power-law " }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Phi]( t)\ = \ \[Phi]\_0\ 1\/\((1 + t/\[Tau])\)\^\[Gamma]\ \[Tilde] \ t\^\(-\[Gamma]\)\)]], " if ", Cell[BoxData[ \(TraditionalForm\`t/\[Tau] \[Rule] \[Infinity]\)]] }], "NumberedEquation", CellTags->"eq-7"], Cell[TextData[{ "with ", Cell[BoxData[ \(TraditionalForm\`0 < \[Gamma] < 1\)]], ". In specific experiments the transition between the KWW and the power \ (1.3.5) law can be observed provided the range of time domain extends over \ several decades [", ButtonBox["8", ButtonData:>"Gl\[ODoubleDot]ckle-1991", ButtonStyle->"Hyperlink"], "]. In fact it was possible to find an analytic function interpolating \ between the KWW and the power law. The interpolating function is a \ Mittag-Leffler function which is contained in the generalized function class \ of Fox's H-functions [", ButtonBox["9", ButtonData:>"Fox-1961", ButtonStyle->"Hyperlink"], "]. " }], "Text"], Cell[TextData[{ "The Mittag-Leffler function as special member of the class of Fox's \ H-functions describes anomalous relaxation processes. These powers occur as \ solutions of a generalized relaxation equation which we discuss here. The \ basis of the generalization is the integral representation (", ButtonBox["1.3.3", ButtonData:>"eq-5", ButtonStyle->"Hyperlink"], ") of a standard relaxation process. The generalization consists in \ introducing a fractional integral order in (", ButtonBox["1.3.3", ButtonData:>"eq-5", ButtonStyle->"Hyperlink"], ") by " }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[Phi]( t)\ - \[Phi]\_0\ = \ \(\(-\[Tau]\^\(-q\)\)\ \(\(d\^\(-q\)\) \(\ \[Phi](t)\)\)\/dt\^\(-q\) = \(\(:\)\(\ \)\(\(\[Tau]\^\(-q\)\) \(\ \[ScriptCapitalD]\_\(0, \ t\)\%\(-q\)\) \(\[Phi]( t)\)\)\)\)\)]]], "NumberedEquation", CellTags->"eq-8"], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`q\)]], ", the fractional integral order, is a real constant greater than zero [", ButtonBox["8", ButtonData:>"Gl\[ODoubleDot]ckle-1991", ButtonStyle->"Hyperlink"], ",", ButtonBox["10", ButtonData:>"Gl\[ODoubleDot]ckle-1993a", ButtonStyle->"Hyperlink"], ", ", ButtonBox["11", ButtonData:>"Schneider-1989", ButtonStyle->"Hyperlink"], "]. The symbol ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(0, \ t\)\%\(-q\)\)]], " denotes the Riemann-Liouville integral operator defined by (1.2.9). This \ generalization of a standard relaxation process assumes that anomalous \ relaxation processes are deeply connected with memory integrals. In fact a \ link exists between anomalous relaxation of type (", ButtonBox["1.3.6", ButtonData:>"eq-8", ButtonStyle->"Hyperlink"], ") and the Zwanzig [", ButtonBox["12", ButtonData:>"Zwanzig-1965", ButtonStyle->"Hyperlink"], "] projection operator technique which leads to the integral equation" }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(d\[Phi](t)\)\/dt = \(\(-\(\[Integral]\_0\%t\( K( t - t')\) \(\[Phi](t')\)\ \[DifferentialD]t'\)\) = \ \(K( t)\)\ *\ \(\[Phi](t)\)\)\)]]], "NumberedEquation", CellTags->"eq-9"], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`*\)]], " means Laplace convolution. The kernel ", Cell[BoxData[ \(TraditionalForm\`K(t)\)]], " can be constructed in phase space [", ButtonBox["12", ButtonData:>"Zwanzig-1965", ButtonStyle->"Hyperlink"], ",", ButtonBox["13", ButtonData:>"Gl\[ODoubleDot]ckle-1994", ButtonStyle->"Hyperlink"], "] on a hamiltonian based microscopic model. The integral in (", ButtonBox["1.3.7", ButtonData:>"eq-9", ButtonStyle->"Hyperlink"], ") is called a memory integral. This name was coined because the memory \ integral remembers all instances from ", Cell[BoxData[ \(TraditionalForm\`t' = 0\)]], " up to ", Cell[BoxData[ \(TraditionalForm\`t' = t\)]], " and contributes to the current time ", Cell[BoxData[ \(TraditionalForm\`t\)]], " the total amount of information collected on ", Cell[BoxData[ \(TraditionalForm\`\[Phi]\)]], " during that period. Modeling the memory kernel by an inverse power-law \ decay of the form" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`K(t)\ = \ K\_0\ t\^\(q - 2\)\)]], " with ", Cell[BoxData[ \(TraditionalForm\`0 < q \[LessEqual] 2\)]] }], "Text"], Cell[TextData[{ "we find from (", ButtonBox["1.3.7", ButtonData:>"eq-9", ButtonStyle->"Hyperlink"], ")" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(d\[Phi](t)\)\/dt = \(-\[Tau]\^\(-q\)\) \(\ \[ScriptCapitalD]\_\(0, \ t\)\%\(1 - q\)\) \(\[Phi](t)\)\)]], " " }], "NumberedEquation", CellTags->"eq-10"], Cell[TextData[{ "where the relaxation time is given by ", Cell[BoxData[ \(TraditionalForm\`\[Tau]\^\(-q\) = \(K\_0\) \(\[CapitalGamma]( q - 1)\)\)]], ". Applying ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(0, \ t\)\%\(-1\)\)]], " to both sides of (", ButtonBox["1.3.8", ButtonData:>"eq-10", ButtonStyle->"Hyperlink"], ") leads to the fractional integral equation (", ButtonBox["1.3.6", ButtonData:>"eq-8", ButtonStyle->"Hyperlink"], "). Equation (", ButtonBox["1.3.6", ButtonData:>"eq-8", ButtonStyle->"Hyperlink"], ") is a linear Volterra integral equation of the second kind. The solution \ of such an equation is gained either by a power series ansatz or by \ Laplace-Mellin techniques. We prefer the second solution procedure because \ this method directly connects the solution to Fox's H-functions. The first \ step to solve equation (", ButtonBox["1.3.6", ButtonData:>"eq-8", ButtonStyle->"Hyperlink"], ") is to Laplace transform (", ButtonBox["1.3.6", ButtonData:>"eq-8", ButtonStyle->"Hyperlink"], ") and gain an algebraic solution in Laplace space. The Laplace transform \ of equation (", ButtonBox["1.3.6", ButtonData:>"eq-8", ButtonStyle->"Hyperlink"], ") in ", StyleBox["Mathematica", FontSlant->"Italic"], " follows from" }], "Text"], Cell[BoxData[ \(\(Assume[q > 0];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(equation8\ = \[Phi][ t] - \[Phi]\_0\ + \ \(\[Tau]\^\(-q\)\) \[ScriptCapitalD]\_\(0, \ \ t\)\%\(-q\)[\[Phi][t]] == 0\)], "Input"], Cell[BoxData[ \(\[Tau]\^\(-q\)\ \[ScriptCapitalD]\_\(0, t\)\%\(-q\)[\[Phi][ t]] - \[Phi]\_0 + \[Phi][t] == 0\)], "Output"] }, Open ]], Cell[TextData[{ "under the assumption ", Cell[BoxData[ \(TraditionalForm\`q > 0\)]], ". " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(leq\ = \ \[ScriptCapitalL]\_t\%s[equation8]\)], "Input"], Cell[BoxData[ \(\[ScriptCapitalL]\_t\%s[\[Phi][t]] + s\^\(-q\)\ \[Tau]\^\(-q\)\ \[ScriptCapitalL]\_t\%s[\[Phi][ t]] - \[Phi]\_0\/s == 0\)], "Output"] }, Open ]], Cell[TextData[{ "The algebraic solution of (", ButtonBox["1.3.6", ButtonData:>"eq-8", ButtonStyle->"Hyperlink"], ") in the Laplace space is given by" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(s1 = Solve[leq, \[ScriptCapitalL]\_t\%s[\[Phi][t]]] // Flatten\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalL]\_t\%s[\[Phi][ t]] \[Rule] \[Phi]\_0\/\(s\ \((1 + s\^\(-q\)\ \ \[Tau]\^\(-q\))\)\)}\)], "Output"] }, Open ]], Cell[TextData[{ "Since this expression contains terms with arbitrary powers ", Cell[BoxData[ \(TraditionalForm\`q\)]], ", we face the problem to calculate the inverse Laplace transform. At this \ point we note that Miller and Ross [", ButtonBox["3", ButtonData:>"Miller-1993", ButtonStyle->"Hyperlink"], "] developed a solution strategy for fractional differential equations that \ works well for the case if the fractional order ", Cell[BoxData[ \(TraditionalForm\`q\)]], " is a rational number. A way out of this restriction and applicable to \ arbitrary ", Cell[BoxData[ \(TraditionalForm\`q > 0\)]], " is the additional transform to Mellin space. The inclusion of the Mellin \ transform allows us to resolve the pole structure of the algebraic expression \ in the complex plane. The Mellin transform of the Laplace solution becomes" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(str\ = \(\[ScriptCapitalM]\_s\%p[s1] // PowerExpand\) // Simplify\)], "Input"], Cell[BoxData[ InterpretationBox[\("Conditions to solve the integral:\n\ "\[InvisibleSpace]\(Arg[\[Tau]\^q] \[NotEqual] \[Pi] && 1 + Re[\(\(-1\) + p\)\/q] > 0 && Re[p\/q] < 1\/Re[q]\)\), SequenceForm[ "Conditions to solve the integral:\n", And[ Unequal[ Arg[ Power[ \[Tau], q]], Pi], Greater[ Plus[ 1, Re[ Times[ Plus[ -1, p], Power[ q, -1]]]], 0], Less[ Re[ Times[ p, Power[ q, -1]]], Power[ Re[ q], -1]]]], Editable->False]], "Print"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "p", "]"}], " ", \(\[ScriptCapitalM]\_t\%\(1 - p\)[\[Phi][t]]\)}], "\[Rule]", \(\(\[Pi]\ \[Tau]\^\(1 - p\)\ Csc[\(\[Pi] - p\ \[Pi]\)\/q]\ \ \[Phi]\_0\)\/q\)}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "A shift of the Mellin variable ", Cell[BoxData[ \(TraditionalForm\`p\)]], " allows us to rewrite the result in the form" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(strh = str\ /. \ {Rule \[Rule] Equal, p \[Rule] 1 - p}\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - p\), "]"}], " ", \(\[ScriptCapitalM]\_t\%p[\[Phi][t]]\)}], "==", \(\(\[Pi]\ \[Tau]\^p\ Csc[\(\[Pi] - \((1 - p)\)\ \[Pi]\)\/q]\ \ \[Phi]\_0\)\/q\)}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "The solution of equation (", ButtonBox["1.3.6", ButtonData:>"eq-8", ButtonStyle->"Hyperlink"], ") in Mellin space then reads" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(solh = \(Solve[strh, \[ScriptCapitalM]\_t\%p[\[Phi][t]]] // Flatten\) // MapAll[Expand, #] &\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{\(\[ScriptCapitalM]\_t\%p[\[Phi][t]]\), "\[Rule]", FractionBox[\(\[Pi]\ \[Tau]\^p\ Csc[\(p\ \[Pi]\)\/q]\ \[Phi]\_0\), RowBox[{"q", " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - p\), "]"}]}]]}], "}"}]], "Output"] }, Open ]], Cell["\<\ Since the inverse Mellin transform is directly connected with the definition \ of a Fox's H-function, we can use this link to derive the solution as \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(solution = \((\[ScriptCapitalM]\^\(-1\))\)\_p\%t[solh]\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{\(\[Phi][t]\), "\[Rule]", RowBox[{ RowBox[{ SubscriptBox[ StyleBox["E", FontSlant->"Italic"], \(q, 1\)], "[", " ", \(-\((t\/\[Tau])\)\^q\), "]"}], " ", \(\[Phi]\_0\)}]}], "}"}]], "Output"] }, Open ]], Cell["In conventional notation this result reads", "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Phi]( t)\ = \ \(\[Phi]\_0\) \(\(E\_\(q, 1\)\)(\(-\((t\/\[Tau])\)\^q\))\)\)]], "." }], "NumberedEquation"], Cell[TextData[{ "The result is a Mittag-Leffler function ", Cell[BoxData[ \(TraditionalForm\`\(E\_\(q, 1\)\)( z)\ = \ \[Sum]\_\(k = 0\)\%\[Infinity] z\^k\/\(\[CapitalGamma](q\ \ k + 1)\)\)]], ". For ", Cell[BoxData[ \(TraditionalForm\`q \[Rule] 1\)]], " this series approaches the exponential function. The derivation of the \ solution was possible since the Mellin representation of the solution is \ represented by \[CapitalGamma]-functions. Whenever we are able to represent \ the algebraic solution in terms of \[CapitalGamma]-functions, we can \ transform the solution from the Mellin space to the time domain. The \ mathematical link is the Barnes type integral [", ButtonBox["10", ButtonData:>"Gl\[ODoubleDot]ckle-1993a", ButtonStyle->"Hyperlink"], ",", ButtonBox["14", ButtonData:>"Braaksma-1964", ButtonStyle->"Hyperlink"], "] defining either the inverse Mellin transform or the Fox's H-functions. \ Knowing this connection enables us to write down in a straight forward manner \ the Fox's H-function from the solution in Mellin space. The Mittag-Leffler \ function is connected to the class of Fox's H-functions by" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{\(\[Phi]\_0\/q\), RowBox[{ SubsuperscriptBox[ StyleBox["\[ScriptCapitalH]", FontSize->16], \(1, 2\), \(1, 1\)], "[", RowBox[{\(t/\[Tau]\), "|", GridBox[{ {\(\({{0, 1/q}}\)\(|\)\), \({}\)}, {\(\({{0, 1/q}}\)\(|\)\), \({{0, 1}}\)} }]}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ SubscriptBox[ StyleBox["E", FontSlant->"Italic"], \(q, 1\)], "[", " ", \(-\((t\/\[Tau])\)\^q\), "]"}], " ", \(\[Phi]\_0\)}]], "Output"] }, Open ]], Cell[TextData[{ "demonstrating that the solution of the generalized relaxation equation is \ equivalently represented by a Fox's H-function. The log-log plot of the \ solution (see Fig. 1) demonstrates that the solution is (for ", Cell[BoxData[ \(TraditionalForm\`0 < q < 1\)]], ") monotonically decaying with ", Cell[BoxData[ \(TraditionalForm\`\[Phi](t) \[Proportional] t\^\(-q\)\)]], "for ", Cell[BoxData[ \(TraditionalForm\`t \[Rule] \[Infinity]\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PowerSeries", "[", RowBox[{ RowBox[{\(\[Phi]\_0\/q\), RowBox[{ SubsuperscriptBox[ StyleBox["\[ScriptCapitalH]", FontSize->16], \(1, 2\), \(1, 1\)], "[", RowBox[{\(t/\[Tau]\), "|", GridBox[{ {\(\({{0, 1/q}}\)\(|\)\), \({}\)}, {\(\({{0, 1/q}}\)\(|\)\), \({{0, 1}}\)} }]}], "]"}]}], ",", \({t, \[Infinity], 1}\)}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", FractionBox[\(\((t\/\[Tau])\)\^\(\(-2\)\ q\)\), RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - 2\ q\), "]"}]]}], "+", FractionBox[\(\((t\/\[Tau])\)\^\(-q\)\), RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - q\), "]"}]]}], ")"}], " ", \(\[Phi]\_0\)}]], "Output"] }, Open ]], Cell["The behavior for small times is given by", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PowerSeries", "[", RowBox[{ RowBox[{\(\[Phi]\_0\/q\), RowBox[{ SubsuperscriptBox[ StyleBox["\[ScriptCapitalH]", FontSize->16], \(1, 2\), \(1, 1\)], "[", RowBox[{\(t/\[Tau]\), "|", GridBox[{ {\(\({{0, 1/q}}\)\(|\)\), \({}\)}, {\(\({{0, 1/q}}\)\(|\)\), \({{0, 1}}\)} }]}], "]"}]}], ",", \({t, 0, 1}\)}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"1", "-", FractionBox[\(\((t\/\[Tau])\)\^q\), RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 + q\), "]"}]]}], ")"}], " ", \(\[Phi]\_0\)}]], "Output"] }, Open ]], Cell[TextData[{ "showing that the Mittag-Leffler function reaches the initial condition ", Cell[BoxData[ \(TraditionalForm\`\[Phi]\_0\)]], "." }], "Text"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.778453 0.151985 0.603319 0.467778 [ [.01853 -0.0125 -23 -12.5625 ] [.01853 -0.0125 23 0 ] [.17051 -0.0125 -20 -12.5625 ] [.17051 -0.0125 20 0 ] [.3225 -0.0125 -17 -12.5625 ] [.3225 -0.0125 17 0 ] [.47448 -0.0125 -14 -12.5625 ] [.47448 -0.0125 14 0 ] [.62647 -0.0125 -11 -12.5625 ] [.62647 -0.0125 11 0 ] [.77845 -0.0125 -5 -12.5625 ] [.77845 -0.0125 5 0 ] [.93044 -0.0125 -8 -12.5625 ] [.93044 -0.0125 8 0 ] [1.025 0 0 -6.28125 ] [1.025 0 22 6.28125 ] [-0.0125 .13554 -22 -6.28125 ] [-0.0125 .13554 0 6.28125 ] [-0.0125 .21791 -28 -6.28125 ] [-0.0125 .21791 0 6.28125 ] [-0.0125 .27636 -22 -6.28125 ] [-0.0125 .27636 0 6.28125 ] [-0.0125 .35873 -22 -6.28125 ] [-0.0125 .35873 0 6.28125 ] [-0.0125 .4625 -22 -6.28125 ] [-0.0125 .4625 0 6.28125 ] [-0.0125 .53086 -22 -6.28125 ] [-0.0125 .53086 0 6.28125 ] [-0.0125 .60332 -10 -6.28125 ] [-0.0125 .60332 0 6.28125 ] [0 .64303 -13.2813 0 ] [0 .64303 13.2813 12.5625 ] [ -0.0005 -0.0005 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid .01853 0 m .01853 .00625 L s gsave .01853 -0.0125 -84 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.00001) show 105.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .17051 0 m .17051 .00625 L s gsave .17051 -0.0125 -81 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.0001) show 99.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .3225 0 m .3225 .00625 L s gsave .3225 -0.0125 -78 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.001) show 93.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .47448 0 m .47448 .00625 L s gsave .47448 -0.0125 -75 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.01) show 87.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .62647 0 m .62647 .00625 L s gsave .62647 -0.0125 -72 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.1) show 81.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .77845 0 m .77845 .00625 L s gsave .77845 -0.0125 -66 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1) show 69.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .93044 0 m .93044 .00625 L s gsave .93044 -0.0125 -69 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (10) show 75.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .001 w .06428 0 m .06428 .00375 L s .09104 0 m .09104 .00375 L s .11003 0 m .11003 .00375 L s .12476 0 m .12476 .00375 L s .13679 0 m .13679 .00375 L s .14697 0 m .14697 .00375 L s .15578 0 m .15578 .00375 L s .16356 0 m .16356 .00375 L s .21626 0 m .21626 .00375 L s .24303 0 m .24303 .00375 L s .26202 0 m .26202 .00375 L s .27674 0 m .27674 .00375 L s .28878 0 m .28878 .00375 L s .29895 0 m .29895 .00375 L s .30777 0 m .30777 .00375 L s .31554 0 m .31554 .00375 L s .36825 0 m .36825 .00375 L s .39501 0 m .39501 .00375 L s .414 0 m .414 .00375 L s .42873 0 m .42873 .00375 L s .44076 0 m .44076 .00375 L s .45094 0 m .45094 .00375 L s .45975 0 m .45975 .00375 L s .46753 0 m .46753 .00375 L s .52023 0 m .52023 .00375 L s .547 0 m .547 .00375 L s .56599 0 m .56599 .00375 L s .58072 0 m .58072 .00375 L s .59275 0 m .59275 .00375 L s .60292 0 m .60292 .00375 L s .61174 0 m .61174 .00375 L s .61951 0 m .61951 .00375 L s .67222 0 m .67222 .00375 L s .69898 0 m .69898 .00375 L s .71797 0 m .71797 .00375 L s .7327 0 m .7327 .00375 L s .74474 0 m .74474 .00375 L s .75491 0 m .75491 .00375 L s .76372 0 m .76372 .00375 L s .7715 0 m .7715 .00375 L s .82421 0 m .82421 .00375 L s .85097 0 m .85097 .00375 L s .86996 0 m .86996 .00375 L s .88469 0 m .88469 .00375 L s .89672 0 m .89672 .00375 L s .9069 0 m .9069 .00375 L s .91571 0 m .91571 .00375 L s .92348 0 m .92348 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave 1.025 0 -61 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (t) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 69.000000 12.812500 moveto (\\220) show 75.000000 12.812500 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (t) show 81.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Math2Mono %%+ font Courier grestore 0 .13554 m .00625 .13554 L s gsave -0.0125 .13554 -83 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.1) show 81.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore 0 .21791 m .00625 .21791 L s gsave -0.0125 .21791 -89 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.15) show 87.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore 0 .27636 m .00625 .27636 L s gsave -0.0125 .27636 -83 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.2) show 81.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore 0 .35873 m .00625 .35873 L s gsave -0.0125 .35873 -83 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.3) show 81.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore 0 .4625 m .00625 .4625 L s gsave -0.0125 .4625 -83 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.5) show 81.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore 0 .53086 m .00625 .53086 L s gsave -0.0125 .53086 -83 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0.7) show 81.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore 0 .60332 m .00625 .60332 L s gsave -0.0125 .60332 -71 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1) show 69.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .001 w 0 .1549 m .00375 .1549 L s 0 .17258 m .00375 .17258 L s 0 .18884 m .00375 .18884 L s 0 .2039 m .00375 .2039 L s 0 .23417 m .00375 .23417 L s 0 .24923 m .00375 .24923 L s 0 .26324 m .00375 .26324 L s 0 .41717 m .00375 .41717 L s 0 .49954 m .00375 .49954 L s 0 .5703 m .00375 .5703 L s .25 Mabswid 0 0 m 0 .61803 L s gsave 0 .64303 -74.2813 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (f) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 69.000000 12.812500 moveto (\\220) show 75.000000 12.812500 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (f) show 81.000000 14.250000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 7.125000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (0) show 85.562500 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Math2Mono %%+ font Courier grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 0 1 r .5 Mabswid .02381 .60321 m .53416 .58456 L .57686 .57472 L .60577 .56536 L .62486 .55764 L .66831 .53413 L .69618 .51361 L .71714 .49474 L .76465 .43907 L .81333 .3617 L .84035 .31042 L .85886 .27262 L .87279 .24305 L .88497 .21664 L .89489 .19485 L .90402 .17463 L .91176 .15741 L .91843 .14253 L .92487 .12817 L .93052 .11555 L .93604 .10323 L .94095 .09227 L .94536 .08246 L .94975 .0727 L .95371 .0639 L .95731 .05591 L .96094 .04788 L .96425 .04057 L .9676 .03321 L .97067 .0265 L .9735 .02041 L .97619 .01472 L s % End of Graphics MathPictureEnd \ \>"], "NumberedFigure", ImageSize->{337, 208.188}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgC5003ok>C5D^cTa@00oncTaE;/iC5003ok>C5D^cTa@004NcTa@800004 k>C50P0000C/icTa@800004k>C50P0000C/iC50P0000C/icTa@800004k>C50P0000C/iC50P0000C/icTa@800004 k>C50P0000?/iC50P0000C/iC50P0000C/iC51@00027/iC5000@k>C500@0003/iC500@0003/iC500@0003/iC500@0003/iC500@0 003/iC500<0003/icTa@040000k>C5k>C500002>cTa@040000k>C5k>C5 00000^cTa@040000k>C5k>C500000^cTa@040000k>C5k>C500001>cTa@030000k>C5k>C500[/icTaNcTa@0000S/icTaNcTa@0000;/icTaNcTa@0000C/icT aNcTa@0@k>C500@0003/iC500@0003/iC500<0003/iC5k>C500002^cTa@030000k>C5k>C5027/icTaNcTa@0Sk>C500D0003/iC5k>C502_/icTaNcTa@0000S/icT aNcTa@0000;/icTaNcTa@0000;/icTaNcTa@0000;/icTaNcTa@00 00C/icTaNcTa@04k>C500@0003/iC500@0003/iC500@0 003/iC500@0003/iC500<0003/iC5k>C5 00002>cTa@040000k>C5k>C500000^cTa@040000k>C5k>C500001>cTa@030000k>C5k>C5013/icTaNcTa@0000S/icTaNcTa@0000C/icTaNcTa@0Fk>C500@0003/iC500<0003/iC5k>C502?/icTaNcTaNcTa@000002 k>C500<0003/icTa@040000k>C5k>C500002>cTa@040000k>C5k>C500000^cT a@040000k>C5k>C500000^cTa@040000k>C5k>C500000^cTa@040000k>C5k>C500001>cTa@030000 k>C5k>C500C/icTaNcTa@0000S/icTaNcTa@0000;/icTaNcTa@00 00;/icTaNcTa@0000C/icTaNcTa@0:k>C500@0003/iC500@0 003/iC500@0003/iC500<0003/icTa@040000k>C5k>C5 00002>cTa@040000k>C5k>C500001>cTa@030000k>C5k>C501K/icTaNcTa@0000[/icTaNcTa@0Qk>C500<0003/iC5k>C5k>C5000000;/icT aNcTa@0[k>C5000@k>C500@0003/iC500@0003/iC500@0003/iC500@0003/iC500@0003/iC500<0003/icT a@040000k>C5k>C500002>cTa@040000k>C5k>C500000^cTa@040000k>C5k>C500000^cTa@040000 k>C5k>C500001>cTa@030000k>C5k>C500[/icTaNcTa@0000S/icTaNcTa@00 00;/icTaNcTa@0000C/icTaNcTa@0@k>C500@0003/iC500@0 003/iC500<0003/iC5k>C500002^cTa@030000k>C5k>C5 027/icTaNcTa@0Sk>C500D0003/iC5k>C502_/iC50P0000C/icTa@800004k>C50P0000O/iC50P0000C/icTa@80000=k>C50P0000[/icTa@800004k>C50P00 01?/iC50P0001W/iC50P0002C/icT a@80000^k>C5003ok>C5D^cTa@00oncTaE;/iC500<0003/icTa@030000k>C5k>C500?/icTa@00oncTaCk/icTaNcTa@00 00?/icTaNcTa@03k>C500<0003/icTa@007ncTaOl0000F00002NcTa@030000 k>C5k>C500C/icTaNcTa@03k>C500<0003/icTa@007ncTa@030000k>C5k>C5 00;/icTaNcTa@0:k>C500<0003/icTa@030000k>C5k>C500;/icT aNcTaNcTa@000003k>C500<0003/iC50000k>C5000000c/icT aNcTa@04k>C500<0003/iC5k>C5k>C5000000?/icTa@000002 k>C500D0003/iC5k>C500G/icTaNcTa@02k>C500D0 003/iC5k>C500000^cTa@050000k>C50000k>C5000000_/icTaNcTa@05k>C500<0003/iC5k>C5k>C5000000;/icT aNcTa@0000;/icTa@000>cTa@00000;k>C500<0003/iC5k>C5 00;/icTaNcTaNcTa@000002k>C500H0003/iC500<0003/iC5k>C500G/icTaNcTa@02k>C500D0003/iC5k>C50000k>C500000^cTa@80000Lk>C51@0000C/icTaNcTa@03k>C500<0 003/iC5k>C500;/icTaNcTa@0Wk>C500<0003/iC5k>C502O/icTaNcTa@0Wk>C500<0003/iC5k>C502K/icTaNcTa@0Kk>C500<0003/iC5k>C5k>C51000 00C/icTaNcTa@3ok>C59NcTa@030000k>C5k>C500S/icT aNcTa@3ok>C52ncTa@03003ok>C5k>C502;/icTaNcTa@3ok>C52^cTa@03003o k>C5k>C502?/icTaNcTa@3ok>C52^cTa@03003ok>C5k>C502?/icTaNcTa@3ok>C52^cTa@03003ok>C5k>C502?/icTaNcTa@3ok>C52NcT a@03003ok>C5k>C502C/icTaNcTa@3ok>C52NcTa@03003ok>C5k>C502C/icTaNcTa@3ok>C52>cTa@03003ok>C5k>C502G/icTaNcTa@3o k>C52>cTa@03003ok>C5k>C502G/icTaNcTa@3ok>C51ncTa@03003ok>C5k>C5 02K/icTaNcTa@3ok>C51ncTa@03003ok>C5k>C502K/icT aNcTa@3ok>C51^cTa@03003ok>C5k>C502O/icTaNcTa@3ok>C51^cTa@03003o k>C5k>C502O/icTaNcTa@3ok>C51^cTa@03003ok>C5k>C502O/icTaNcTa@3ok>C51NcTa@03003ok>C5k>C502S/icTaNcTa@3ok>C51NcT a@03003ok>C5k>C502S/icTaNcTa@3ok>C51>cTa@03003ok>C5k>C502W/icTaNcTa@3ok>C51>cTa@03003ok>C5k>C502W/icTaNcTa@3o k>C51>cTa@03003ok>C5k>C502W/icTaNcTa@3ok>C50ncTa@03003ok>C5k>C5 02[/icTaNcTa@3ok>C50ncTa@03003ok>C5k>C502[/icT aNcTa@3ok>C50^cTa@03003ok>C5k>C502_/icTaNcTa@3ok>C50NcTa@03003o k>C5k>C502c/icTaNcTa@3ok>C50NcTa@03003ok>C5k>C502c/icTaNcTa@3ok>C500<00?o/iC5k>C50?o/iC5000Ok>C500<0003/iC5k>C502k/icT aNcTa@3nk>C500<00?o/iC5k>C50?g/iC5000Ok>C500<0003/iC5k>C502o/icTaNcTa@3m k>C500<00?o/iC5k>C50?c/iC5000O k>C500<0003/icTa@03003ok>C5k>C5033/icTa@800003k>C51@00 00G/icTaNcTa@3kk>C500<00?o/iC5k>C500002^cT a@030000k>C5k>C500G/iC5k>C5037/icTaNcTa@00 00[/icTaNcTa@05k>C500<0003/iC5k>C503;/icTaNcTa@0000[/icTaNcTa@05k>C500<0003/iC5k>C5 03;/icTaNcTa@0000[/icTaNcTa@05k>C500<0003/iC5k>C503?/iC500<0003/iC5k>C503?/icTaNcTa@3hk>C500<00?o/icTa@007ncTa@80003i k>C500<00?o/icTa@007ncTa@030000k>C5k>C50?S/iC5000O k>C500<0003/iC5k>C503G/icTaNcTa@3gk>C500<0 0?o/iC5k>C50?K/iC5000Ok>C50P00 0?O/iC5000Ok>C500<0003/iC5k>C503K/icTaNcTa@3ek>C500<00?o/iC5k>C50?G/iC5000Ok>C50P000?K/iC5000Ok>C500<0003/icTa@03003ok>C5k>C503S/icTaNcTa@3dk>C500<00?o/i>cT a@007ncTa@030000k>C5k>C50??/iC5000Ok>C50P000?C/iC5000Ok>C500<0003/iC5k>C503[/icT aNcTa@3bk>C500<00?o/i^cTa@001>cTa@800004k>C50P0000?/iC500<0003/iC5k>C503_/icTaNcTa@0000[/icTaNcTaNcTa@000002k>C500<0003/icTa@<0003ak>C500<00?o/incT a@000ncTa@040000k>C5k>C500002^cTa@030000k>C5k>C500C/icTaNcTa@04k>C500<0 003/iC5k>C503_/icTaNcTa@0000[/icT aNcTa@02k>C50P0000O/icTaNcTa@3`k>C500<00?o/icTa@000ncTa@040000 k>C5k>C500002^cTa@030000k>C5k>C500;/icTaNcTa@06k>C500<0003/icT a@03003ok>C5k>C503c/iC50`0000K/icTaNcTa@3_ k>C500<00?o/iC500<00?o/iC5k>C50>k/iC5000Ok>C500<0003/iC5k>C5 03k/icTaNcTa@3]k>C500<00?o/iC500<0 0?o/iC5k>C50>c/iC5000Ok>C500<0 003/icTa@03003ok>C5k>C5043/icTaNcTa@3[k>C500<00?o/iC500<00?o/iC5k>C50>[/iC5000:k>C50P0000C/iC500<0003/iC5k>C504;/icTaNcTa@0000S/icTaNcTa@07k>C50`00 0>[/iC50009k>C500@0003/iC500<0003/iC5k>C50>W/iC50009k>C500@0003/iC500<0 003/iC5k>C50>W/iC50009k>C500@0003/iC500@0003/iC500<0003/icTa@03003ok>C5k>C504C/iC500<0003/icTa@03003ok>C5k>C504C/icTaNcTa@3Wk>C500<00?o/iC5k>C50>O/iC5000Ok>C500<0003/iC5k>C504K/icT aNcTa@3Vk>C500<00?o/iC5k>C50>G/iC5000Ok>C500<0003/iC5k>C504O/icTaNcTa@3T k>C500<00?o/icTa@007ncTa@030000k>C5k>C50>C/iC5000O k>C500<0003/iC5k>C504W/icTaNcTa@3Sk>C500<0 0?o/iC5k>C50>;/iC5000Ok>C500<0 003/iC5k>C504[/icTaNcTa@3Qk>C500<00?o/iC5k>C50>3/iC5000Ok>C500<0003/icTa@03003ok>C5k>C504c/icTaNcTa@3Ok>C500<00?o/iC50P0000C/iC5k>C50=o/iC50009k>C500@0003/iC500@0003/iC500<0003/iC5k>C504k/icTaNcTa@0000[/icTaNcTa@05k>C50`00 0=k/ik>C50009k>C500@0003/iC500<0003/icT a@030000k>C5k>C50=g/iC50009k>C500@0003/iC500@0 003/iC500<0003/icTa@03003ok>C5k>C5053/iC500<0003/icTa@03003ok>C5k>C5053/icTaNcTa@3K k>C500<00?o/iC5k>C50=_/iC5000O k>C500<0003/iC5k>C505;/icTaNcTa@3Ik>C500<0 0?o/iC5k>C50=W/iC5000Ok>C500<0 003/icTa@03003ok>C5k>C505C/icTaNcTa@3Gk>C500<00?o/iC5k>C50=O/iC5000Ok>C500<0003/iC5k>C505K/icTaNcTa@3Fk>C500<00?o/iC5k>C50=G/iC5000Ok>C500<0003/icT a@03003ok>C5k>C505S/iC5k>C505S/icT aNcTa@3Ck>C500<00?o/iC5k>C50=;/iC5000Ok>C500<0003/iC5k>C505[/icTaNcTa@3A k>C500<00?o/iC5k>C50=7/iC5000O k>C500<0003/icTa@03003ok>C5k>C505c/icTaNcTa@3?k>C500<0 0?o/iC5k>C50C5000Ok>C500<0 003/iC5k>C505o/icTaNcTa@3=k>C500<00?o/iC50P0000C/iC5k>C50C50009k>C500@0003/iC500@0003/iC50`000<_/iC50009k>C500@0003/iC500<0003/icTa@030000 k>C5k>C50<[/iC50009k>C500@0003/iC50P0000O/icTaNcTa@39k>C500<00?o/iC5k>C500002NcTa@030000 k>C5k>C500K/icTaNcTa@38k>C500<00?o/icTa@002^cTa@80000:k>C50`00 00K/icTaNcTa@37k>C500<00?o/iC5k>C50C5000Ok>C500<0003/iC5k>C506K/icTaNcTa@35k>C500<00?o/iC5k>C50C5000Ok>C500<0003/iC5k>C506W/icT aNcTa@32k>C500<00?o/iC500<00?o/iC5k>C50<3/iC5000Ok>C500<0003/iC5k>C506g/icTaNcTa@2nk>C500<00?o/iC5k>C50;g/iC5000Ok>C500<0003/iC5000O k>C500<0003/iC5k>C507;/icTa@800005k>C500<0 003/iC5k>C50;S/iC5k>C500002^cT a@030000k>C5k>C500G/iC50009k>C500@0003/iC500<0 003/iC5k>C50;G/iC50009k>C500@0003/iC500<0003/icTa@030000k>C5k>C50;?/iC5k>C500002>cTa@040000k>C5k>C500001^cTa@030000k>C5k>C50;7/icTa@002^cT a@800009k>C5100000K/icTaNcTa@2`k>C500<00?o/icTa@007ncTa@030000 k>C5k>C50:k/iC5k>C50:c/iC5k>C50:[/iC5k>C50:S/iC5k>C50:K/iC5k>C50:?/iC51000ohc/icTaNcTa@2Kk>C51000oi3/icTaNcTa@2G k>C51000oiC/icTaNcTa@2Ck>C51000oiS/icTaNcTa@23 k>C54000oic/icTaNcTa@1Wk>C57000ojc/icTaNcTa@1; k>C57000olS/icTaNcTa@0_k>C57000onC/iC5k>C501?/icTaNcTa@05k>C50`0000C/icTaNcTa@05k>C500<0003/icT aNcTa@05k>C500<0003/icTaNcTa@05k>C500<0003/iC5k>C50?o/iC5003ok>C5D^cTa@00oncT aE;/iC5003ok>C5D^cTa@00oncTaE;/iC5003ok>C5D^cTa@00oncT aE;/iC5003ok>C5D^cTa@005^cTa@030000k>C5k>C500;/icTaNcTa@04 k>C500<0003/iC5:NcTa@005^cTa@<00003k>C500<0003/iC50P000?o/iC5000Ek>C500D0003/iC5k>C5 00;/icTa@000>cTa@000>cTa@80003ok>C5:NcTa@005NcTa@050000k>C50000k>C50000 00;/icTaNcTa@02k>C500H0003/icTa@000>cTa@000003k>C500T0003/icTa@030000k>C5k>C500;/icTaNcTa@03 k>C500<0003/iC5k>C50?o/iC5003ok>C5D^cTa@00oncTaE;/iC50000\ \>"], ImageRangeCache->{{{138.063, 474.063}, {276.25, 69.0625}} -> {-9.16785, \ -0.883585, 0.0238685, 0.00775509}}], Cell[TextData[{ "The Mittag-Leffler function ", Cell[BoxData[ \(TraditionalForm\`\(E\_\(q, 1\)\)(z)\)]], " with ", Cell[BoxData[ \(TraditionalForm\`q = 2/3\)]], "." }], "SmallText"], Cell["\<\ So far we demonstrated that a fractional generalization of the standard \ relaxation equation possesses a solution which asymptotically allows a power \ law. Its closed analytic expression is given by a Fox's H-function \ representation.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], ".2 Anomalous Diffusion" }], "Subsection", CellTags->"Anomalous Diffusion"], Cell[TextData[{ "Many experiments indicate that diffusion processes usually do not follow \ the standard Gaussian behavior. In turn the mean square displacement ", Cell[BoxData[ \(TraditionalForm\`\[LeftAngleBracket]\(r(t)\)\^2\[RightAngleBracket]\ \ \[Proportional] \ t\)]], " for a Gaussian process changes to ", Cell[BoxData[ \(TraditionalForm\`\[LeftAngleBracket]\(r(t)\)\^2\[RightAngleBracket] \ \[Proportional] \ t\^\(2/d\_w\)\)]], " where the anomalous diffusion exponent ", Cell[BoxData[ \(TraditionalForm\`d\_w\)]], " differs from ", Cell[BoxData[ \(TraditionalForm\`2\)]], " the value for standard diffusion. The deviation from a linear dependence \ to a power law is an indication for anomalous diffusion. Anomalous diffusion \ in which the mean square distance between diffusing quantities increases \ slower or faster than linearly in time has been observed in a large number of \ physical and biological systems from macroscopic surface growth to DNA \ sequences [", ButtonBox["15", ButtonData:>"West-1994", ButtonStyle->"Hyperlink"], "]. One of the first investigations discussing fractional diffusion goes \ back to Wyss [", ButtonBox["16", ButtonData:>"Wyss-1986", ButtonStyle->"Hyperlink"], "] and O'Shaugnessy and Procaccia [", ButtonBox["17", ButtonData:>"Schaugnessy-1985", ButtonStyle->"Hyperlink"], "]. A method for solving fractional diffusion equations using Fox's \ H-functions has been presented by Schneider and Wyss [", ButtonBox["11", ButtonData:>"Schneider-1989", ButtonStyle->"Hyperlink"], "]. " }], "Text"], Cell[TextData[{ "The motivation for the anomalous diffusion equation being discussed here \ follows the ideas already outlined in the section on ", ButtonBox["anomalous relaxation", ButtonData:>"Anomalous Relaxation", ButtonStyle->"Hyperlink"], " starting from the standard model and generalizing the equation by \ incorporating the initial condition. The standard (Fickean) diffusion \ equation in ", Cell[BoxData[ FormBox[ StyleBox[\(1 + 1\), FontSlant->"Italic"], TraditionalForm]]], "-dimensions reads" }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_t\( \[Rho](x, t)\)\ = \[PartialD]\_\(x, x\)\(\[Rho](x, t)\)\)]]], "NumberedEquation", CellTags->"eq-11"], Cell[TextData[{ "with an additional initial condition ", Cell[BoxData[ \(TraditionalForm\`\[Rho](x, t = 0) = \(\[Rho]\_0\)(x)\)]], ". The equation in (", ButtonBox["1.3.10", ButtonData:>"eq-11", ButtonStyle->"Hyperlink"], ") is given in a scaled representation where the diffusion constant is \ incorporated as a factor in time. Our starting point is the memory-diffusion \ equation" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_t\( \[Rho](x, t)\)\ = \ \[Integral]\_0\%t\( K( t - \[Tau])\)\ \[PartialD]\_\(x, x\)\(\[Rho]( x, \[Tau])\)\ \[DifferentialD]\[Tau]\)]], "," }], "NumberedEquation", CellTags->"eq-12"], Cell[TextData[{ "that has already been motivated and derived recently [", ButtonBox["18", ButtonData:>"Compte-1996", ButtonStyle->"Hyperlink"], ",", ButtonBox["19", ButtonData:>"West-1997", ButtonStyle->"Hyperlink"], "]." }], "Text"], Cell[TextData[{ "Again \[LongDash] like in the case of relaxation \[LongDash] we assume \ that the memory kernel takes on a power law ", Cell[BoxData[ \(TraditionalForm\`K(t) = \(D\_0\) t\^\(\[Beta] - 1\)/\(\[CapitalGamma](\[Beta])\)\)]], " with ", Cell[BoxData[ \(TraditionalForm\`0 < \[Beta] < 1\)]], ". Then we can express (", ButtonBox["1.3.11", ButtonData:>"eq-12", ButtonStyle->"Hyperlink"], ") by" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_t \[Rho]\ = \ \ \(D\_0\/\(\[CapitalGamma](\[Beta])\)\) \(\[Integral]\_0\%t\(\((t - \ \[Tau])\)\^\(\[Beta] - 1\)\) \[PartialD]\_\(x, x\)\(\[Rho]( x, \[Tau])\)\ \[DifferentialD]\[Tau]\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Beta] > 0\)]] }], "NumberedEquation", CellTags->"eq-14"], Cell[TextData[{ "which \[LongDash] in terms of Riemann-Liouville operators ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(0, \ t\)\%\[Alpha]\)]], " \[LongDash] may be written as" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(0, \ t\)\%1\) \(\[Rho](x, t)\)\ = \ D\_0\ \ \(\(\[ScriptCapitalD]\_\(0, \ t\)\%\(-\[Beta]\)\)(\[PartialD]\_\(x, x\)\(\[Rho](x, t)\))\)\)]], "." }], "NumberedEquation", CellTags->"eq-15"], Cell[TextData[{ "Applying an integration ", Cell[BoxData[ \(TraditionalForm\`\[ScriptCapitalD]\_\(0, \ t\)\%\(-1\)\)]], " to both sides of (", ButtonBox["1.3.13", ButtonData:>"eq-15", ButtonStyle->"Hyperlink"], ") we find" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Rho](x, t) - \(\[Rho]\_0\)(x)\ = \ D\_0\ \(\(\[ScriptCapitalD]\_\(0, \ t\)\%\(-\((1 + \[Beta])\)\)\)(\[PartialD]\_\(x, x\)\(\[Rho]( x, t)\))\)\)]], "." }], "NumberedEquation", CellTags->"eq-16"], Cell[TextData[{ "A differentiation of order ", Cell[BoxData[ \(TraditionalForm\`\((1 + \[Beta])\)\)]], " of (", ButtonBox["1.3.14", ButtonData:>"eq-16", ButtonStyle->"Hyperlink"], ") replaces the integral representation of the generalized diffusion \ equation by its differential representation" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(0, \ t\)\%\(1 + \[Beta]\)\) \(\[Rho](x, t)\)\ - \(\(\[Rho]\_0\)( x)\)\ t\^\(-\((1 + \ \[Beta])\)\)\/\(\[CapitalGamma](\(-\[Beta]\))\) = \ D\_0\ \[PartialD]\_\(x, x\)\(\[Rho](x, t)\)\)]], "." }], "NumberedEquation", CellTags->"eq-17"], Cell[TextData[{ "This generalized diffusion equation incorporates in addition to the \ fractional differentiation in time the initial condition ", Cell[BoxData[ \(TraditionalForm\`\[Rho]\_0\)]], " for the density ", Cell[BoxData[ \(TraditionalForm\`\[Rho]\)]], ". Replacing the fractional order ", Cell[BoxData[ \(TraditionalForm\`1 + \[Beta]\)]], " by ", Cell[BoxData[ \(TraditionalForm\`q\)]], ", we find the simplified equation" }], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\[ScriptCapitalD]\_\(0, \ t\)\%q\) \(\[Rho](x, t)\)\ - \(\(\[Rho]\_0\)( x)\)\ t\^\(-q\)\/\(\[CapitalGamma](1 - q)\) = \ D\_0\ \[PartialD]\_\(x, x\)\(\[Rho](x, t)\)\)]], " \twith ", Cell[BoxData[ \(TraditionalForm\`1 < q < 2\)]], "." }], "NumberedEquation", CellTags->"eq-18"], Cell[TextData[{ "The solution of equation (", ButtonBox["1.3.16", ButtonData:>"eq-18", ButtonStyle->"Hyperlink"], ") follows in ", StyleBox["Mathematica", FontSlant->"Italic"], " by the following steps:" }], "Text"], Cell[BoxData[ \(\(Assume[q > 0];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(equation18 = \[ScriptCapitalD]\_\(0, \ t\)\%q[\[Rho][x, t]] - \[Rho]\_0[ x] t\^\(-q\)\/\[CapitalGamma][1 - q] == D\_0\ \[PartialD]\_\(x, x\)\[Rho][x, t]\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(\[ScriptCapitalD]\_\(0, t\)\%q[\[Rho][x, t]]\), "-", FractionBox[\(t\^\(-q\)\ \[Rho]\_0[x]\), RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - q\), "]"}]]}], "==", RowBox[{\(D\_0\), " ", RowBox[{ SuperscriptBox["\[Rho]", TagBox[\((2, 0)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}]}]}]], "Output"] }, Open ]], Cell[TextData[{ "First applying the Laplace transform to equation (", ButtonBox["1.3.16", ButtonData:>"eq-18", ButtonStyle->"Hyperlink"], ")" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(equation18Laplace\ = \[ScriptCapitalL]\_t\%s[equation18]\)], "Input"], Cell[BoxData[ RowBox[{\(\(-C1[x]\) + s\^q\ \[ScriptCapitalL]\_t\%s[\[Rho][x, t]] - s\^\(\(-1\) + q\)\ \[Rho]\_0[x]\), "==", RowBox[{ RowBox[{\(\[ScriptCapitalL]\_t\%s\), "[", RowBox[{ SuperscriptBox["\[Rho]", TagBox[\((2, 0)\), Derivative], MultilineFunction->None], "[", \(x, t\), "]"}], "]"}], " ", \(D\_0\)}]}]], "Output"] }, Open ]], Cell["\<\ The second step consists of a Fourier transform of the equation in Laplace \ coordinates\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(foulapgl2 = \[ScriptCapitalF]\_x\%k[ equation18Laplace /. {\[ScriptCapitalL]\_t\%s[\[Rho][x, t]] \[Rule] L[x], \[ScriptCapitalL]\_t\%s[\[PartialD]\_\(x, x\)\[Rho][x, t]] \[Rule] \[PartialD]\_\(x, x\)L[x], \[Rho]\_0[ x] \[Rule] DiracDelta[x], C1[x] \[Rule] 0}]\)], "Input"], Cell[BoxData[ \(\[ScriptCapitalF]\_x\%k[L[x]]\ \((s\^q + k\^2\ D\_0)\) == s\^\(\(-1\) + q\)\/\@\(2\ \[Pi]\)\)], "Output"] }, Open ]], Cell["\<\ The algebraic solution in Fourier and Laplace coordinates follows by\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(foulaploes2 = Solve[foulapgl2, FourierTransform[L[x], x, k]] // Flatten\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalF]\_x\%k[L[x]] \[Rule] s\^\(\(-1\) + q\)\/\(\@\(2\ \[Pi]\)\ \((s\^q + k\^2\ D\_0)\)\)}\)], \ "Output"] }, Open ]], Cell[TextData[{ "The application of the inverse Fourier transform to this solution gives \ the solution in spatial and Laplacian variables ", Cell[BoxData[ \(TraditionalForm\`\((x, s)\)\)]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(laploes2 = Map[InverseFourierTransform[#, k, x] &, foulaploes2, {2}] /. L[x] \[Rule] \[ScriptCapitalL]\_t\%s[\[Rho][x, t]]\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalL]\_t\%s[\[Rho][x, t]] \[Rule] \[ExponentialE]\^\(-\(\(x\ Sign[x]\)\/\@\(s\^\(-q\)\ \ D\_0\)\)\)\/\(2\ s\ \@\(s\^\(-q\)\ D\_0\)\)}\)], "Output"] }, Open ]], Cell[TextData[{ "The result shows that the Laplace solution contains a stretched \ exponential multiplied by a power function. If we restrict our consideration \ to the half space ", Cell[BoxData[ \(TraditionalForm\`x > 0\)]], " and assume that the diffusion constant ", Cell[BoxData[ \(TraditionalForm\`D\_0\)]], " is positive" }], "Text"], Cell[BoxData[ \(Assume[x > 0]; Assume[C1 > 0];\)], "Input"], Cell["we can represent the result in Mellin space as", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(mellaploes2 = \(\[ScriptCapitalM]\_s\%z[ laploes2 /. D\_0 \[Rule] C1 // PowerExpand] // PowerExpand\) // Simplify\)], "Input"], Cell[BoxData[ InterpretationBox[\("Conditions to solve the integral:\n\ "\[InvisibleSpace]\(Re[\(\(-1\) + z\)\/q] > \(-\(1\/2\)\) && Re[\(\(-1\) + q\/2 + z\)\/q] > 0 && Re[\(x\ Sign[x]\)\/\@C1] > 0\)\), SequenceForm[ "Conditions to solve the integral:\n", And[ Greater[ Re[ Times[ Power[ q, -1], Plus[ -1, z]]], Rational[ -1, 2]], Greater[ Re[ Times[ Power[ q, -1], Plus[ -1, Times[ Rational[ 1, 2], q], z]]], 0], Greater[ Re[ Times[ Power[ C1, Rational[ -1, 2]], x, Sign[ x]]], 0]]], Editable->False]], "Print"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", "z", "]"}], " ", \(\[ScriptCapitalM]\_t\%\(1 - z\)[\[Rho][x, t]]\)}], "\[Rule]", FractionBox[ RowBox[{\(C1\^\(\(\(-1\) + z\)\/q\)\), " ", \(x\^\(-\(\(\(-2\) + q + 2\ z\)\/q\)\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\(\(-2\) + q + 2\ z\)\/q\), "]"}], " ", \(Sign[x]\^\(-\(\(\(-2\) + q + 2\ z\)\/q\)\)\)}], "q"]}], "}"}]], "Output"] }, Open ]], Cell["\<\ A shift of the Mellin variable by one gives us the Mellin solution to be \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(melloes2 = Solve[mellaploes2 /. {z \[Rule] 1 - z, Rule \[Rule] Equal}, \[ScriptCapitalM]\_t\%z[\[Rho][x, t]]] // Flatten\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{\(\[ScriptCapitalM]\_t\%z[\[Rho][x, t]]\), "\[Rule]", FractionBox[ RowBox[{\(C1\^\(-\(z\/q\)\)\), " ", \(x\^\(-\(\(\(-2\) + q + 2\ \((1 - z)\)\)\/q\)\)\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(\(\(-2\) + q + 2\ \((1 - z)\)\)\/q\), "]"}], " ", \(Sign[x]\^\(-\(\(\(-2\) + q + 2\ \((1 - z)\)\)\/q\)\)\)}], RowBox[{"q", " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(1 - z\), "]"}]}]]}], "}"}]], "Output"] }, Open ]], Cell["\<\ The inversion of the Mellin transform provides the final result\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(solution\ = \ \(\((\[ScriptCapitalM]\^\(-1\))\)\_z\%t[melloes2] /. C1 \[Rule] D\_0 // PowerExpand\) // Simplify\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{\(\[Rho][x, t]\), "\[Rule]", FractionBox[ RowBox[{ SubsuperscriptBox[ StyleBox["\[ScriptCapitalH]", FontSize->16], \(1, 1\), \(1, 0\)], "[", RowBox[{\(\(x\^\(2/q\)\ Sign[x]\^\(2/q\)\ D\_0\%\(\(-1\)/q\)\)\/t\ \), "|", GridBox[{ {\(\({}\)\(|\)\), \({{1, 1}}\)}, {\(\({{1, 2\/q}}\)\(|\)\), \({}\)} }]}], "]"}], \(q\ x\ Sign[x]\)]}], "}"}]], "Output"] }, Open ]], Cell["In traditional notation this result reads", "Text"], Cell[TextData[{ Cell[BoxData[ RowBox[{\(\[Rho] \((x, t)\)\), "=", FractionBox[ RowBox[{ SubsuperscriptBox[ StyleBox["\[ScriptCapitalH]", FontSize->16], \(1, 1\), \(1, 0\)], "[", RowBox[{\(\(x\^\(2/q\)\ D\_0\%\(\(-1\)/q\)\)\/t\), "|", GridBox[{ {\(\({}\)\(|\)\), \({{1, 1}}\)}, {\(\({{1, 2\/q}}\)\(|\)\), \({}\)} }]}], "]"}], \(q\ x\)]}]]], "." }], "NumberedEquation", CellTags->"eq-22a"], Cell[TextData[{ "The solution of the generalized diffusion equation (", ButtonBox["1.3.16", ButtonData:>"eq-18", ButtonStyle->"Hyperlink"], ") is thus represented by a Fox's H-function of ", Cell[BoxData[ FormBox[ SubsuperscriptBox[ StyleBox["\[ScriptCapitalH]", FontSize->16], \(1, 1\), \(1, 0\)], TraditionalForm]]], " type. This function is given by series representation as follows:" }], "Text"], Cell[TextData[Cell[BoxData[ RowBox[{ RowBox[{ SubsuperscriptBox[ StyleBox["\[ScriptCapitalH]", FontSize->16], \(1, 1\), \(1, 0\)], "[", RowBox[{\(\(x\^\(2/q\)\ D\_0\%\(\(-1\)/q\)\)\/t\), "|", GridBox[{ {\(\({}\)\(|\)\), \({{1, 1}}\)}, {\(\({{1, 2\/q}}\)\(|\)\), \({}\)} }]}], "]"}], "=", "\n", "\t", \(\[Sum]\+\(k = 0\)\%\[Infinity]\(\( q\ \((\(-1\))\)\^k\)\/\(2 \[CapitalGamma] \((1 - \(q\/2\) \ \((1 + k)\))\)\ \(k!\)\)\) \(\(\((\(\(x\^\(2\/q\)\) \ D\_0\%\(\(-1\)/q\)\)\/t)\)\^\(\(q\/2\) \((1 + k)\)\)\)\(.\)\)\)}]]]], "NumberedEquation"], Cell["\<\ A graphical representation of the solution is given in Fig. 2.\ \>", "Text"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .81114 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% SurfaceGraphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0 1.04977 -0.0679587 1.04977 [ [.22795 .16733 -5.79547 -9 ] [.22795 .16733 .20453 0 ] [.44528 .08186 -5.37835 -9 ] [.44528 .08186 .62165 0 ] [.68156 -0.01098 -4.96123 -9 ] [.68156 -0.01098 1.03877 0 ] [.29165 .07573 -9.31117 -12.5625 ] [.29165 .07573 .68883 0 ] [.70096 -0.00478 0 -6.26206 ] [.70096 -0.00478 6 2.73794 ] [.78313 .12104 0 -6.13858 ] [.78313 .12104 6 2.86142 ] [.8565 .23339 0 -6.03127 ] [.8565 .23339 6 2.96873 ] [.9224 .33431 0 -5.93715 ] [.9224 .33431 6 3.06285 ] [.98191 .42546 0 -5.85393 ] [.98191 .42546 6 3.14607 ] [.91861 .21225 0 -8.41865 ] [.91861 .21225 10 4.14385 ] [.02411 .26511 -6 -2.74232 ] [.02411 .26511 0 6.25768 ] [.01692 .31021 -18 -2.78044 ] [.01692 .31021 0 6.21956 ] [.00951 .35664 -18 -2.81981 ] [.00951 .35664 0 6.18019 ] [.00188 .40448 -18 -2.86048 ] [.00188 .40448 0 6.13952 ] [-0.00599 .45379 -18 -2.90254 ] [-0.00599 .45379 0 6.09746 ] [-0.05457 .39542 -16 -3.95494 ] [-0.05457 .39542 0 8.60756 ] [ 0 0 0 0 ] [ 1 .81114 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid .03716 .25514 m .68874 0 L s .23689 .17693 m .24136 .18173 L s [(1)] .22795 .16733 .93182 1 Mshowa .45343 .09214 m .4575 .09728 L s [(2)] .44528 .08186 .79278 1 Mshowa .68874 0 m .69233 .00549 L s [(3)] .68156 -0.01098 .65374 1 Mshowa .125 Mabswid .07572 .24004 m .07856 .24276 L s .11507 .22463 m .11787 .22739 L s .15504 .20898 m .1578 .21178 L s .19564 .19308 m .19837 .19592 L s .27881 .16052 m .28145 .16344 L s .3214 .14384 m .32399 .1468 L s .36469 .12689 m .36724 .12989 L s .40869 .10966 m .41119 .1127 L s .49891 .07433 m .5013 .07746 L s .54517 .05622 m .5475 .05939 L s .59221 .0378 m .59448 .04101 L s .64006 .01906 m .64227 .02231 L s gsave .29165 .07573 -70.3112 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (x) show 69.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .25 Mabswid .68874 0 m .96935 .42924 L s .68874 0 m .68263 .00239 L s [(1)] .70096 -0.00478 -1 .39157 Mshowa .7708 .12553 m .76464 .12778 L s [(2)] .78313 .12104 -1 .36413 Mshowa .84407 .23761 m .83786 .23973 L s [(3)] .8565 .23339 -1 .34028 Mshowa .9099 .3383 m .90365 .34029 L s [(4)] .9224 .33431 -1 .31937 Mshowa .96935 .42924 m .96306 .43113 L s [(5)] .98191 .42546 -1 .30087 Mshowa .125 Mabswid .70593 .0263 m .70226 .02771 L s .72272 .05198 m .71904 .05338 L s .73912 .07706 m .73543 .07845 L s .75514 .10158 m .75145 .10294 L s .78611 .14895 m .78241 .15028 L s .80108 .17185 m .79737 .17317 L s .81573 .19425 m .81201 .19555 L s .83006 .21617 m .82633 .21745 L s .8578 .2586 m .85407 .25986 L s .87123 .27915 m .8675 .28039 L s .88439 .29928 m .88065 .3005 L s .89727 .31899 m .89353 .3202 L s .92227 .35722 m .91851 .3584 L s .93439 .37576 m .93063 .37693 L s .94627 .39394 m .94251 .3951 L s .95792 .41176 m .95416 .41291 L s gsave .91861 .21225 -61 -12.4187 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (t) show 69.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore .25 Mabswid .03716 .25514 m 0 .48963 L s .03634 .26033 m .04245 .25795 L s [(0)] .02411 .26511 1 -0.3906 Mshowa .02918 .30552 m .0353 .30318 L s [(0.1)] .01692 .31021 1 -0.38213 Mshowa .0218 .35205 m .02795 .34976 L s [(0.2)] .00951 .35664 1 -0.37338 Mshowa .0142 .39999 m .02037 .39775 L s [(0.3)] .00188 .40448 1 -0.36434 Mshowa .00638 .4494 m .01256 .4472 L s [(0.4)] -0.00599 .45379 1 -0.35499 Mshowa .125 Mabswid .03492 .26927 m .03859 .26784 L s .0335 .27825 m .03717 .27683 L s .03207 .28729 m .03574 .28587 L s .03062 .29638 m .0343 .29497 L s .02772 .31472 m .0314 .31332 L s .02625 .32397 m .02993 .32258 L s .02478 .33328 m .02846 .33189 L s .02329 .34264 m .02698 .34125 L s .0203 .36153 m .02399 .36016 L s .01879 .37106 m .02248 .36969 L s .01727 .38064 m .02097 .37928 L s .01574 .39029 m .01944 .38893 L s .01266 .40975 m .01636 .40841 L s .0111 .41957 m .0148 .41824 L s .00954 .42945 m .01324 .42813 L s .00796 .4394 m .01167 .43807 L s .00478 .45946 m .00849 .45815 L s .00318 .46959 m .00689 .46828 L s .00156 .47978 m .00528 .47848 L s gsave -0.05457 .39542 -77 -7.95494 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (r) show 75.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Math1Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Courier grestore .25 Mabswid .03716 .25514 m 0 .48963 L s 0 .48963 m .39787 .81114 L s .39787 .81114 m .40529 .59895 L s .40529 .59895 m .03716 .25514 L s .68874 0 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .03716 .25514 m 0 .48963 L s 0 .48963 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .68874 0 m .03716 .25514 L s .40529 .59895 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .39787 .81114 L s .39787 .81114 m .40529 .59895 L s 0 0 m 1 0 L 1 .81114 L 0 .81114 L closepath clip newpath .641 .75 .928 r .39515 .62132 .40423 .62916 .4194 .62537 .41037 .61752 Mtetra .41037 .61752 .4194 .62537 .43466 .62158 .42569 .61371 Mtetra .64 .751 .929 r .42569 .61371 .43466 .62158 .45001 .61778 .44109 .60989 Mtetra .639 .751 .93 r .44109 .60989 .45001 .61778 .46545 .61398 .45659 .60607 Mtetra .639 .752 .93 r .45659 .60607 .46545 .61398 .48099 .61017 .47219 .60225 Mtetra .638 .752 .931 r .47219 .60225 .48099 .61017 .49663 .60635 .48788 .59841 Mtetra .638 .753 .932 r .48788 .59841 .49663 .60635 .51236 .60252 .50368 .59457 Mtetra .637 .754 .933 r .50368 .59457 .51236 .60252 .52819 .59869 .51957 .59072 Mtetra .636 .754 .933 r .51957 .59072 .52819 .59869 .54412 .59484 .53556 .58686 Mtetra .636 .755 .934 r .53556 .58686 .54412 .59484 .56015 .59099 .55165 .58299 Mtetra .635 .755 .935 r .55165 .58299 .56015 .59099 .57629 .58712 .56785 .57912 Mtetra .635 .756 .936 r .56785 .57912 .57629 .58712 .59252 .58325 .58415 .57523 Mtetra .634 .757 .936 r .58415 .57523 .59252 .58325 .60886 .57936 .60056 .57132 Mtetra .634 .758 .937 r .60056 .57132 .60886 .57936 .62531 .57545 .61707 .56741 Mtetra .633 .758 .938 r .61707 .56741 .62531 .57545 .64186 .57153 .63369 .56348 Mtetra .633 .759 .939 r .63369 .56348 .64186 .57153 .65852 .5676 .65042 .55953 Mtetra .632 .76 .939 r .65042 .55953 .65852 .5676 .67528 .56364 .66726 .55556 Mtetra .632 .761 .94 r .66726 .55556 .67528 .56364 .69216 .55967 .68421 .55158 Mtetra .632 .761 .941 r .68421 .55158 .69216 .55967 .70915 .55568 .70127 .54757 Mtetra .631 .762 .941 r .70127 .54757 .70915 .55568 .72625 .55166 .71845 .54353 Mtetra .631 .763 .942 r .71845 .54353 .72625 .55166 .74346 .54761 .73574 .53947 Mtetra .631 .764 .943 r .73574 .53947 .74346 .54761 .76078 .54354 .75314 .53538 Mtetra .631 .765 .943 r .75314 .53538 .76078 .54354 .77822 .53943 .77067 .53126 Mtetra .631 .766 .944 r .77067 .53126 .77822 .53943 .79578 .53529 .7883 .52709 Mtetra .7883 .52709 .79578 .53529 .81345 .53112 .80606 .52289 Mtetra .631 .767 .945 r .80606 .52289 .81345 .53112 .83124 .5269 .82393 .51865 Mtetra .632 .768 .945 r .82393 .51865 .83124 .5269 .84914 .52264 .84193 .51436 Mtetra .632 .769 .945 r .84193 .51436 .84914 .52264 .86717 .51833 .86004 .51002 Mtetra .632 .77 .946 r .86004 .51002 .86717 .51833 .88531 .51397 .87827 .50563 Mtetra .633 .77 .946 r .87827 .50563 .88531 .51397 .90358 .50956 .89663 .50117 Mtetra .634 .771 .946 r .89663 .50117 .90358 .50956 .92196 .50508 .9151 .49665 Mtetra .635 .772 .946 r .9151 .49665 .92196 .50508 .94046 .50054 .9337 .49207 Mtetra .636 .773 .946 r .9337 .49207 .94046 .50054 .95908 .49594 .95241 .48741 Mtetra .637 .773 .945 r .95241 .48741 .95908 .49594 .97782 .49126 .97125 .48267 Mtetra .64 .75 .928 r .38597 .61342 .39515 .62132 .41037 .61752 .40125 .6096 Mtetra .64 .751 .929 r .40125 .6096 .41037 .61752 .42569 .61371 .41661 .60577 Mtetra .639 .751 .93 r .41661 .60577 .42569 .61371 .44109 .60989 .43208 .60194 Mtetra .638 .752 .93 r .43208 .60194 .44109 .60989 .45659 .60607 .44763 .59811 Mtetra .638 .752 .931 r .44763 .59811 .45659 .60607 .47219 .60225 .46329 .59427 Mtetra .637 .753 .932 r .46329 .59427 .47219 .60225 .48788 .59841 .47904 .59042 Mtetra .636 .753 .933 r .47904 .59042 .48788 .59841 .50368 .59457 .49489 .58656 Mtetra .636 .754 .934 r .49489 .58656 .50368 .59457 .51957 .59072 .51084 .5827 Mtetra .635 .755 .934 r .51084 .5827 .51957 .59072 .53556 .58686 .5269 .57883 Mtetra .635 .755 .935 r .5269 .57883 .53556 .58686 .55165 .58299 .54306 .57495 Mtetra .634 .756 .936 r .54306 .57495 .55165 .58299 .56785 .57912 .55932 .57106 Mtetra .633 .757 .937 r .55932 .57106 .56785 .57912 .58415 .57523 .57569 .56716 Mtetra .633 .758 .938 r .57569 .56716 .58415 .57523 .60056 .57132 .59216 .56325 Mtetra .632 .758 .938 r .59216 .56325 .60056 .57132 .61707 .56741 .60874 .55932 Mtetra .632 .759 .939 r .60874 .55932 .61707 .56741 .63369 .56348 .62543 .55538 Mtetra .631 .76 .94 r .62543 .55538 .63369 .56348 .65042 .55953 .64223 .55142 Mtetra .631 .761 .941 r .64223 .55142 .65042 .55953 .66726 .55556 .65915 .54744 Mtetra .63 .762 .941 r .65915 .54744 .66726 .55556 .68421 .55158 .67617 .54345 Mtetra .63 .762 .942 r .67617 .54345 .68421 .55158 .70127 .54757 .69331 .53942 Mtetra .63 .763 .943 r .69331 .53942 .70127 .54757 .71845 .54353 .71056 .53538 Mtetra .63 .764 .944 r .71056 .53538 .71845 .54353 .73574 .53947 .72793 .5313 Mtetra .63 .765 .944 r .72793 .5313 .73574 .53947 .75314 .53538 .74542 .52719 Mtetra .63 .766 .945 r .74542 .52719 .75314 .53538 .77067 .53126 .76302 .52305 Mtetra .63 .767 .945 r .76302 .52305 .77067 .53126 .7883 .52709 .78074 .51887 Mtetra .63 .768 .946 r .78074 .51887 .7883 .52709 .80606 .52289 .79859 .51464 Mtetra .63 .769 .946 r .79859 .51464 .80606 .52289 .82393 .51865 .81655 .51038 Mtetra .63 .77 .947 r .81655 .51038 .82393 .51865 .84193 .51436 .83463 .50606 Mtetra .631 .77 .947 r .83463 .50606 .84193 .51436 .86004 .51002 .85283 .50168 Mtetra .632 .771 .947 r .85283 .50168 .86004 .51002 .87827 .50563 .87116 .49725 Mtetra .632 .772 .947 r .87116 .49725 .87827 .50563 .89663 .50117 .8896 .49276 Mtetra .633 .773 .947 r .8896 .49276 .89663 .50117 .9151 .49665 .90817 .48819 Mtetra .634 .773 .947 r .90817 .48819 .9151 .49665 .9337 .49207 .92686 .48355 Mtetra .635 .774 .947 r .92686 .48355 .9337 .49207 .95241 .48741 .94567 .47883 Mtetra .637 .775 .947 r .94567 .47883 .95241 .48741 .97125 .48267 .9646 .47403 Mtetra .639 .75 .929 r .3767 .60545 .38597 .61342 .40125 .6096 .39202 .60162 Mtetra .639 .751 .93 r .39202 .60162 .40125 .6096 .41661 .60577 .40744 .59778 Mtetra .638 .751 .931 r .40744 .59778 .41661 .60577 .43208 .60194 .42296 .59393 Mtetra .637 .752 .931 r .42296 .59393 .43208 .60194 .44763 .59811 .43857 .59008 Mtetra .637 .753 .932 r .43857 .59008 .44763 .59811 .46329 .59427 .45429 .58623 Mtetra .636 .753 .933 r .45429 .58623 .46329 .59427 .47904 .59042 .4701 .58237 Mtetra .635 .754 .934 r .4701 .58237 .47904 .59042 .49489 .58656 .48601 .5785 Mtetra .635 .755 .935 r .48601 .5785 .49489 .58656 .51084 .5827 .50202 .57463 Mtetra .634 .755 .935 r .50202 .57463 .51084 .5827 .5269 .57883 .51814 .57075 Mtetra .633 .756 .936 r .51814 .57075 .5269 .57883 .54306 .57495 .53436 .56686 Mtetra .633 .757 .937 r .53436 .56686 .54306 .57495 .55932 .57106 .55069 .56296 Mtetra .632 .758 .938 r .55069 .56296 .55932 .57106 .57569 .56716 .56712 .55905 Mtetra .631 .758 .939 r .56712 .55905 .57569 .56716 .59216 .56325 .58366 .55513 Mtetra .631 .759 .94 r .58366 .55513 .59216 .56325 .60874 .55932 .60032 .55119 Mtetra .63 .76 .941 r .60032 .55119 .60874 .55932 .62543 .55538 .61708 .54724 Mtetra .63 .761 .941 r .61708 .54724 .62543 .55538 .64223 .55142 .63395 .54328 Mtetra .629 .762 .942 r .63395 .54328 .64223 .55142 .65915 .54744 .65094 .53929 Mtetra .629 .763 .943 r .65094 .53929 .65915 .54744 .67617 .54345 .66804 .53528 Mtetra .629 .764 .944 r .66804 .53528 .67617 .54345 .69331 .53942 .68525 .53125 Mtetra .628 .765 .944 r .68525 .53125 .69331 .53942 .71056 .53538 .70259 .52719 Mtetra .628 .765 .945 r .70259 .52719 .71056 .53538 .72793 .5313 .72004 .5231 Mtetra .628 .766 .946 r .72004 .5231 .72793 .5313 .74542 .52719 .7376 .51898 Mtetra .628 .767 .946 r .7376 .51898 .74542 .52719 .76302 .52305 .75529 .51482 Mtetra .628 .768 .947 r .75529 .51482 .76302 .52305 .78074 .51887 .7731 .51061 Mtetra .628 .769 .947 r .7731 .51061 .78074 .51887 .79859 .51464 .79103 .50637 Mtetra .629 .77 .948 r .79103 .50637 .79859 .51464 .81655 .51038 .80908 .50207 Mtetra .629 .771 .948 r .80908 .50207 .81655 .51038 .83463 .50606 .82725 .49772 Mtetra .63 .772 .948 r .82725 .49772 .83463 .50606 .85283 .50168 .84554 .49332 Mtetra .631 .773 .949 r .84554 .49332 .85283 .50168 .87116 .49725 .86396 .48885 Mtetra .631 .774 .949 r .86396 .48885 .87116 .49725 .8896 .49276 .8825 .48431 Mtetra .632 .774 .949 r .8825 .48431 .8896 .49276 .90817 .48819 .90116 .47969 Mtetra .634 .775 .948 r .90116 .47969 .90817 .48819 .92686 .48355 .91994 .475 Mtetra .635 .776 .948 r .91994 .475 .92686 .48355 .94567 .47883 .93885 .47022 Mtetra .637 .776 .948 r .93885 .47022 .94567 .47883 .9646 .47403 .95788 .46534 Mtetra .638 .751 .93 r .36732 .59742 .3767 .60545 .39202 .60162 .3827 .59357 Mtetra .638 .751 .931 r .3827 .59357 .39202 .60162 .40744 .59778 .39817 .58972 Mtetra .637 .752 .931 r .39817 .58972 .40744 .59778 .42296 .59393 .41374 .58586 Mtetra .636 .752 .932 r .41374 .58586 .42296 .59393 .43857 .59008 .42941 .582 Mtetra .636 .753 .933 r .42941 .582 .43857 .59008 .45429 .58623 .44518 .57813 Mtetra .635 .754 .934 r .44518 .57813 .45429 .58623 .4701 .58237 .46105 .57426 Mtetra .634 .754 .935 r .46105 .57426 .4701 .58237 .48601 .5785 .47703 .57039 Mtetra .633 .755 .936 r .47703 .57039 .48601 .5785 .50202 .57463 .4931 .5665 Mtetra .633 .756 .937 r .4931 .5665 .50202 .57463 .51814 .57075 .50928 .56262 Mtetra .632 .757 .937 r .50928 .56262 .51814 .57075 .53436 .56686 .52557 .55872 Mtetra .631 .757 .938 r .52557 .55872 .53436 .56686 .55069 .56296 .54196 .55481 Mtetra .631 .758 .939 r .54196 .55481 .55069 .56296 .56712 .55905 .55846 .5509 Mtetra .63 .759 .94 r .55846 .5509 .56712 .55905 .58366 .55513 .57507 .54697 Mtetra .629 .76 .941 r .57507 .54697 .58366 .55513 .60032 .55119 .59179 .54303 Mtetra .629 .761 .942 r .59179 .54303 .60032 .55119 .61708 .54724 .60863 .53907 Mtetra .628 .762 .943 r .60863 .53907 .61708 .54724 .63395 .54328 .62557 .5351 Mtetra .628 .763 .944 r .62557 .5351 .63395 .54328 .65094 .53929 .64263 .53111 Mtetra .627 .764 .945 r .64263 .53111 .65094 .53929 .66804 .53528 .65981 .52709 Mtetra .627 .765 .945 r .65981 .52709 .66804 .53528 .68525 .53125 .67711 .52305 Mtetra .627 .766 .946 r .67711 .52305 .68525 .53125 .70259 .52719 .69452 .51898 Mtetra .627 .767 .947 r .69452 .51898 .70259 .52719 .72004 .5231 .71205 .51488 Mtetra .626 .768 .947 r .71205 .51488 .72004 .5231 .7376 .51898 .7297 .51074 Mtetra .626 .769 .948 r .7297 .51074 .7376 .51898 .75529 .51482 .74747 .50656 Mtetra .627 .77 .949 r .74747 .50656 .75529 .51482 .7731 .51061 .76536 .50234 Mtetra .627 .771 .949 r .76536 .50234 .7731 .51061 .79103 .50637 .78338 .49807 Mtetra .627 .772 .949 r .78338 .49807 .79103 .50637 .80908 .50207 .80152 .49375 Mtetra .628 .773 .95 r .80152 .49375 .80908 .50207 .82725 .49772 .81978 .48937 Mtetra .629 .774 .95 r .81978 .48937 .82725 .49772 .84554 .49332 .83816 .48493 Mtetra .63 .774 .95 r .83816 .48493 .84554 .49332 .86396 .48885 .85667 .48041 Mtetra .631 .775 .95 r .85667 .48041 .86396 .48885 .8825 .48431 .87531 .47583 Mtetra .632 .776 .95 r .87531 .47583 .8825 .48431 .90116 .47969 .89406 .47116 Mtetra .633 .777 .95 r .89406 .47116 .90116 .47969 .91994 .475 .91295 .4664 Mtetra .635 .777 .949 r .91295 .4664 .91994 .475 .93885 .47022 .93195 .46156 Mtetra .637 .778 .949 r .93195 .46156 .93885 .47022 .95788 .46534 .95108 .45661 Mtetra .637 .751 .931 r .35783 .58933 .36732 .59742 .3827 .59357 .37326 .58547 Mtetra .637 .752 .931 r .37326 .58547 .3827 .59357 .39817 .58972 .38879 .5816 Mtetra .636 .752 .932 r .38879 .5816 .39817 .58972 .41374 .58586 .40442 .57773 Mtetra .635 .753 .933 r .40442 .57773 .41374 .58586 .42941 .582 .42015 .57386 Mtetra .634 .754 .934 r .42015 .57386 .42941 .582 .44518 .57813 .43598 .56998 Mtetra .633 .754 .935 r .43598 .56998 .44518 .57813 .46105 .57426 .45191 .56611 Mtetra .633 .755 .936 r .45191 .56611 .46105 .57426 .47703 .57039 .46794 .56222 Mtetra .632 .756 .937 r .46794 .56222 .47703 .57039 .4931 .5665 .48408 .55833 Mtetra .631 .757 .938 r .48408 .55833 .4931 .5665 .50928 .56262 .50032 .55444 Mtetra .63 .757 .939 r .50032 .55444 .50928 .56262 .52557 .55872 .51667 .55054 Mtetra .63 .758 .94 r .51667 .55054 .52557 .55872 .54196 .55481 .53313 .54663 Mtetra .629 .759 .941 r .53313 .54663 .54196 .55481 .55846 .5509 .5497 .54271 Mtetra .628 .76 .942 r .5497 .54271 .55846 .5509 .57507 .54697 .56638 .53878 Mtetra .628 .761 .943 r .56638 .53878 .57507 .54697 .59179 .54303 .58317 .53483 Mtetra .627 .762 .944 r .58317 .53483 .59179 .54303 .60863 .53907 .60008 .53087 Mtetra .626 .763 .944 r .60008 .53087 .60863 .53907 .62557 .5351 .6171 .5269 Mtetra .626 .764 .945 r .6171 .5269 .62557 .5351 .64263 .53111 .63423 .5229 Mtetra .625 .765 .946 r .63423 .5229 .64263 .53111 .65981 .52709 .65149 .51887 Mtetra .625 .766 .947 r .65149 .51887 .65981 .52709 .67711 .52305 .66886 .51483 Mtetra .625 .767 .948 r .66886 .51483 .67711 .52305 .69452 .51898 .68635 .51075 Mtetra .625 .768 .949 r .68635 .51075 .69452 .51898 .71205 .51488 .70397 .50663 Mtetra .625 .769 .949 r .70397 .50663 .71205 .51488 .7297 .51074 .7217 .50248 Mtetra .625 .77 .95 r .7217 .50248 .7297 .51074 .74747 .50656 .73956 .49829 Mtetra .625 .771 .95 r .73956 .49829 .74747 .50656 .76536 .50234 .75754 .49405 Mtetra .625 .772 .951 r .75754 .49405 .76536 .50234 .78338 .49807 .77564 .48976 Mtetra .626 .773 .951 r .77564 .48976 .78338 .49807 .80152 .49375 .79387 .48541 Mtetra .627 .774 .951 r .79387 .48541 .80152 .49375 .81978 .48937 .81222 .481 Mtetra .627 .775 .952 r .81222 .481 .81978 .48937 .83816 .48493 .8307 .47652 Mtetra .629 .776 .952 r .8307 .47652 .83816 .48493 .85667 .48041 .84931 .47196 Mtetra .63 .777 .952 r .84931 .47196 .85667 .48041 .87531 .47583 .86803 .46732 Mtetra .631 .778 .951 r .86803 .46732 .87531 .47583 .89406 .47116 .88689 .4626 Mtetra .633 .779 .951 r .88689 .4626 .89406 .47116 .91295 .4664 .90587 .45778 Mtetra .635 .779 .95 r .90587 .45778 .91295 .4664 .93195 .46156 .92497 .45285 Mtetra .637 .78 .95 r .92497 .45285 .93195 .46156 .95108 .45661 .94419 .44782 Mtetra .636 .751 .931 r .34824 .58117 .35783 .58933 .37326 .58547 .36373 .5773 Mtetra .635 .752 .932 r .36373 .5773 .37326 .58547 .38879 .5816 .37931 .57342 Mtetra .635 .753 .933 r .37931 .57342 .38879 .5816 .40442 .57773 .39499 .56954 Mtetra .634 .753 .934 r .39499 .56954 .40442 .57773 .42015 .57386 .41078 .56566 Mtetra .633 .754 .935 r .41078 .56566 .42015 .57386 .43598 .56998 .42667 .56178 Mtetra .632 .755 .936 r .42667 .56178 .43598 .56998 .45191 .56611 .44265 .5579 Mtetra .631 .756 .937 r .44265 .5579 .45191 .56611 .46794 .56222 .45875 .55401 Mtetra .63 .756 .938 r .45875 .55401 .46794 .56222 .48408 .55833 .47495 .55012 Mtetra .629 .757 .939 r .47495 .55012 .48408 .55833 .50032 .55444 .49126 .54622 Mtetra .629 .758 .94 r .49126 .54622 .50032 .55444 .51667 .55054 .50767 .54232 Mtetra .628 .759 .941 r .50767 .54232 .51667 .55054 .53313 .54663 .5242 .53841 Mtetra .627 .76 .942 r .5242 .53841 .53313 .54663 .5497 .54271 .54083 .53449 Mtetra .626 .761 .943 r .54083 .53449 .5497 .54271 .56638 .53878 .55758 .53055 Mtetra .626 .762 .944 r .55758 .53055 .56638 .53878 .58317 .53483 .57445 .52661 Mtetra .625 .763 .945 r .57445 .52661 .58317 .53483 .60008 .53087 .59142 .52265 Mtetra .624 .764 .946 r .59142 .52265 .60008 .53087 .6171 .5269 .60852 .51867 Mtetra .624 .765 .947 r .60852 .51867 .6171 .5269 .63423 .5229 .62573 .51467 Mtetra .624 .766 .948 r .62573 .51467 .63423 .5229 .65149 .51887 .64306 .51064 Mtetra .623 .767 .949 r .64306 .51064 .65149 .51887 .66886 .51483 .66052 .50659 Mtetra .623 .769 .95 r .66052 .50659 .66886 .51483 .68635 .51075 .67809 .5025 Mtetra .623 .77 .95 r .67809 .5025 .68635 .51075 .70397 .50663 .69579 .49838 Mtetra .623 .771 .951 r .69579 .49838 .70397 .50663 .7217 .50248 .71361 .49422 Mtetra .623 .772 .952 r .71361 .49422 .7217 .50248 .73956 .49829 .73155 .49001 Mtetra .623 .773 .952 r .73155 .49001 .73956 .49829 .75754 .49405 .74962 .48575 Mtetra .624 .774 .953 r .74962 .48575 .75754 .49405 .77564 .48976 .76781 .48144 Mtetra .624 .775 .953 r .76781 .48144 .77564 .48976 .79387 .48541 .78613 .47706 Mtetra .625 .776 .953 r .78613 .47706 .79387 .48541 .81222 .481 .80458 .47261 Mtetra .626 .777 .953 r .80458 .47261 .81222 .481 .8307 .47652 .82315 .46809 Mtetra .628 .778 .953 r .82315 .46809 .8307 .47652 .84931 .47196 .84185 .46349 Mtetra .629 .779 .953 r .84185 .46349 .84931 .47196 .86803 .46732 .86068 .4588 Mtetra .631 .78 .953 r .86068 .4588 .86803 .46732 .88689 .4626 .87963 .45401 Mtetra .633 .781 .952 r .87963 .45401 .88689 .4626 .90587 .45778 .8987 .44911 Mtetra .635 .781 .952 r .8987 .44911 .90587 .45778 .92497 .45285 .9179 .44411 Mtetra .637 .782 .951 r .9179 .44411 .92497 .45285 .94419 .44782 .93723 .43898 Mtetra .635 .752 .932 r .33854 .57296 .34824 .58117 .36373 .5773 .35408 .56907 Mtetra .634 .752 .933 r .35408 .56907 .36373 .5773 .37931 .57342 .36972 .56519 Mtetra .633 .753 .934 r .36972 .56519 .37931 .57342 .39499 .56954 .38546 .5613 Mtetra .632 .754 .935 r .38546 .5613 .39499 .56954 .41078 .56566 .4013 .55742 Mtetra .631 .755 .936 r .4013 .55742 .41078 .56566 .42667 .56178 .41725 .55353 Mtetra .63 .755 .937 r .41725 .55353 .42667 .56178 .44265 .5579 .43329 .54964 Mtetra .63 .756 .938 r .43329 .54964 .44265 .5579 .45875 .55401 .44945 .54575 Mtetra .629 .757 .939 r .44945 .54575 .45875 .55401 .47495 .55012 .46571 .54186 Mtetra .628 .758 .941 r .46571 .54186 .47495 .55012 .49126 .54622 .48208 .53796 Mtetra .627 .759 .942 r .48208 .53796 .49126 .54622 .50767 .54232 .49856 .53406 Mtetra .626 .76 .943 r .49856 .53406 .50767 .54232 .5242 .53841 .51516 .53015 Mtetra .625 .761 .944 r .51516 .53015 .5242 .53841 .54083 .53449 .53186 .52623 Mtetra .624 .762 .945 r .53186 .52623 .54083 .53449 .55758 .53055 .54868 .5223 Mtetra .624 .763 .946 r .54868 .5223 .55758 .53055 .57445 .52661 .56562 .51836 Mtetra .623 .764 .947 r .56562 .51836 .57445 .52661 .59142 .52265 .58267 .5144 Mtetra .622 .765 .948 r .58267 .5144 .59142 .52265 .60852 .51867 .59984 .51042 Mtetra .622 .767 .949 r .59984 .51042 .60852 .51867 .62573 .51467 .61713 .50642 Mtetra .621 .768 .95 r .61713 .50642 .62573 .51467 .64306 .51064 .63454 .5024 Mtetra .621 .769 .951 r .63454 .5024 .64306 .51064 .66052 .50659 .65207 .49834 Mtetra .621 .77 .952 r .65207 .49834 .66052 .50659 .67809 .5025 .66973 .49425 Mtetra .621 .771 .952 r .66973 .49425 .67809 .5025 .69579 .49838 .68751 .49012 Mtetra .621 .773 .953 r .68751 .49012 .69579 .49838 .71361 .49422 .70542 .48595 Mtetra .621 .774 .954 r .70542 .48595 .71361 .49422 .73155 .49001 .72345 .48173 Mtetra .621 .775 .954 r .72345 .48173 .73155 .49001 .74962 .48575 .74161 .47745 Mtetra .622 .776 .955 r .74161 .47745 .74962 .48575 .76781 .48144 .75989 .47311 Mtetra .623 .777 .955 r .75989 .47311 .76781 .48144 .78613 .47706 .77831 .46871 Mtetra .624 .778 .955 r .77831 .46871 .78613 .47706 .80458 .47261 .79685 .46422 Mtetra .625 .779 .955 r .79685 .46422 .80458 .47261 .82315 .46809 .81551 .45966 Mtetra .627 .78 .955 r .81551 .45966 .82315 .46809 .84185 .46349 .83431 .455 Mtetra .628 .781 .955 r .83431 .455 .84185 .46349 .86068 .4588 .85323 .45025 Mtetra .63 .782 .954 r .85323 .45025 .86068 .4588 .87963 .45401 .87228 .44539 Mtetra .632 .783 .954 r .87228 .44539 .87963 .45401 .8987 .44911 .89146 .44041 Mtetra .635 .783 .953 r .89146 .44041 .8987 .44911 .9179 .44411 .91075 .43532 Mtetra .638 .784 .952 r .91075 .43532 .9179 .44411 .93723 .43898 .93018 .43009 Mtetra .634 .752 .933 r .32873 .56468 .33854 .57296 .35408 .56907 .34432 .56079 Mtetra .633 .753 .934 r .34432 .56079 .35408 .56907 .36972 .56519 .36002 .5569 Mtetra .632 .754 .935 r .36002 .5569 .36972 .56519 .38546 .5613 .37581 .55301 Mtetra .631 .754 .937 r .37581 .55301 .38546 .5613 .4013 .55742 .39171 .54912 Mtetra .63 .755 .938 r .39171 .54912 .4013 .55742 .41725 .55353 .40772 .54523 Mtetra .629 .756 .939 r .40772 .54523 .41725 .55353 .43329 .54964 .42382 .54134 Mtetra .628 .757 .94 r .42382 .54134 .43329 .54964 .44945 .54575 .44004 .53746 Mtetra .627 .758 .941 r .44004 .53746 .44945 .54575 .46571 .54186 .45637 .53357 Mtetra .626 .759 .942 r .45637 .53357 .46571 .54186 .48208 .53796 .4728 .52967 Mtetra .625 .76 .943 r .4728 .52967 .48208 .53796 .49856 .53406 .48935 .52578 Mtetra .624 .761 .944 r .48935 .52578 .49856 .53406 .51516 .53015 .50601 .52187 Mtetra .623 .762 .946 r .50601 .52187 .51516 .53015 .53186 .52623 .52278 .51796 Mtetra .622 .763 .947 r .52278 .51796 .53186 .52623 .54868 .5223 .53967 .51403 Mtetra .621 .764 .948 r .53967 .51403 .54868 .5223 .56562 .51836 .55668 .5101 Mtetra .621 .766 .949 r .55668 .5101 .56562 .51836 .58267 .5144 .57381 .50614 Mtetra .62 .767 .95 r .57381 .50614 .58267 .5144 .59984 .51042 .59105 .50217 Mtetra .619 .768 .951 r .59105 .50217 .59984 .51042 .61713 .50642 .60842 .49817 Mtetra .619 .769 .952 r .60842 .49817 .61713 .50642 .63454 .5024 .62591 .49415 Mtetra .619 .771 .953 r .62591 .49415 .63454 .5024 .65207 .49834 .64353 .4901 Mtetra .619 .772 .954 r .64353 .4901 .65207 .49834 .66973 .49425 .66127 .486 Mtetra .618 .773 .955 r .66127 .486 .66973 .49425 .68751 .49012 .67914 .48187 Mtetra .619 .774 .955 r .67914 .48187 .68751 .49012 .70542 .48595 .69713 .47769 Mtetra .619 .776 .956 r .69713 .47769 .70542 .48595 .72345 .48173 .71525 .47345 Mtetra .62 .777 .956 r .71525 .47345 .72345 .48173 .74161 .47745 .7335 .46916 Mtetra .62 .778 .957 r .7335 .46916 .74161 .47745 .75989 .47311 .75188 .46479 Mtetra .621 .779 .957 r .75188 .46479 .75989 .47311 .77831 .46871 .77038 .46035 Mtetra .622 .781 .957 r .77038 .46035 .77831 .46871 .79685 .46422 .78902 .45583 Mtetra .624 .782 .957 r .78902 .45583 .79685 .46422 .81551 .45966 .80778 .45122 Mtetra .626 .783 .957 r .80778 .45122 .81551 .45966 .83431 .455 .82668 .44651 Mtetra .628 .784 .956 r .82668 .44651 .83431 .455 .85323 .45025 .8457 .44168 Mtetra .63 .784 .956 r .8457 .44168 .85323 .45025 .87228 .44539 .86485 .43675 Mtetra .633 .785 .955 r .86485 .43675 .87228 .44539 .89146 .44041 .88412 .43168 Mtetra .635 .786 .954 r .88412 .43168 .89146 .44041 .91075 .43532 .90352 .42648 Mtetra .638 .786 .952 r .90352 .42648 .91075 .43532 .93018 .43009 .92304 .42113 Mtetra .632 .752 .934 r .3188 .55634 .32873 .56468 .34432 .56079 .33445 .55244 Mtetra .631 .753 .936 r .33445 .55244 .34432 .56079 .36002 .5569 .3502 .54855 Mtetra .63 .754 .937 r .3502 .54855 .36002 .5569 .37581 .55301 .36605 .54466 Mtetra .629 .755 .938 r .36605 .54466 .37581 .55301 .39171 .54912 .38201 .54077 Mtetra .628 .756 .939 r .38201 .54077 .39171 .54912 .40772 .54523 .39807 .53689 Mtetra .627 .757 .94 r .39807 .53689 .40772 .54523 .42382 .54134 .41424 .533 Mtetra .626 .758 .941 r .41424 .533 .42382 .54134 .44004 .53746 .43052 .52912 Mtetra .625 .759 .943 r .43052 .52912 .44004 .53746 .45637 .53357 .44691 .52524 Mtetra .624 .76 .944 r .44691 .52524 .45637 .53357 .4728 .52967 .46341 .52135 Mtetra .623 .761 .945 r .46341 .52135 .4728 .52967 .48935 .52578 .48002 .51746 Mtetra .622 .762 .946 r .48002 .51746 .48935 .52578 .50601 .52187 .49675 .51357 Mtetra .621 .763 .947 r .49675 .51357 .50601 .52187 .52278 .51796 .51359 .50966 Mtetra .62 .764 .949 r .51359 .50966 .52278 .51796 .53967 .51403 .53055 .50575 Mtetra .619 .766 .95 r .53055 .50575 .53967 .51403 .55668 .5101 .54764 .50182 Mtetra .618 .767 .951 r .54764 .50182 .55668 .5101 .57381 .50614 .56484 .49788 Mtetra .617 .768 .952 r .56484 .49788 .57381 .50614 .59105 .50217 .58216 .49392 Mtetra .617 .77 .953 r .58216 .49392 .59105 .50217 .60842 .49817 .59961 .48993 Mtetra .616 .771 .954 r .59961 .48993 .60842 .49817 .62591 .49415 .61718 .48591 Mtetra .616 .772 .955 r .61718 .48591 .62591 .49415 .64353 .4901 .63488 .48186 Mtetra .616 .774 .956 r .63488 .48186 .64353 .4901 .66127 .486 .6527 .47777 Mtetra .616 .775 .957 r .6527 .47777 .66127 .486 .67914 .48187 .67066 .47363 Mtetra .616 .777 .958 r .67066 .47363 .67914 .48187 .69713 .47769 .68874 .46944 Mtetra .617 .778 .958 r .68874 .46944 .69713 .47769 .71525 .47345 .70695 .46519 Mtetra .617 .779 .959 r .70695 .46519 .71525 .47345 .7335 .46916 .72529 .46087 Mtetra .618 .781 .959 r .72529 .46087 .7335 .46916 .75188 .46479 .74376 .45648 Mtetra .62 .782 .959 r .74376 .45648 .75188 .46479 .77038 .46035 .76237 .45201 Mtetra .621 .783 .959 r .76237 .45201 .77038 .46035 .78902 .45583 .7811 .44744 Mtetra .623 .784 .959 r .7811 .44744 .78902 .45583 .80778 .45122 .79996 .44278 Mtetra .625 .785 .959 r .79996 .44278 .80778 .45122 .82668 .44651 .81895 .438 Mtetra .627 .786 .958 r .81895 .438 .82668 .44651 .8457 .44168 .83807 .4331 Mtetra .63 .787 .957 r .83807 .4331 .8457 .44168 .86485 .43675 .85732 .42808 Mtetra .633 .787 .956 r .85732 .42808 .86485 .43675 .88412 .43168 .87669 .42291 Mtetra .636 .788 .955 r .87669 .42291 .88412 .43168 .90352 .42648 .89619 .41759 Mtetra .64 .788 .953 r .89619 .41759 .90352 .42648 .92304 .42113 .91581 .41211 Mtetra .631 .753 .936 r .30876 .54794 .3188 .55634 .33445 .55244 .32447 .54405 Mtetra .629 .754 .937 r .32447 .54405 .33445 .55244 .3502 .54855 .34027 .54015 Mtetra .628 .755 .938 r .34027 .54015 .3502 .54855 .36605 .54466 .35618 .53627 Mtetra .627 .756 .939 r .35618 .53627 .36605 .54466 .38201 .54077 .37219 .53238 Mtetra .626 .756 .94 r .37219 .53238 .38201 .54077 .39807 .53689 .38831 .5285 Mtetra .625 .758 .942 r .38831 .5285 .39807 .53689 .41424 .533 .40454 .52463 Mtetra .624 .759 .943 r .40454 .52463 .41424 .533 .43052 .52912 .42088 .52075 Mtetra .622 .76 .944 r .42088 .52075 .43052 .52912 .44691 .52524 .43733 .51688 Mtetra .621 .761 .946 r .43733 .51688 .44691 .52524 .46341 .52135 .4539 .51301 Mtetra .62 .762 .947 r .4539 .51301 .46341 .52135 .48002 .51746 .47058 .50913 Mtetra .619 .763 .948 r .47058 .50913 .48002 .51746 .49675 .51357 .48737 .50525 Mtetra .618 .764 .95 r .48737 .50525 .49675 .51357 .51359 .50966 .50429 .50136 Mtetra .617 .766 .951 r .50429 .50136 .51359 .50966 .53055 .50575 .52132 .49746 Mtetra .616 .767 .952 r .52132 .49746 .53055 .50575 .54764 .50182 .53848 .49355 Mtetra .615 .769 .953 r .53848 .49355 .54764 .50182 .56484 .49788 .55576 .48962 Mtetra .615 .77 .955 r .55576 .48962 .56484 .49788 .58216 .49392 .57316 .48567 Mtetra .614 .771 .956 r .57316 .48567 .58216 .49392 .59961 .48993 .59069 .48169 Mtetra .614 .773 .957 r .59069 .48169 .59961 .48993 .61718 .48591 .60834 .47768 Mtetra .613 .774 .958 r .60834 .47768 .61718 .48591 .63488 .48186 .62612 .47364 Mtetra .613 .776 .959 r .62612 .47364 .63488 .48186 .6527 .47777 .64403 .46955 Mtetra .613 .777 .959 r .64403 .46955 .6527 .47777 .67066 .47363 .66207 .46541 Mtetra .614 .779 .96 r .66207 .46541 .67066 .47363 .68874 .46944 .68025 .46121 Mtetra .614 .78 .961 r .68025 .46121 .68874 .46944 .70695 .46519 .69855 .45695 Mtetra .615 .782 .961 r .69855 .45695 .70695 .46519 .72529 .46087 .71698 .45261 Mtetra .616 .783 .961 r .71698 .45261 .72529 .46087 .74376 .45648 .73555 .44819 Mtetra .618 .784 .961 r .73555 .44819 .74376 .45648 .76237 .45201 .75425 .44368 Mtetra .62 .786 .961 r .75425 .44368 .76237 .45201 .7811 .44744 .77308 .43907 Mtetra .622 .787 .961 r .77308 .43907 .7811 .44744 .79996 .44278 .79204 .43434 Mtetra .624 .788 .96 r .79204 .43434 .79996 .44278 .81895 .438 .81113 .42949 Mtetra .627 .789 .959 r .81113 .42949 .81895 .438 .83807 .4331 .83035 .42451 Mtetra .63 .789 .958 r .83035 .42451 .83807 .4331 .85732 .42808 .8497 .41938 Mtetra .634 .79 .957 r .8497 .41938 .85732 .42808 .87669 .42291 .86917 .4141 Mtetra .637 .79 .955 r .86917 .4141 .87669 .42291 .89619 .41759 .88877 .40865 Mtetra .641 .79 .954 r .88877 .40865 .89619 .41759 .91581 .41211 .90849 .40302 Mtetra .629 .753 .937 r .29861 .53949 .30876 .54794 .32447 .54405 .31436 .5356 Mtetra .628 .754 .938 r .31436 .5356 .32447 .54405 .34027 .54015 .33022 .53171 Mtetra .626 .755 .939 r .33022 .53171 .34027 .54015 .35618 .53627 .34619 .52783 Mtetra .625 .756 .941 r .34619 .52783 .35618 .53627 .37219 .53238 .36226 .52395 Mtetra .624 .757 .942 r .36226 .52395 .37219 .53238 .38831 .5285 .37844 .52008 Mtetra .623 .758 .943 r .37844 .52008 .38831 .5285 .40454 .52463 .39473 .51622 Mtetra .621 .759 .945 r .39473 .51622 .40454 .52463 .42088 .52075 .41113 .51236 Mtetra .62 .761 .946 r .41113 .51236 .42088 .52075 .43733 .51688 .42764 .5085 Mtetra .619 .762 .948 r .42764 .5085 .43733 .51688 .4539 .51301 .44427 .50464 Mtetra .617 .763 .949 r .44427 .50464 .4539 .51301 .47058 .50913 .46102 .50079 Mtetra .616 .764 .95 r .46102 .50079 .47058 .50913 .48737 .50525 .47788 .49693 Mtetra .615 .766 .952 r .47788 .49693 .48737 .50525 .50429 .50136 .49487 .49306 Mtetra .614 .767 .953 r .49487 .49306 .50429 .50136 .52132 .49746 .51198 .48918 Mtetra .613 .769 .955 r .51198 .48918 .52132 .49746 .53848 .49355 .52921 .48529 Mtetra .612 .77 .956 r .52921 .48529 .53848 .49355 .55576 .48962 .54656 .48137 Mtetra .611 .772 .957 r .54656 .48137 .55576 .48962 .57316 .48567 .56404 .47744 Mtetra .611 .773 .958 r .56404 .47744 .57316 .48567 .59069 .48169 .58165 .47348 Mtetra .61 .775 .959 r .58165 .47348 .59069 .48169 .60834 .47768 .59939 .46948 Mtetra .61 .777 .96 r .59939 .46948 .60834 .47768 .62612 .47364 .61725 .46545 Mtetra .61 .778 .961 r .61725 .46545 .62612 .47364 .64403 .46955 .63525 .46136 Mtetra .61 .78 .962 r .63525 .46136 .64403 .46955 .66207 .46541 .65338 .45722 Mtetra .611 .781 .963 r .65338 .45722 .66207 .46541 .68025 .46121 .67165 .45302 Mtetra .612 .783 .963 r .67165 .45302 .68025 .46121 .69855 .45695 .69004 .44874 Mtetra .613 .784 .964 r .69004 .44874 .69855 .45695 .71698 .45261 .70857 .44438 Mtetra .614 .786 .964 r .70857 .44438 .71698 .45261 .73555 .44819 .72724 .43993 Mtetra .616 .787 .964 r .72724 .43993 .73555 .44819 .75425 .44368 .74603 .43538 Mtetra .618 .789 .963 r .74603 .43538 .75425 .44368 .77308 .43907 .76496 .43071 Mtetra .621 .79 .963 r .76496 .43071 .77308 .43907 .79204 .43434 .78402 .42591 Mtetra .624 .791 .962 r .78402 .42591 .79204 .43434 .81113 .42949 .80321 .42098 Mtetra .627 .792 .961 r .80321 .42098 .81113 .42949 .83035 .42451 .82253 .4159 Mtetra .631 .792 .96 r .82253 .4159 .83035 .42451 .8497 .41938 .84198 .41065 Mtetra .635 .793 .958 r .84198 .41065 .8497 .41938 .86917 .4141 .86156 .40523 Mtetra .639 .793 .956 r .86156 .40523 .86917 .4141 .88877 .40865 .88126 .39963 Mtetra .644 .793 .954 r .88126 .39963 .88877 .40865 .90849 .40302 .90107 .39383 Mtetra .627 .754 .938 r .28833 .53099 .29861 .53949 .31436 .5356 .30414 .5271 Mtetra .626 .755 .94 r .30414 .5271 .31436 .5356 .33022 .53171 .32005 .52322 Mtetra .624 .756 .941 r .32005 .52322 .33022 .53171 .34619 .52783 .33607 .51934 Mtetra .623 .757 .942 r .33607 .51934 .34619 .52783 .36226 .52395 .3522 .51548 Mtetra .621 .758 .944 r .3522 .51548 .36226 .52395 .37844 .52008 .36844 .51163 Mtetra .62 .759 .945 r .36844 .51163 .37844 .52008 .39473 .51622 .38479 .50778 Mtetra .619 .76 .947 r .38479 .50778 .39473 .51622 .41113 .51236 .40125 .50394 Mtetra .617 .762 .948 r .40125 .50394 .41113 .51236 .42764 .5085 .41783 .50011 Mtetra .616 .763 .95 r .41783 .50011 .42764 .5085 .44427 .50464 .43453 .49627 Mtetra .614 .764 .951 r .43453 .49627 .44427 .50464 .46102 .50079 .45134 .49244 Mtetra .613 .766 .953 r .45134 .49244 .46102 .50079 .47788 .49693 .46827 .4886 Mtetra .612 .767 .954 r .46827 .4886 .47788 .49693 .49487 .49306 .48533 .48476 Mtetra .611 .769 .956 r .48533 .48476 .49487 .49306 .51198 .48918 .50251 .48091 Mtetra .61 .77 .957 r .50251 .48091 .51198 .48918 .52921 .48529 .51982 .47704 Mtetra .609 .772 .958 r .51982 .47704 .52921 .48529 .54656 .48137 .53725 .47316 Mtetra .608 .774 .96 r .53725 .47316 .54656 .48137 .56404 .47744 .55481 .46924 Mtetra .607 .775 .961 r .55481 .46924 .56404 .47744 .58165 .47348 .5725 .4653 Mtetra .607 .777 .962 r .5725 .4653 .58165 .47348 .59939 .46948 .59032 .46132 Mtetra .607 .779 .963 r .59032 .46132 .59939 .46948 .61725 .46545 .60827 .4573 Mtetra .607 .781 .964 r .60827 .4573 .61725 .46545 .63525 .46136 .62636 .45322 Mtetra .607 .782 .965 r .62636 .45322 .63525 .46136 .65338 .45722 .64458 .44908 Mtetra .608 .784 .965 r .64458 .44908 .65338 .45722 .67165 .45302 .66294 .44487 Mtetra .609 .786 .966 r .66294 .44487 .67165 .45302 .69004 .44874 .68143 .44058 Mtetra .61 .787 .966 r .68143 .44058 .69004 .44874 .70857 .44438 .70006 .4362 Mtetra .612 .789 .966 r .70006 .4362 .70857 .44438 .72724 .43993 .71882 .43171 Mtetra .614 .79 .966 r .71882 .43171 .72724 .43993 .74603 .43538 .73771 .4271 Mtetra .617 .792 .966 r .73771 .4271 .74603 .43538 .76496 .43071 .75674 .42237 Mtetra .62 .793 .965 r .75674 .42237 .76496 .43071 .78402 .42591 .7759 .41749 Mtetra .624 .794 .964 r .7759 .41749 .78402 .42591 .80321 .42098 .7952 .41246 Mtetra .628 .795 .962 r .7952 .41246 .80321 .42098 .82253 .4159 .81462 .40727 Mtetra .632 .795 .961 r .81462 .40727 .82253 .4159 .84198 .41065 .83417 .40189 Mtetra .637 .795 .959 r .83417 .40189 .84198 .41065 .86156 .40523 .85384 .39631 Mtetra .641 .795 .956 r .85384 .39631 .86156 .40523 .88126 .39963 .87364 .39053 Mtetra .647 .795 .954 r .87364 .39053 .88126 .39963 .90107 .39383 .89356 .38453 Mtetra .625 .754 .94 r .27793 .52243 .28833 .53099 .30414 .5271 .29379 .51855 Mtetra .623 .755 .941 r .29379 .51855 .30414 .5271 .32005 .52322 .30976 .51468 Mtetra .622 .757 .943 r .30976 .51468 .32005 .52322 .33607 .51934 .32583 .51083 Mtetra .62 .758 .944 r .32583 .51083 .33607 .51934 .3522 .51548 .34202 .50698 Mtetra .619 .759 .946 r .34202 .50698 .3522 .51548 .36844 .51163 .35832 .50315 Mtetra .617 .76 .947 r .35832 .50315 .36844 .51163 .38479 .50778 .37473 .49933 Mtetra .616 .762 .949 r .37473 .49933 .38479 .50778 .40125 .50394 .39125 .49551 Mtetra .614 .763 .95 r .39125 .49551 .40125 .50394 .41783 .50011 .40789 .49171 Mtetra .612 .764 .952 r .40789 .49171 .41783 .50011 .43453 .49627 .42466 .4879 Mtetra .611 .766 .954 r .42466 .4879 .43453 .49627 .45134 .49244 .44154 .4841 Mtetra .61 .767 .955 r .44154 .4841 .45134 .49244 .46827 .4886 .45854 .4803 Mtetra .608 .769 .957 r .45854 .4803 .46827 .4886 .48533 .48476 .47567 .47649 Mtetra .607 .771 .958 r .47567 .47649 .48533 .48476 .50251 .48091 .49292 .47267 Mtetra .606 .772 .96 r .49292 .47267 .50251 .48091 .51982 .47704 .5103 .46883 Mtetra .605 .774 .961 r .5103 .46883 .51982 .47704 .53725 .47316 .52781 .46498 Mtetra .604 .776 .963 r .52781 .46498 .53725 .47316 .55481 .46924 .54546 .46109 Mtetra .603 .778 .964 r .54546 .46109 .55481 .46924 .5725 .4653 .56323 .45718 Mtetra .603 .78 .965 r .56323 .45718 .5725 .4653 .59032 .46132 .58114 .45322 Mtetra .603 .782 .966 r .58114 .45322 .59032 .46132 .60827 .4573 .59918 .44921 Mtetra .603 .783 .967 r .59918 .44921 .60827 .4573 .62636 .45322 .61736 .44515 Mtetra .604 .785 .968 r .61736 .44515 .62636 .45322 .64458 .44908 .63567 .44101 Mtetra .605 .787 .968 r .63567 .44101 .64458 .44908 .66294 .44487 .65412 .43679 Mtetra .606 .789 .969 r .65412 .43679 .66294 .44487 .68143 .44058 .67271 .43248 Mtetra .608 .791 .969 r .67271 .43248 .68143 .44058 .70006 .4362 .69143 .42807 Mtetra .61 .792 .969 r .69143 .42807 .70006 .4362 .71882 .43171 .71029 .42353 Mtetra .613 .794 .968 r .71029 .42353 .71882 .43171 .73771 .4271 .72929 .41887 Mtetra .616 .795 .968 r .72929 .41887 .73771 .4271 .75674 .42237 .74842 .41406 Mtetra .62 .796 .967 r .74842 .41406 .75674 .42237 .7759 .41749 .76768 .40909 Mtetra .624 .797 .965 r .76768 .40909 .7759 .41749 .7952 .41246 .78708 .40395 Mtetra .629 .798 .964 r .78708 .40395 .7952 .41246 .81462 .40727 .8066 .39861 Mtetra .634 .798 .962 r .8066 .39861 .81462 .40727 .83417 .40189 .82625 .39308 Mtetra .639 .798 .959 r .82625 .39308 .83417 .40189 .85384 .39631 .84603 .38732 Mtetra .645 .798 .956 r .84603 .38732 .85384 .39631 .87364 .39053 .86592 .38133 Mtetra .65 .797 .953 r .86592 .38133 .87364 .39053 .89356 .38453 .88593 .3751 Mtetra .623 .755 .941 r .2674 .51382 .27793 .52243 .29379 .51855 .28331 .50996 Mtetra .621 .756 .943 r .28331 .50996 .29379 .51855 .30976 .51468 .29934 .50611 Mtetra .619 .757 .944 r .29934 .50611 .30976 .51468 .32583 .51083 .31547 .50228 Mtetra .617 .759 .946 r .31547 .50228 .32583 .51083 .34202 .50698 .33171 .49846 Mtetra .616 .76 .948 r .33171 .49846 .34202 .50698 .35832 .50315 .34807 .49466 Mtetra .614 .761 .949 r .34807 .49466 .35832 .50315 .37473 .49933 .36454 .49086 Mtetra .612 .763 .951 r .36454 .49086 .37473 .49933 .39125 .49551 .38112 .48708 Mtetra .611 .764 .953 r .38112 .48708 .39125 .49551 .40789 .49171 .39783 .48331 Mtetra .609 .766 .955 r .39783 .48331 .40789 .49171 .42466 .4879 .41466 .47954 Mtetra .607 .767 .956 r .41466 .47954 .42466 .4879 .44154 .4841 .43161 .47578 Mtetra .606 .769 .958 r .43161 .47578 .44154 .4841 .45854 .4803 .44868 .47201 Mtetra .604 .771 .96 r .44868 .47201 .45854 .4803 .47567 .47649 .46588 .46824 Mtetra .603 .773 .961 r .46588 .46824 .47567 .47649 .49292 .47267 .48321 .46447 Mtetra .601 .775 .963 r .48321 .46447 .49292 .47267 .5103 .46883 .50067 .46067 Mtetra .6 .776 .965 r .50067 .46067 .5103 .46883 .52781 .46498 .51826 .45685 Mtetra .599 .778 .966 r .51826 .45685 .52781 .46498 .54546 .46109 .53598 .45301 Mtetra .599 .78 .967 r .53598 .45301 .54546 .46109 .56323 .45718 .55384 .44912 Mtetra .599 .782 .968 r .55384 .44912 .56323 .45718 .58114 .45322 .57183 .44519 Mtetra .599 .785 .969 r .57183 .44519 .58114 .45322 .59918 .44921 .58996 .4412 Mtetra .599 .787 .97 r .58996 .4412 .59918 .44921 .61736 .44515 .60823 .43715 Mtetra .6 .789 .971 r .60823 .43715 .61736 .44515 .63567 .44101 .62664 .43301 Mtetra .601 .791 .971 r .62664 .43301 .63567 .44101 .65412 .43679 .64518 .42879 Mtetra .603 .793 .972 r .64518 .42879 .65412 .43679 .67271 .43248 .66387 .42445 Mtetra .605 .794 .972 r .66387 .42445 .67271 .43248 .69143 .42807 .68269 .42 Mtetra .608 .796 .971 r .68269 .42 .69143 .42807 .71029 .42353 .70165 .41542 Mtetra .611 .798 .971 r .70165 .41542 .71029 .42353 .72929 .41887 .72075 .41069 Mtetra .615 .799 .97 r .72075 .41069 .72929 .41887 .74842 .41406 .73999 .40579 Mtetra .62 .8 .969 r .73999 .40579 .74842 .41406 .76768 .40909 .75935 .4007 Mtetra .625 .801 .967 r .75935 .4007 .76768 .40909 .78708 .40395 .77885 .39542 Mtetra .63 .801 .965 r .77885 .39542 .78708 .40395 .8066 .39861 .79848 .38993 Mtetra .636 .801 .962 r .79848 .38993 .8066 .39861 .82625 .39308 .81823 .3842 Mtetra .642 .801 .959 r .81823 .3842 .82625 .39308 .84603 .38732 .8381 .37823 Mtetra .649 .8 .956 r .8381 .37823 .84603 .38732 .86592 .38133 .85809 .372 Mtetra .655 .799 .952 r .85809 .372 .86592 .38133 .88593 .3751 .8782 .3655 Mtetra .62 .756 .943 r .25674 .50518 .2674 .51382 .28331 .50996 .27271 .50133 Mtetra .618 .757 .945 r .27271 .50133 .28331 .50996 .29934 .50611 .28878 .49751 Mtetra .616 .758 .946 r .28878 .49751 .29934 .50611 .31547 .50228 .30497 .49371 Mtetra .614 .759 .948 r .30497 .49371 .31547 .50228 .33171 .49846 .32127 .48992 Mtetra .612 .761 .95 r .32127 .48992 .33171 .49846 .34807 .49466 .33768 .48615 Mtetra .61 .762 .952 r .33768 .48615 .34807 .49466 .36454 .49086 .35421 .4824 Mtetra .608 .764 .954 r .35421 .4824 .36454 .49086 .38112 .48708 .37086 .47866 Mtetra .607 .766 .956 r .37086 .47866 .38112 .48708 .39783 .48331 .38763 .47493 Mtetra .605 .767 .958 r .38763 .47493 .39783 .48331 .41466 .47954 .40453 .47121 Mtetra .603 .769 .959 r .40453 .47121 .41466 .47954 .43161 .47578 .42154 .46749 Mtetra .601 .771 .961 r .42154 .46749 .43161 .47578 .44868 .47201 .43869 .46378 Mtetra .599 .773 .963 r .43869 .46378 .44868 .47201 .46588 .46824 .45596 .46006 Mtetra .598 .775 .965 r .45596 .46006 .46588 .46824 .48321 .46447 .47336 .45632 Mtetra .596 .777 .966 r .47336 .45632 .48321 .46447 .50067 .46067 .4909 .45258 Mtetra .595 .779 .968 r .4909 .45258 .50067 .46067 .51826 .45685 .50857 .4488 Mtetra .594 .781 .969 r .50857 .4488 .51826 .45685 .53598 .45301 .52638 .445 Mtetra .594 .783 .971 r .52638 .445 .53598 .45301 .55384 .44912 .54432 .44115 Mtetra .594 .786 .972 r .54432 .44115 .55384 .44912 .57183 .44519 .5624 .43725 Mtetra .594 .788 .973 r .5624 .43725 .57183 .44519 .58996 .4412 .58062 .43329 Mtetra .594 .79 .974 r .58062 .43329 .58996 .4412 .60823 .43715 .59898 .42924 Mtetra .595 .792 .974 r .59898 .42924 .60823 .43715 .62664 .43301 .61749 .42511 Mtetra .597 .794 .975 r .61749 .42511 .62664 .43301 .64518 .42879 .63613 .42087 Mtetra .599 .796 .975 r .63613 .42087 .64518 .42879 .66387 .42445 .65492 .41652 Mtetra .602 .798 .975 r .65492 .41652 .66387 .42445 .68269 .42 .67384 .41202 Mtetra .606 .8 .974 r .67384 .41202 .68269 .42 .70165 .41542 .6929 .40737 Mtetra .61 .802 .973 r .6929 .40737 .70165 .41542 .72075 .41069 .7121 .40255 Mtetra .615 .803 .972 r .7121 .40255 .72075 .41069 .73999 .40579 .73144 .39754 Mtetra .62 .804 .97 r .73144 .39754 .73999 .40579 .75935 .4007 .75091 .39233 Mtetra .626 .805 .968 r .75091 .39233 .75935 .4007 .77885 .39542 .77051 .38688 Mtetra .633 .805 .965 r .77051 .38688 .77885 .39542 .79848 .38993 .79024 .3812 Mtetra .64 .805 .962 r .79024 .3812 .79848 .38993 .81823 .3842 .81009 .37525 Mtetra .647 .804 .958 r .81009 .37525 .81823 .3842 .8381 .37823 .83006 .36902 Mtetra .654 .802 .954 r .83006 .36902 .8381 .37823 .85809 .372 .85015 .3625 Mtetra .661 .8 .949 r .85015 .3625 .85809 .372 .8782 .3655 .87034 .35568 Mtetra .617 .756 .945 r .24595 .49649 .25674 .50518 .27271 .50133 .26197 .49268 Mtetra .615 .758 .947 r .26197 .49268 .27271 .50133 .28878 .49751 .2781 .48889 Mtetra .613 .759 .949 r .2781 .48889 .28878 .49751 .30497 .49371 .29434 .48512 Mtetra .611 .76 .951 r .29434 .48512 .30497 .49371 .32127 .48992 .31069 .48137 Mtetra .609 .762 .953 r .31069 .48137 .32127 .48992 .33768 .48615 .32717 .47765 Mtetra .606 .764 .955 r .32717 .47765 .33768 .48615 .35421 .4824 .34376 .47394 Mtetra .604 .765 .957 r .34376 .47394 .35421 .4824 .37086 .47866 .36047 .47025 Mtetra .602 .767 .959 r .36047 .47025 .37086 .47866 .38763 .47493 .3773 .46658 Mtetra .6 .769 .961 r .3773 .46658 .38763 .47493 .40453 .47121 .39426 .46291 Mtetra .598 .771 .963 r .39426 .46291 .40453 .47121 .42154 .46749 .41135 .45925 Mtetra .596 .773 .965 r .41135 .45925 .42154 .46749 .43869 .46378 .42856 .4556 Mtetra .594 .775 .966 r .42856 .4556 .43869 .46378 .45596 .46006 .44591 .45194 Mtetra .592 .777 .968 r .44591 .45194 .45596 .46006 .47336 .45632 .46338 .44826 Mtetra .591 .779 .97 r .46338 .44826 .47336 .45632 .4909 .45258 .481 .44457 Mtetra .589 .782 .972 r .481 .44457 .4909 .45258 .50857 .4488 .49875 .44086 Mtetra .588 .784 .973 r .49875 .44086 .50857 .4488 .52638 .445 .51664 .4371 Mtetra .588 .787 .975 r .51664 .4371 .52638 .445 .54432 .44115 .53467 .4333 Mtetra .588 .789 .976 r .53467 .4333 .54432 .44115 .5624 .43725 .55284 .42943 Mtetra .588 .791 .977 r .55284 .42943 .5624 .43725 .58062 .43329 .57116 .42549 Mtetra .589 .794 .977 r .57116 .42549 .58062 .43329 .59898 .42924 .58961 .42146 Mtetra .591 .796 .978 r .58961 .42146 .59898 .42924 .61749 .42511 .60821 .41733 Mtetra .593 .798 .978 r .60821 .41733 .61749 .42511 .63613 .42087 .62696 .41308 Mtetra .596 .801 .978 r .62696 .41308 .63613 .42087 .65492 .41652 .64584 .40868 Mtetra .6 .803 .977 r .64584 .40868 .65492 .41652 .67384 .41202 .66487 .40413 Mtetra .604 .805 .977 r .66487 .40413 .67384 .41202 .6929 .40737 .68404 .3994 Mtetra .609 .806 .975 r .68404 .3994 .6929 .40737 .7121 .40255 .70334 .39448 Mtetra .615 .807 .974 r .70334 .39448 .7121 .40255 .73144 .39754 .72278 .38933 Mtetra .622 .808 .972 r .72278 .38933 .73144 .39754 .75091 .39233 .74236 .38395 Mtetra .629 .809 .969 r .74236 .38395 .75091 .39233 .77051 .38688 .76206 .37831 Mtetra .636 .808 .965 r .76206 .37831 .77051 .38688 .79024 .3812 .78189 .37239 Mtetra .644 .808 .962 r .78189 .37239 .79024 .3812 .81009 .37525 .80184 .36618 Mtetra .652 .806 .957 r .80184 .36618 .81009 .37525 .83006 .36902 .82191 .35965 Mtetra .66 .804 .952 r .82191 .35965 .83006 .36902 .85015 .3625 .84208 .35279 Mtetra .668 .801 .946 r .84208 .35279 .85015 .3625 .87034 .35568 .86236 .34559 Mtetra .614 .757 .947 r .23502 .48777 .24595 .49649 .26197 .49268 .25109 .48399 Mtetra .611 .759 .949 r .25109 .48399 .26197 .49268 .2781 .48889 .26727 .48024 Mtetra .609 .76 .951 r .26727 .48024 .2781 .48889 .29434 .48512 .28357 .47652 Mtetra .607 .762 .953 r .28357 .47652 .29434 .48512 .31069 .48137 .29998 .47283 Mtetra .604 .763 .955 r .29998 .47283 .31069 .48137 .32717 .47765 .31651 .46915 Mtetra .602 .765 .957 r .31651 .46915 .32717 .47765 .34376 .47394 .33316 .46551 Mtetra .599 .767 .96 r .33316 .46551 .34376 .47394 .36047 .47025 .34993 .46188 Mtetra .597 .769 .962 r .34993 .46188 .36047 .47025 .3773 .46658 .36683 .45827 Mtetra .594 .771 .964 r .36683 .45827 .3773 .46658 .39426 .46291 .38385 .45467 Mtetra .592 .773 .966 r .38385 .45467 .39426 .46291 .41135 .45925 .40101 .45108 Mtetra .59 .775 .968 r .40101 .45108 .41135 .45925 .42856 .4556 .41829 .4475 Mtetra .588 .777 .97 r .41829 .4475 .42856 .4556 .44591 .45194 .43571 .44391 Mtetra .586 .78 .972 r .43571 .44391 .44591 .45194 .46338 .44826 .45327 .44031 Mtetra .584 .782 .974 r .45327 .44031 .46338 .44826 .481 .44457 .47096 .43669 Mtetra .583 .785 .976 r .47096 .43669 .481 .44457 .49875 .44086 .48879 .43303 Mtetra .582 .787 .977 r .48879 .43303 .49875 .44086 .51664 .4371 .50677 .42933 Mtetra .581 .79 .978 r .50677 .42933 .51664 .4371 .53467 .4333 .52489 .42558 Mtetra .581 .793 .98 r .52489 .42558 .53467 .4333 .55284 .42943 .54315 .42175 Mtetra .582 .795 .98 r .54315 .42175 .55284 .42943 .57116 .42549 .56156 .41784 Mtetra .583 .798 .981 r .56156 .41784 .57116 .42549 .58961 .42146 .58011 .41383 Mtetra .586 .8 .981 r .58011 .41383 .58961 .42146 .60821 .41733 .59881 .40969 Mtetra .589 .803 .981 r .59881 .40969 .60821 .41733 .62696 .41308 .61765 .40541 Mtetra .593 .805 .981 r .61765 .40541 .62696 .41308 .64584 .40868 .63664 .40097 Mtetra .597 .808 .98 r .63664 .40097 .64584 .40868 .66487 .40413 .65578 .39635 Mtetra .603 .809 .979 r .65578 .39635 .66487 .40413 .68404 .3994 .67505 .39152 Mtetra .609 .811 .978 r .67505 .39152 .68404 .3994 .70334 .39448 .69446 .38646 Mtetra .617 .812 .975 r .69446 .38646 .70334 .39448 .72278 .38933 .71401 .38115 Mtetra .624 .813 .973 r .71401 .38115 .72278 .38933 .74236 .38395 .73369 .37556 Mtetra .633 .813 .969 r .73369 .37556 .74236 .38395 .76206 .37831 .75349 .36968 Mtetra .642 .812 .965 r .75349 .36968 .76206 .37831 .78189 .37239 .77342 .36348 Mtetra .651 .811 .96 r .77342 .36348 .78189 .37239 .80184 .36618 .79347 .35694 Mtetra .659 .808 .955 r .79347 .35694 .80184 .36618 .82191 .35965 .81362 .35005 Mtetra .668 .805 .948 r .81362 .35005 .82191 .35965 .84208 .35279 .83389 .34279 Mtetra .677 .801 .942 r .83389 .34279 .84208 .35279 .86236 .34559 .85425 .33515 Mtetra .61 .758 .949 r .22395 .47903 .23502 .48777 .25109 .48399 .24007 .4753 Mtetra .607 .759 .951 r .24007 .4753 .25109 .48399 .26727 .48024 .25631 .4716 Mtetra .605 .761 .954 r .25631 .4716 .26727 .48024 .28357 .47652 .27265 .46793 Mtetra .602 .763 .956 r .27265 .46793 .28357 .47652 .29998 .47283 .28912 .46429 Mtetra .599 .765 .958 r .28912 .46429 .29998 .47283 .31651 .46915 .30571 .46069 Mtetra .596 .767 .961 r .30571 .46069 .31651 .46915 .33316 .46551 .32241 .45711 Mtetra .594 .769 .963 r .32241 .45711 .33316 .46551 .34993 .46188 .33925 .45356 Mtetra .591 .771 .965 r .33925 .45356 .34993 .46188 .36683 .45827 .35621 .45003 Mtetra .588 .773 .968 r .35621 .45003 .36683 .45827 .38385 .45467 .3733 .44651 Mtetra .585 .775 .97 r .3733 .44651 .38385 .45467 .40101 .45108 .39052 .44301 Mtetra .583 .778 .972 r .39052 .44301 .40101 .45108 .41829 .4475 .40788 .43951 Mtetra .58 .78 .974 r .40788 .43951 .41829 .4475 .43571 .44391 .42537 .436 Mtetra .578 .783 .976 r .42537 .436 .43571 .44391 .45327 .44031 .443 .43249 Mtetra .576 .785 .978 r .443 .43249 .45327 .44031 .47096 .43669 .46078 .42894 Mtetra .575 .788 .98 r .46078 .42894 .47096 .43669 .48879 .43303 .47869 .42536 Mtetra .574 .791 .981 r .47869 .42536 .48879 .43303 .50677 .42933 .49675 .42173 Mtetra .574 .794 .983 r .49675 .42173 .50677 .42933 .52489 .42558 .51496 .41803 Mtetra .574 .797 .984 r .51496 .41803 .52489 .42558 .54315 .42175 .53332 .41425 Mtetra .575 .8 .984 r .53332 .41425 .54315 .42175 .56156 .41784 .55182 .41037 Mtetra .577 .803 .985 r .55182 .41037 .56156 .41784 .58011 .41383 .57047 .40637 Mtetra .58 .805 .985 r .57047 .40637 .58011 .41383 .59881 .40969 .58927 .40222 Mtetra .584 .808 .985 r .58927 .40222 .59881 .40969 .61765 .40541 .60822 .39791 Mtetra .589 .811 .984 r .60822 .39791 .61765 .40541 .63664 .40097 .62732 .3934 Mtetra .595 .813 .983 r .62732 .3934 .63664 .40097 .65578 .39635 .64655 .38868 Mtetra .602 .815 .981 r .64655 .38868 .65578 .39635 .67505 .39152 .66594 .38372 Mtetra .61 .816 .979 r .66594 .38372 .67505 .39152 .69446 .38646 .68545 .37849 Mtetra .619 .817 .976 r .68545 .37849 .69446 .38646 .71401 .38115 .70511 .37297 Mtetra .629 .817 .973 r .70511 .37297 .71401 .38115 .73369 .37556 .72489 .36713 Mtetra .638 .817 .969 r .72489 .36713 .73369 .37556 .75349 .36968 .7448 .36095 Mtetra .648 .815 .963 r .7448 .36095 .75349 .36968 .77342 .36348 .76482 .35441 Mtetra .658 .813 .958 r .76482 .35441 .77342 .36348 .79347 .35694 .78496 .34748 Mtetra .668 .81 .951 r .78496 .34748 .79347 .35694 .81362 .35005 .80521 .34016 Mtetra .678 .805 .943 r .80521 .34016 .81362 .35005 .83389 .34279 .82555 .33242 Mtetra .686 .8 .935 r .82555 .33242 .83389 .34279 .85425 .33515 .84599 .32426 Mtetra .606 .759 .952 r .21274 .47027 .22395 .47903 .24007 .4753 .22891 .46659 Mtetra .603 .76 .954 r .22891 .46659 .24007 .4753 .25631 .4716 .24519 .46295 Mtetra .6 .762 .957 r .24519 .46295 .25631 .4716 .27265 .46793 .26159 .45935 Mtetra .597 .764 .959 r .26159 .45935 .27265 .46793 .28912 .46429 .27811 .45579 Mtetra .593 .766 .962 r .27811 .45579 .28912 .46429 .30571 .46069 .29475 .45227 Mtetra .59 .768 .964 r .29475 .45227 .30571 .46069 .32241 .45711 .31152 .44878 Mtetra .587 .77 .967 r .31152 .44878 .32241 .45711 .33925 .45356 .32841 .44532 Mtetra .584 .773 .969 r .32841 .44532 .33925 .45356 .35621 .45003 .34544 .44188 Mtetra .58 .775 .972 r .34544 .44188 .35621 .45003 .3733 .44651 .36259 .43846 Mtetra .577 .778 .974 r .36259 .43846 .3733 .44651 .39052 .44301 .37988 .43506 Mtetra .574 .78 .976 r .37988 .43506 .39052 .44301 .40788 .43951 .39731 .43166 Mtetra .571 .783 .979 r .39731 .43166 .40788 .43951 .42537 .436 .41488 .42825 Mtetra .569 .786 .981 r .41488 .42825 .42537 .436 .443 .43249 .43259 .42483 Mtetra .567 .789 .983 r .43259 .42483 .443 .43249 .46078 .42894 .45044 .42138 Mtetra .565 .792 .984 r .45044 .42138 .46078 .42894 .47869 .42536 .46844 .41789 Mtetra .565 .795 .986 r .46844 .41789 .47869 .42536 .49675 .42173 .48659 .41433 Mtetra .565 .798 .987 r .48659 .41433 .49675 .42173 .51496 .41803 .50489 .4107 Mtetra .565 .801 .988 r .50489 .4107 .51496 .41803 .53332 .41425 .52334 .40696 Mtetra .567 .804 .988 r .52334 .40696 .53332 .41425 .55182 .41037 .54194 .40311 Mtetra .57 .808 .989 r .54194 .40311 .55182 .41037 .57047 .40637 .5607 .39911 Mtetra .574 .811 .989 r .5607 .39911 .57047 .40637 .58927 .40222 .5796 .39494 Mtetra .579 .814 .988 r .5796 .39494 .58927 .40222 .60822 .39791 .59866 .39058 Mtetra .586 .816 .987 r .59866 .39058 .60822 .39791 .62732 .3934 .61786 .38598 Mtetra .594 .819 .986 r .61786 .38598 .62732 .3934 .64655 .38868 .6372 .38114 Mtetra .603 .821 .983 r .6372 .38114 .64655 .38868 .66594 .38372 .65669 .37601 Mtetra .613 .822 .981 r .65669 .37601 .66594 .38372 .68545 .37849 .67632 .37056 Mtetra .623 .822 .977 r .67632 .37056 .68545 .37849 .70511 .37297 .69608 .36478 Mtetra .635 .822 .972 r .69608 .36478 .70511 .37297 .72489 .36713 .71596 .35862 Mtetra .646 .821 .967 r .71596 .35862 .72489 .36713 .7448 .36095 .73597 .35208 Mtetra .657 .818 .961 r .73597 .35208 .7448 .36095 .76482 .35441 .75609 .34511 Mtetra .668 .814 .953 r .75609 .34511 .76482 .35441 .78496 .34748 .77632 .33772 Mtetra .679 .81 .945 r .77632 .33772 .78496 .34748 .80521 .34016 .79665 .32987 Mtetra .688 .804 .936 r .79665 .32987 .80521 .34016 .82555 .33242 .81706 .32156 Mtetra .697 .797 .927 r .81706 .32156 .82555 .33242 .84599 .32426 .83757 .31279 Mtetra .601 .76 .955 r .20138 .4615 .21274 .47027 .22891 .46659 .21759 .45789 Mtetra .598 .761 .957 r .21759 .45789 .22891 .46659 .24519 .46295 .23393 .45433 Mtetra .594 .763 .96 r .23393 .45433 .24519 .46295 .26159 .45935 .25038 .45081 Mtetra .59 .765 .963 r .25038 .45081 .26159 .45935 .27811 .45579 .26695 .44734 Mtetra .587 .768 .965 r .26695 .44734 .27811 .45579 .29475 .45227 .28365 .44392 Mtetra .583 .77 .968 r .28365 .44392 .29475 .45227 .31152 .44878 .30047 .44053 Mtetra .579 .772 .971 r .30047 .44053 .31152 .44878 .32841 .44532 .31742 .43717 Mtetra .575 .775 .974 r .31742 .43717 .32841 .44532 .34544 .44188 .33451 .43385 Mtetra .571 .777 .976 r .33451 .43385 .34544 .44188 .36259 .43846 .35173 .43055 Mtetra .568 .78 .979 r .35173 .43055 .36259 .43846 .37988 .43506 .36908 .42726 Mtetra .564 .783 .981 r .36908 .42726 .37988 .43506 .39731 .43166 .38658 .42398 Mtetra .561 .786 .983 r .38658 .42398 .39731 .43166 .41488 .42825 .40422 .42069 Mtetra .558 .789 .985 r .40422 .42069 .41488 .42825 .43259 .42483 .42201 .41739 Mtetra .556 .792 .987 r .42201 .41739 .43259 .42483 .45044 .42138 .43995 .41404 Mtetra .554 .796 .989 r .43995 .41404 .45044 .42138 .46844 .41789 .45804 .41065 Mtetra .554 .799 .99 r .45804 .41065 .46844 .41789 .48659 .41433 .47628 .40718 Mtetra .554 .802 .991 r .47628 .40718 .48659 .41433 .50489 .4107 .49467 .40361 Mtetra .555 .806 .992 r .49467 .40361 .50489 .4107 .52334 .40696 .51322 .39993 Mtetra .558 .81 .992 r .51322 .39993 .52334 .40696 .54194 .40311 .53192 .3961 Mtetra .562 .813 .992 r .53192 .3961 .54194 .40311 .5607 .39911 .55078 .39209 Mtetra .568 .817 .992 r .55078 .39209 .5607 .39911 .5796 .39494 .56979 .38788 Mtetra .575 .82 .991 r .56979 .38788 .5796 .39494 .59866 .39058 .58895 .38344 Mtetra .584 .823 .99 r .58895 .38344 .59866 .39058 .61786 .38598 .60826 .37873 Mtetra .594 .825 .988 r .60826 .37873 .61786 .38598 .6372 .38114 .62772 .37371 Mtetra .605 .827 .985 r .62772 .37371 .6372 .38114 .65669 .37601 .64731 .36836 Mtetra .617 .828 .981 r .64731 .36836 .65669 .37601 .67632 .37056 .66705 .36264 Mtetra .63 .828 .977 r .66705 .36264 .67632 .37056 .69608 .36478 .68691 .35652 Mtetra .643 .827 .971 r .68691 .35652 .69608 .36478 .71596 .35862 .7069 .34997 Mtetra .656 .824 .964 r .7069 .34997 .71596 .35862 .73597 .35208 .727 .34297 Mtetra .669 .82 .956 r .727 .34297 .73597 .35208 .75609 .34511 .74722 .33549 Mtetra .68 .814 .947 r .74722 .33549 .75609 .34511 .77632 .33772 .76753 .32752 Mtetra .691 .808 .937 r .76753 .32752 .77632 .33772 .79665 .32987 .78793 .31904 Mtetra .7 .8 .927 r .78793 .31904 .79665 .32987 .81706 .32156 .80841 .31006 Mtetra .708 .791 .916 r .80841 .31006 .81706 .32156 .83757 .31279 .82897 .30058 Mtetra .595 .761 .958 r .18986 .45273 .20138 .4615 .21759 .45789 .20612 .44921 Mtetra .591 .763 .961 r .20612 .44921 .21759 .45789 .23393 .45433 .2225 .44574 Mtetra .587 .765 .963 r .2225 .44574 .23393 .45433 .25038 .45081 .239 .44233 Mtetra .583 .767 .966 r .239 .44233 .25038 .45081 .26695 .44734 .25562 .43896 Mtetra .579 .769 .969 r .25562 .43896 .26695 .44734 .28365 .44392 .27237 .43565 Mtetra .574 .772 .972 r .27237 .43565 .28365 .44392 .30047 .44053 .28925 .43239 Mtetra .57 .774 .975 r .28925 .43239 .30047 .44053 .31742 .43717 .30626 .42916 Mtetra .565 .777 .978 r .30626 .42916 .31742 .43717 .33451 .43385 .32341 .42597 Mtetra .56 .78 .981 r .32341 .42597 .33451 .43385 .35173 .43055 .34069 .42281 Mtetra .556 .783 .983 r .34069 .42281 .35173 .43055 .36908 .42726 .35812 .41967 Mtetra .552 .786 .986 r .35812 .41967 .36908 .42726 .38658 .42398 .37569 .41652 Mtetra .548 .789 .988 r .37569 .41652 .38658 .42398 .40422 .42069 .3934 .41338 Mtetra .545 .793 .99 r .3934 .41338 .40422 .42069 .42201 .41739 .41127 .4102 Mtetra .543 .796 .992 r .41127 .4102 .42201 .41739 .43995 .41404 .42929 .40698 Mtetra .541 .8 .993 r .42929 .40698 .43995 .41404 .45804 .41065 .44747 .4037 Mtetra .541 .803 .994 r .44747 .4037 .45804 .41065 .47628 .40718 .4658 .40032 Mtetra .541 .807 .995 r .4658 .40032 .47628 .40718 .49467 .40361 .48428 .39683 Mtetra .544 .811 .995 r .48428 .39683 .49467 .40361 .51322 .39993 .50293 .39319 Mtetra .548 .815 .996 r .50293 .39319 .51322 .39993 .53192 .3961 .52174 .38938 Mtetra .554 .819 .995 r .52174 .38938 .53192 .3961 .55078 .39209 .5407 .38535 Mtetra .561 .823 .995 r .5407 .38535 .55078 .39209 .56979 .38788 .55982 .38108 Mtetra .571 .827 .994 r .55982 .38108 .56979 .38788 .58895 .38344 .57909 .37652 Mtetra .582 .83 .992 r .57909 .37652 .58895 .38344 .60826 .37873 .59852 .37164 Mtetra .595 .832 .989 r .59852 .37164 .60826 .37873 .62772 .37371 .61808 .36639 Mtetra .609 .834 .986 r .61808 .36639 .62772 .37371 .64731 .36836 .63779 .36075 Mtetra .624 .834 .981 r .63779 .36075 .64731 .36836 .66705 .36264 .65764 .35467 Mtetra .639 .833 .975 r .65764 .35467 .66705 .36264 .68691 .35652 .67761 .34813 Mtetra .654 .83 .968 r .67761 .34813 .68691 .35652 .7069 .34997 .69769 .34108 Mtetra .669 .826 .959 r .69769 .34108 .7069 .34997 .727 .34297 .71789 .33351 Mtetra .682 .82 .949 r .71789 .33351 .727 .34297 .74722 .33549 .73819 .3254 Mtetra .694 .812 .938 r .73819 .3254 .74722 .33549 .76753 .32752 .75857 .31673 Mtetra .704 .803 .926 r .75857 .31673 .76753 .32752 .78793 .31904 .77904 .30751 Mtetra .713 .793 .914 r .77904 .30751 .78793 .31904 .80841 .31006 .79958 .29773 Mtetra .72 .782 .902 r .79958 .29773 .80841 .31006 .82897 .30058 .82019 .28742 Mtetra .589 .762 .961 r .17818 .44398 .18986 .45273 .20612 .44921 .19449 .44056 Mtetra .584 .764 .964 r .19449 .44056 .20612 .44921 .2225 .44574 .21091 .43721 Mtetra .579 .766 .967 r .21091 .43721 .2225 .44574 .239 .44233 .22746 .43391 Mtetra .574 .768 .971 r .22746 .43391 .239 .44233 .25562 .43896 .24413 .43068 Mtetra .569 .771 .974 r .24413 .43068 .25562 .43896 .27237 .43565 .26093 .42751 Mtetra .564 .774 .977 r .26093 .42751 .27237 .43565 .28925 .43239 .27786 .42439 Mtetra .558 .776 .98 r .27786 .42439 .28925 .43239 .30626 .42916 .29493 .42132 Mtetra .553 .779 .983 r .29493 .42132 .30626 .42916 .32341 .42597 .31213 .4183 Mtetra .547 .782 .986 r .31213 .4183 .32341 .42597 .34069 .42281 .32948 .4153 Mtetra .542 .786 .988 r .32948 .4153 .34069 .42281 .35812 .41967 .34697 .41232 Mtetra .537 .789 .991 r .34697 .41232 .35812 .41967 .37569 .41652 .36461 .40934 Mtetra .532 .792 .993 r .36461 .40934 .37569 .41652 .3934 .41338 .38241 .40636 Mtetra .529 .796 .994 r .38241 .40636 .3934 .41338 .41127 .4102 .40035 .40333 Mtetra .526 .8 .996 r .40035 .40333 .41127 .4102 .42929 .40698 .41846 .40026 Mtetra .525 .804 .997 r .41846 .40026 .42929 .40698 .44747 .4037 .43672 .3971 Mtetra .525 .808 .998 r .43672 .3971 .44747 .4037 .4658 .40032 .45514 .39382 Mtetra .526 .812 .998 r .45514 .39382 .4658 .40032 .48428 .39683 .47373 .39041 Mtetra .53 .817 .998 r .47373 .39041 .48428 .39683 .50293 .39319 .49248 .38681 Mtetra .536 .821 .998 r .49248 .38681 .50293 .39319 .52174 .38938 .51139 .38299 Mtetra .545 .826 .998 r .51139 .38299 .52174 .38938 .5407 .38535 .53047 .37892 Mtetra .555 .83 .997 r .53047 .37892 .5407 .38535 .55982 .38108 .5497 .37454 Mtetra .568 .834 .995 r .5497 .37454 .55982 .38108 .57909 .37652 .56909 .36981 Mtetra .583 .838 .993 r .56909 .36981 .57909 .37652 .59852 .37164 .58862 .3647 Mtetra .599 .84 .99 r .58862 .3647 .59852 .37164 .61808 .36639 .60831 .35915 Mtetra .617 .841 .985 r .60831 .35915 .61808 .36639 .63779 .36075 .62813 .35312 Mtetra .635 .84 .979 r .62813 .35312 .63779 .36075 .65764 .35467 .64808 .34658 Mtetra .652 .837 .971 r .64808 .34658 .65764 .35467 .67761 .34813 .66815 .33949 Mtetra .669 .833 .962 r .66815 .33949 .67761 .34813 .69769 .34108 .68833 .33182 Mtetra .684 .826 .951 r .68833 .33182 .69769 .34108 .71789 .33351 .70861 .32355 Mtetra .698 .817 .939 r .70861 .32355 .71789 .33351 .73819 .3254 .72899 .31466 Mtetra .709 .807 .926 r .72899 .31466 .73819 .3254 .75857 .31673 .74944 .30515 Mtetra .718 .795 .912 r .74944 .30515 .75857 .31673 .77904 .30751 .76997 .29504 Mtetra .725 .783 .898 r .76997 .29504 .77904 .30751 .79958 .29773 .79055 .28433 Mtetra .73 .77 .884 r .79055 .28433 .79958 .29773 .82019 .28742 .81119 .27307 Mtetra .581 .763 .965 r .16633 .43528 .17818 .44398 .19449 .44056 .18268 .43198 Mtetra .575 .765 .968 r .18268 .43198 .19449 .44056 .21091 .43721 .19915 .42876 Mtetra .57 .767 .972 r .19915 .42876 .21091 .43721 .22746 .43391 .21574 .42561 Mtetra .564 .77 .975 r .21574 .42561 .22746 .43391 .24413 .43068 .23246 .42254 Mtetra .557 .773 .979 r .23246 .42254 .24413 .43068 .26093 .42751 .24931 .41953 Mtetra .551 .775 .982 r .24931 .41953 .26093 .42751 .27786 .42439 .26629 .41659 Mtetra .544 .778 .985 r .26629 .41659 .27786 .42439 .29493 .42132 .28341 .41371 Mtetra .537 .782 .988 r .28341 .41371 .29493 .42132 .31213 .4183 .30068 .41087 Mtetra .53 .785 .991 r .30068 .41087 .31213 .4183 .32948 .4153 .31808 .40807 Mtetra .524 .788 .993 r .31808 .40807 .32948 .4153 .34697 .41232 .33564 .40529 Mtetra .518 .792 .995 r .33564 .40529 .34697 .41232 .36461 .40934 .35335 .40251 Mtetra .513 .795 .997 r .35335 .40251 .36461 .40934 .38241 .40636 .37122 .39971 Mtetra .509 .799 .998 r .37122 .39971 .38241 .40636 .40035 .40333 .38925 .39686 Mtetra .506 .803 .999 r .38925 .39686 .40035 .40333 .41846 .40026 .40744 .39395 Mtetra .504 .807 .999 r .40744 .39395 .41846 .40026 .43672 .3971 .42579 .39092 Mtetra .505 .812 1 r .42579 .39092 .43672 .3971 .45514 .39382 .44431 .38776 Mtetra .509 .817 1 r .44431 .38776 .45514 .39382 .47373 .39041 .463 .38441 Mtetra .515 .822 1 r .463 .38441 .47373 .39041 .49248 .38681 .48186 .38084 Mtetra .524 .828 1 r .48186 .38084 .49248 .38681 .51139 .38299 .50088 .37699 Mtetra .536 .833 .999 r .50088 .37699 .51139 .38299 .53047 .37892 .52006 .37283 Mtetra .55 .838 .998 r .52006 .37283 .53047 .37892 .5497 .37454 .53941 .36829 Mtetra .568 .843 .996 r .53941 .36829 .5497 .37454 .56909 .36981 .55892 .36333 Mtetra .587 .847 .994 r .55892 .36333 .56909 .36981 .58862 .3647 .57857 .35789 Mtetra .608 .848 .989 r .57857 .35789 .58862 .3647 .60831 .35915 .59837 .35192 Mtetra .629 .848 .983 r .59837 .35192 .60831 .35915 .62813 .35312 .6183 .34539 Mtetra .65 .846 .975 r .6183 .34539 .62813 .35312 .64808 .34658 .63836 .33824 Mtetra .669 .84 .965 r .63836 .33824 .64808 .34658 .66815 .33949 .65853 .33045 Mtetra .687 .832 .953 r .65853 .33045 .66815 .33949 .68833 .33182 .6788 .32199 Mtetra .702 .822 .939 r .6788 .32199 .68833 .33182 .70861 .32355 .69917 .31284 Mtetra .715 .81 .925 r .69917 .31284 .70861 .32355 .72899 .31466 .71961 .30301 Mtetra .724 .797 .909 r .71961 .30301 .72899 .31466 .74944 .30515 .74012 .2925 Mtetra .731 .783 .894 r .74012 .2925 .74944 .30515 .76997 .29504 .76069 .28134 Mtetra .736 .768 .878 r .76069 .28134 .76997 .29504 .79055 .28433 .78131 .26957 Mtetra .739 .754 .864 r .78131 .26957 .79055 .28433 .81119 .27307 .80197 .25724 Mtetra .572 .764 .969 r .15431 .42662 .16633 .43528 .18268 .43198 .1707 .42348 Mtetra .565 .766 .973 r .1707 .42348 .18268 .43198 .19915 .42876 .1872 .42042 Mtetra .558 .769 .977 r .1872 .42042 .19915 .42876 .21574 .42561 .20384 .41745 Mtetra .55 .771 .98 r .20384 .41745 .21574 .42561 .23246 .42254 .2206 .41456 Mtetra .543 .774 .984 r .2206 .41456 .23246 .42254 .24931 .41953 .23749 .41176 Mtetra .534 .777 .987 r .23749 .41176 .24931 .41953 .26629 .41659 .25452 .40903 Mtetra .526 .78 .99 r .25452 .40903 .26629 .41659 .28341 .41371 .2717 .40637 Mtetra .518 .783 .993 r .2717 .40637 .28341 .41371 .30068 .41087 .28902 .40377 Mtetra .509 .787 .995 r .28902 .40377 .30068 .41087 .31808 .40807 .30649 .4012 Mtetra .501 .79 .997 r .30649 .4012 .31808 .40807 .33564 .40529 .32411 .39865 Mtetra .494 .793 .998 r .32411 .39865 .33564 .40529 .35335 .40251 .34189 .3961 Mtetra .488 .797 .999 r .34189 .3961 .35335 .40251 .37122 .39971 .35983 .39352 Mtetra .483 .801 1 r .35983 .39352 .37122 .39971 .38925 .39686 .37794 .39088 Mtetra .48 .805 1 r .37794 .39088 .38925 .39686 .40744 .39395 .39622 .38814 Mtetra .479 .81 1 r .39622 .38814 .40744 .39395 .42579 .39092 .41466 .38527 Mtetra .482 .815 .999 r .41466 .38527 .42579 .39092 .44431 .38776 .43328 .38221 Mtetra .487 .821 .999 r .43328 .38221 .44431 .38776 .463 .38441 .45208 .37892 Mtetra .497 .827 .999 r .45208 .37892 .463 .38441 .48186 .38084 .47104 .37534 Mtetra .51 .834 .999 r .47104 .37534 .48186 .38084 .50088 .37699 .49018 .37143 Mtetra .527 .841 .999 r .49018 .37143 .50088 .37699 .52006 .37283 .50949 .36711 Mtetra .548 .847 .998 r .50949 .36711 .52006 .37283 .53941 .36829 .52896 .36232 Mtetra .571 .853 .996 r .52896 .36232 .53941 .36829 .55892 .36333 .54858 .35702 Mtetra .596 .856 .993 r .54858 .35702 .55892 .36333 .57857 .35789 .56836 .35113 Mtetra .622 .857 .987 r .56836 .35113 .57857 .35789 .59837 .35192 .58827 .3446 Mtetra .647 .855 .979 r .58827 .3446 .59837 .35192 .6183 .34539 .60832 .33739 Mtetra .67 .849 .968 r .60832 .33739 .6183 .34539 .63836 .33824 .62848 .32946 Mtetra .69 .84 .955 r .62848 .32946 .63836 .33824 .65853 .33045 .64875 .32078 Mtetra .707 .828 .939 r .64875 .32078 .65853 .33045 .6788 .32199 .6691 .31132 Mtetra .721 .814 .923 r .6691 .31132 .6788 .32199 .69917 .31284 .68954 .3011 Mtetra .731 .798 .905 r .68954 .3011 .69917 .31284 .71961 .30301 .71004 .29012 Mtetra .738 .782 .888 r .71004 .29012 .71961 .30301 .74012 .2925 .73059 .27843 Mtetra .743 .765 .871 r .73059 .27843 .74012 .2925 .76069 .28134 .75119 .26606 Mtetra .745 .749 .856 r .75119 .26606 .76069 .28134 .78131 .26957 .77182 .2531 Mtetra .745 .734 .841 r .77182 .2531 .78131 .26957 .80197 .25724 .79249 .23962 Mtetra .56 .764 .974 r .14211 .41806 .15431 .42662 .1707 .42348 .15853 .41509 Mtetra .552 .767 .978 r .15853 .41509 .1707 .42348 .1872 .42042 .17507 .41223 Mtetra .543 .77 .982 r .17507 .41223 .1872 .42042 .20384 .41745 .19174 .40947 Mtetra .534 .772 .985 r .19174 .40947 .20384 .41745 .2206 .41456 .20854 .40682 Mtetra .524 .775 .989 r .20854 .40682 .2206 .41456 .23749 .41176 .22547 .40426 Mtetra .514 .778 .992 r .22547 .40426 .23749 .41176 .25452 .40903 .24255 .40179 Mtetra .503 .781 .995 r .24255 .40179 .25452 .40903 .2717 .40637 .25977 .3994 Mtetra .492 .784 .997 r .25977 .3994 .2717 .40637 .28902 .40377 .27714 .39706 Mtetra .482 .787 .998 r .27714 .39706 .28902 .40377 .30649 .4012 .29467 .39478 Mtetra .472 .79 .999 r .29467 .39478 .30649 .4012 .32411 .39865 .31236 .3925 Mtetra .462 .793 .999 r .31236 .3925 .32411 .39865 .34189 .3961 .33021 .39022 Mtetra .455 .796 .999 r .33021 .39022 .34189 .3961 .35983 .39352 .34822 .3879 Mtetra .449 .8 .998 r .34822 .3879 .35983 .39352 .37794 .39088 .36641 .38549 Mtetra .446 .805 .997 r .36641 .38549 .37794 .39088 .39622 .38814 .38478 .38295 Mtetra .447 .81 .996 r .38478 .38295 .39622 .38814 .41466 .38527 .40332 .38023 Mtetra .452 .816 .995 r .40332 .38023 .41466 .38527 .43328 .38221 .42205 .37727 Mtetra .462 .824 .995 r .42205 .37727 .43328 .38221 .45208 .37892 .44095 .37401 Mtetra .477 .832 .995 r .44095 .37401 .45208 .37892 .47104 .37534 .46003 .37039 Mtetra .497 .841 .996 r .46003 .37039 .47104 .37534 .49018 .37143 .47929 .36633 Mtetra .522 .85 .997 r .47929 .36633 .49018 .37143 .50949 .36711 .49872 .36176 Mtetra .55 .858 .997 r .49872 .36176 .50949 .36711 .52896 .36232 .51832 .35661 Mtetra .581 .864 .995 r .51832 .35661 .52896 .36232 .54858 .35702 .53807 .35081 Mtetra .612 .866 .991 r .53807 .35081 .54858 .35702 .56836 .35113 .55797 .3443 Mtetra .643 .865 .983 r .55797 .3443 .56836 .35113 .58827 .3446 .57801 .33701 Mtetra .671 .859 .971 r .57801 .33701 .58827 .3446 .60832 .33739 .59816 .32891 Mtetra .695 .848 .956 r .59816 .32891 .60832 .33739 .62848 .32946 .61843 .31996 Mtetra .714 .834 .939 r .61843 .31996 .62848 .32946 .64875 .32078 .63878 .31013 Mtetra .729 .818 .92 r .63878 .31013 .64875 .32078 .6691 .31132 .65921 .29944 Mtetra .739 .799 .9 r .65921 .29944 .6691 .31132 .68954 .3011 .6797 .28791 Mtetra .746 .78 .881 r .6797 .28791 .68954 .3011 .71004 .29012 .70025 .27558 Mtetra .749 .761 .862 r .70025 .27558 .71004 .29012 .73059 .27843 .72083 .26251 Mtetra .75 .743 .845 r .72083 .26251 .73059 .27843 .75119 .26606 .74144 .2488 Mtetra .75 .726 .83 r .74144 .2488 .75119 .26606 .77182 .2531 .76208 .23455 Mtetra .747 .711 .817 r .76208 .23455 .77182 .2531 .79249 .23962 .78275 .21988 Mtetra .546 .765 .979 r .12971 .40961 .14211 .41806 .15853 .41509 .14616 .40686 Mtetra .536 .768 .983 r .14616 .40686 .15853 .41509 .17507 .41223 .16273 .40424 Mtetra .525 .77 .987 r .16273 .40424 .17507 .41223 .19174 .40947 .17943 .40174 Mtetra .513 .773 .99 r .17943 .40174 .19174 .40947 .20854 .40682 .19626 .39936 Mtetra .5 .775 .994 r .19626 .39936 .20854 .40682 .22547 .40426 .21324 .3971 Mtetra .487 .778 .996 r .21324 .3971 .22547 .40426 .24255 .40179 .23035 .39494 Mtetra .473 .78 .998 r .23035 .39494 .24255 .40179 .25977 .3994 .24762 .39287 Mtetra .459 .783 .998 r .24762 .39287 .25977 .3994 .27714 .39706 .26504 .39087 Mtetra .445 .785 .998 r .26504 .39087 .27714 .39706 .29467 .39478 .28262 .38892 Mtetra .432 .787 .997 r .28262 .38892 .29467 .39478 .31236 .3925 .30036 .38698 Mtetra .42 .789 .994 r .30036 .38698 .31236 .3925 .33021 .39022 .31828 .38501 Mtetra .411 .792 .992 r .31828 .38501 .33021 .39022 .34822 .3879 .33638 .38298 Mtetra .405 .795 .989 r .33638 .38298 .34822 .3879 .36641 .38549 .35465 .38083 Mtetra .404 .8 .986 r .35465 .38083 .36641 .38549 .38478 .38295 .37311 .37851 Mtetra .407 .806 .984 r .37311 .37851 .38478 .38295 .40332 .38023 .39175 .37594 Mtetra .417 .815 .984 r .39175 .37594 .40332 .38023 .42205 .37727 .41059 .37305 Mtetra .433 .825 .985 r .41059 .37305 .42205 .37727 .44095 .37401 .42961 .36978 Mtetra .457 .837 .987 r .42961 .36978 .44095 .37401 .46003 .37039 .44881 .36603 Mtetra .486 .849 .991 r .44881 .36603 .46003 .37039 .47929 .36633 .4682 .36171 Mtetra .521 .861 .994 r .4682 .36171 .47929 .36633 .49872 .36176 .48777 .35675 Mtetra .56 .87 .995 r .48777 .35675 .49872 .36176 .51832 .35661 .5075 .35106 Mtetra .599 .876 .992 r .5075 .35106 .51832 .35661 .53807 .35081 .52738 .34456 Mtetra .637 .876 .986 r .52738 .34456 .53807 .35081 .55797 .3443 .54741 .33718 Mtetra .671 .87 .974 r .54741 .33718 .55797 .3443 .57801 .33701 .56756 .32887 Mtetra .7 .858 .958 r .56756 .32887 .57801 .33701 .59816 .32891 .58783 .31958 Mtetra .722 .841 .938 r .58783 .31958 .59816 .32891 .61843 .31996 .60819 .30931 Mtetra .738 .821 .916 r .60819 .30931 .61843 .31996 .63878 .31013 .62862 .29805 Mtetra .748 .799 .893 r .62862 .29805 .63878 .31013 .65921 .29944 .64912 .28585 Mtetra .754 .777 .871 r .64912 .28585 .65921 .29944 .6797 .28791 .66966 .27275 Mtetra .757 .755 .851 r .66966 .27275 .6797 .28791 .70025 .27558 .69023 .25885 Mtetra .756 .735 .833 r .69023 .25885 .70025 .27558 .72083 .26251 .71082 .24427 Mtetra .754 .716 .817 r .71082 .24427 .72083 .26251 .74144 .2488 .73144 .22912 Mtetra .75 .7 .804 r .73144 .22912 .74144 .2488 .76208 .23455 .75207 .21358 Mtetra .745 .686 .794 r .75207 .21358 .76208 .23455 .78275 .21988 .77274 .19779 Mtetra .528 .765 .984 r .11711 .40133 .12971 .40961 .14616 .40686 .13358 .39884 Mtetra .515 .767 .988 r .13358 .39884 .14616 .40686 .16273 .40424 .15017 .39651 Mtetra .501 .77 .992 r .15017 .39651 .16273 .40424 .17943 .40174 .16689 .39433 Mtetra .485 .772 .995 r .16689 .39433 .17943 .40174 .19626 .39936 .18375 .39229 Mtetra .468 .774 .997 r .18375 .39229 .19626 .39936 .21324 .3971 .20076 .39039 Mtetra .451 .775 .998 r .20076 .39039 .21324 .3971 .23035 .39494 .21791 .38861 Mtetra .432 .776 .997 r .21791 .38861 .23035 .39494 .24762 .39287 .23521 .38694 Mtetra .413 .776 .995 r .23521 .38694 .24762 .39287 .26504 .39087 .25267 .38534 Mtetra .395 .777 .991 r .25267 .38534 .26504 .39087 .28262 .38892 .27031 .38378 Mtetra .378 .777 .986 r .27031 .38378 .28262 .38892 .30036 .38698 .28811 .38223 Mtetra .363 .777 .98 r .28811 .38223 .30036 .38698 .31828 .38501 .3061 .38064 Mtetra .353 .779 .973 r .3061 .38064 .31828 .38501 .33638 .38298 .32426 .37894 Mtetra .347 .782 .967 r .32426 .37894 .33638 .38298 .35465 .38083 .34263 .37708 Mtetra .348 .787 .963 r .34263 .37708 .35465 .38083 .37311 .37851 .36118 .37497 Mtetra .357 .796 .961 r .36118 .37497 .37311 .37851 .39175 .37594 .37993 .37254 Mtetra .375 .808 .963 r .37993 .37254 .39175 .37594 .41059 .37305 .39888 .36968 Mtetra .402 .824 .967 r .39888 .36968 .41059 .37305 .42961 .36978 .41803 .3663 Mtetra .438 .841 .975 r .41803 .3663 .42961 .36978 .44881 .36603 .43737 .36229 Mtetra .482 .859 .983 r .43737 .36229 .44881 .36603 .4682 .36171 .4569 .35756 Mtetra .531 .875 .989 r .4569 .35756 .4682 .36171 .48777 .35675 .4766 .35199 Mtetra .582 .885 .991 r .4766 .35199 .48777 .35675 .5075 .35106 .49648 .3455 Mtetra .631 .888 .987 r .49648 .3455 .5075 .35106 .52738 .34456 .5165 .338 Mtetra .673 .882 .976 r .5165 .338 .52738 .34456 .54741 .33718 .53666 .32942 Mtetra .707 .868 .958 r .53666 .32942 .54741 .33718 .56756 .32887 .55694 .31973 Mtetra .732 .848 .935 r .55694 .31973 .56756 .32887 .58783 .31958 .57731 .30889 Mtetra .749 .823 .91 r .57731 .30889 .58783 .31958 .60819 .30931 .59776 .29694 Mtetra .759 .797 .884 r .59776 .29694 .60819 .30931 .62862 .29805 .61826 .28391 Mtetra .763 .772 .86 r .61826 .28391 .62862 .29805 .64912 .28585 .63881 .26988 Mtetra .764 .747 .838 r .63881 .26988 .64912 .28585 .66966 .27275 .65938 .25499 Mtetra .761 .725 .819 r .65938 .25499 .66966 .27275 .69023 .25885 .67996 .23936 Mtetra .757 .705 .802 r .67996 .23936 .69023 .25885 .71082 .24427 .70056 .22319 Mtetra .752 .687 .789 r .70056 .22319 .71082 .24427 .73144 .22912 .72117 .20664 Mtetra .746 .673 .779 r .72117 .20664 .73144 .22912 .75207 .21358 .7418 .18994 Mtetra .74 .66 .772 r .7418 .18994 .75207 .21358 .77274 .19779 .76246 .17326 Mtetra .505 .764 .989 r .10428 .39326 .11711 .40133 .13358 .39884 .12077 .3911 Mtetra .488 .766 .993 r .12077 .3911 .13358 .39884 .15017 .39651 .13737 .38912 Mtetra .469 .767 .995 r .13737 .38912 .15017 .39651 .16689 .39433 .15411 .38733 Mtetra .448 .768 .997 r .15411 .38733 .16689 .39433 .18375 .39229 .17099 .38571 Mtetra .425 .768 .996 r .17099 .38571 .18375 .39229 .20076 .39039 .18801 .38425 Mtetra .401 .767 .994 r .18801 .38425 .20076 .39039 .21791 .38861 .20519 .38294 Mtetra .375 .765 .988 r .20519 .38294 .21791 .38861 .23521 .38694 .22252 .38174 Mtetra .35 .761 .98 r .22252 .38174 .23521 .38694 .25267 .38534 .24002 .38063 Mtetra .325 .758 .97 r .24002 .38063 .25267 .38534 .27031 .38378 .2577 .37956 Mtetra .303 .754 .958 r .2577 .37956 .27031 .38378 .28811 .38223 .27556 .37848 Mtetra .286 .751 .946 r .27556 .37848 .28811 .38223 .3061 .38064 .29361 .37732 Mtetra .274 .751 .934 r .29361 .37732 .3061 .38064 .32426 .37894 .31186 .376 Mtetra .271 .754 .925 r .31186 .376 .32426 .37894 .34263 .37708 .33031 .37445 Mtetra .278 .762 .92 r .33031 .37445 .34263 .37708 .36118 .37497 .34897 .37254 Mtetra .296 .776 .922 r .34897 .37254 .36118 .37497 .37993 .37254 .36783 .37019 Mtetra .328 .796 .929 r .36783 .37019 .37993 .37254 .39888 .36968 .38691 .36726 Mtetra .372 .82 .942 r .38691 .36726 .39888 .36968 .41803 .3663 .4062 .36362 Mtetra .427 .848 .958 r .4062 .36362 .41803 .3663 .43737 .36229 .42569 .35916 Mtetra .491 .873 .974 r .42569 .35916 .43737 .36229 .4569 .35756 .44537 .35375 Mtetra .558 .892 .985 r .44537 .35375 .4569 .35756 .4766 .35199 .46524 .34726 Mtetra .621 .9 .986 r .46524 .34726 .4766 .35199 .49648 .3455 .48526 .33959 Mtetra .675 .896 .976 r .48526 .33959 .49648 .3455 .5165 .338 .50544 .33068 Mtetra .716 .879 .957 r .50544 .33068 .5165 .338 .53666 .32942 .52573 .32046 Mtetra .744 .854 .931 r .52573 .32046 .53666 .32942 .55694 .31973 .54613 .30892 Mtetra .761 .825 .902 r .54613 .30892 .55694 .31973 .57731 .30889 .56661 .29609 Mtetra .77 .794 .872 r .56661 .29609 .57731 .30889 .59776 .29694 .58713 .28203 Mtetra .772 .764 .846 r .58713 .28203 .59776 .29694 .61826 .28391 .60769 .26688 Mtetra .77 .736 .822 r .60769 .26688 .61826 .28391 .63881 .26988 .62827 .25078 Mtetra .766 .712 .802 r .62827 .25078 .63881 .26988 .65938 .25499 .64886 .23392 Mtetra .759 .69 .785 r .64886 .23392 .65938 .25499 .67996 .23936 .66944 .21654 Mtetra .752 .672 .773 r .66944 .21654 .67996 .23936 .70056 .22319 .69004 .19888 Mtetra .745 .658 .764 r .69004 .19888 .70056 .22319 .72117 .20664 .71064 .18117 Mtetra .738 .646 .758 r .71064 .18117 .72117 .20664 .7418 .18994 .73128 .16366 Mtetra .73 .637 .755 r .73128 .16366 .7418 .18994 .76246 .17326 .75196 .14656 Mtetra .474 .761 .993 r .09122 .38547 .10428 .39326 .12077 .3911 .10771 .38371 Mtetra .451 .761 .995 r .10771 .38371 .12077 .3911 .13737 .38912 .12431 .38218 Mtetra .425 .76 .996 r .12431 .38218 .13737 .38912 .15411 .38733 .14106 .38087 Mtetra .396 .758 .993 r .14106 .38087 .15411 .38733 .17099 .38571 .15794 .37977 Mtetra .364 .754 .987 r .15794 .37977 .17099 .38571 .18801 .38425 .17497 .37886 Mtetra .33 .747 .977 r .17497 .37886 .18801 .38425 .20519 .38294 .19216 .37812 Mtetra .294 .739 .963 r .19216 .37812 .20519 .38294 .22252 .38174 .20952 .37752 Mtetra .26 .729 .944 r .20952 .37752 .22252 .38174 .24002 .38063 .22705 .37701 Mtetra .228 .718 .923 r .22705 .37701 .24002 .38063 .2577 .37956 .24476 .37652 Mtetra .201 .708 .9 r .24476 .37652 .2577 .37956 .27556 .37848 .26267 .37599 Mtetra .181 .701 .879 r .26267 .37599 .27556 .37848 .29361 .37732 .28079 .37533 Mtetra .172 .699 .862 r .28079 .37533 .29361 .37732 .31186 .376 .29912 .37444 Mtetra .175 .705 .852 r .29912 .37444 .31186 .376 .33031 .37445 .31766 .37318 Mtetra .193 .719 .851 r .31766 .37318 .33031 .37445 .34897 .37254 .33643 .37144 Mtetra .228 .744 .861 r .33643 .37144 .34897 .37254 .36783 .37019 .35543 .36906 Mtetra .281 .778 .882 r .35543 .36906 .36783 .37019 .38691 .36726 .37466 .36588 Mtetra .351 .819 .911 r .37466 .36588 .38691 .36726 .4062 .36362 .3941 .36175 Mtetra .435 .86 .942 r .3941 .36175 .4062 .36362 .42569 .35916 .41376 .35651 Mtetra .524 .895 .968 r .41376 .35651 .42569 .35916 .44537 .35375 .43362 .35 Mtetra .609 .913 .98 r .43362 .35 .44537 .35375 .46524 .34726 .45366 .34212 Mtetra .679 .911 .975 r .45366 .34212 .46524 .34726 .48526 .33959 .47386 .33275 Mtetra .729 .891 .954 r .47386 .33275 .48526 .33959 .50544 .33068 .4942 .32185 Mtetra .76 .86 .924 r .4942 .32185 .50544 .33068 .52573 .32046 .51464 .3094 Mtetra .776 .823 .89 r .51464 .3094 .52573 .32046 .54613 .30892 .53515 .29546 Mtetra .781 .787 .857 r .53515 .29546 .54613 .30892 .56661 .29609 .55572 .28013 Mtetra .78 .752 .828 r .55572 .28013 .56661 .29609 .58713 .28203 .57632 .26357 Mtetra .775 .722 .803 r .57632 .26357 .58713 .28203 .60769 .26688 .59692 .246 Mtetra .768 .696 .782 r .59692 .246 .60769 .26688 .62827 .25078 .61752 .22769 Mtetra .76 .674 .767 r .61752 .22769 .62827 .25078 .64886 .23392 .63811 .20892 Mtetra .751 .655 .755 r .63811 .20892 .64886 .23392 .66944 .21654 .65869 .19001 Mtetra .742 .641 .747 r .65869 .19001 .66944 .21654 .69004 .19888 .67928 .17125 Mtetra .734 .63 .743 r .67928 .17125 .69004 .19888 .71064 .18117 .6999 .15291 Mtetra .726 .622 .742 r .6999 .15291 .71064 .18117 .73128 .16366 .72057 .13525 Mtetra .718 .617 .744 r .72057 .13525 .73128 .16366 .75196 .14656 .74132 .11845 Mtetra .432 .754 .995 r .0779 .37805 .09122 .38547 .10771 .38371 .09437 .3768 Mtetra .399 .751 .993 r .09437 .3768 .10771 .38371 .12431 .38218 .11097 .37582 Mtetra .362 .745 .988 r .11097 .37582 .12431 .38218 .14106 .38087 .1277 .37512 Mtetra .32 .736 .977 r .1277 .37512 .14106 .38087 .15794 .37977 .14457 .37467 Mtetra .275 .723 .959 r .14457 .37467 .15794 .37977 .17497 .37886 .16159 .37445 Mtetra .227 .707 .935 r .16159 .37445 .17497 .37886 .19216 .37812 .17878 .37443 Mtetra .179 .687 .904 r .17878 .37443 .19216 .37812 .20952 .37752 .19614 .37457 Mtetra .135 .665 .868 r .19614 .37457 .20952 .37752 .22705 .37701 .21369 .37479 Mtetra .096 .644 .83 r .21369 .37479 .22705 .37701 .24476 .37652 .23144 .37501 Mtetra .067 .626 .794 r .23144 .37501 .24476 .37652 .26267 .37599 .2494 .37514 Mtetra .05 .616 .765 r .2494 .37514 .26267 .37599 .28079 .37533 .26758 .37505 Mtetra .048 .616 .746 r .26758 .37505 .28079 .37533 .29912 .37444 .28599 .37459 Mtetra .065 .629 .741 r .28599 .37459 .29912 .37444 .31766 .37318 .30464 .3736 Mtetra .102 .657 .752 r .30464 .3736 .31766 .37318 .33643 .37144 .32355 .3719 Mtetra .162 .702 .781 r .32355 .3719 .33643 .37144 .35543 .36906 .3427 .36928 Mtetra .248 .761 .827 r .3427 .36928 .35543 .36906 .37466 .36588 .36209 .36555 Mtetra .356 .827 .883 r .36209 .36555 .37466 .36588 .3941 .36175 .38173 .36051 Mtetra .476 .887 .934 r .38173 .36051 .3941 .36175 .41376 .35651 .40159 .35397 Mtetra .592 .923 .966 r .40159 .35397 .41376 .35651 .43362 .35 .42166 .34577 Mtetra .684 .927 .97 r .42166 .34577 .43362 .35 .45366 .34212 .4419 .3358 Mtetra .745 .903 .948 r .4419 .3358 .45366 .34212 .47386 .33275 .46229 .32399 Mtetra .778 .864 .913 r .46229 .32399 .47386 .33275 .4942 .32185 .4828 .31036 Mtetra .791 .819 .874 r .4828 .31036 .4942 .32185 .51464 .3094 .50339 .29498 Mtetra .793 .775 .837 r .50339 .29498 .51464 .3094 .53515 .29546 .52403 .27801 Mtetra .787 .737 .806 r .52403 .27801 .53515 .29546 .55572 .28013 .54468 .2597 Mtetra .779 .704 .78 r .54468 .2597 .55572 .28013 .57632 .26357 .56533 .24035 Mtetra .769 .676 .761 r .56533 .24035 .57632 .26357 .59692 .246 .58596 .22032 Mtetra .758 .654 .746 r .58596 .22032 .59692 .246 .61752 .22769 .60656 .19998 Mtetra .748 .636 .736 r .60656 .19998 .61752 .22769 .63811 .20892 .62715 .17972 Mtetra .738 .622 .73 r .62715 .17972 .63811 .20892 .65869 .19001 .64773 .1599 Mtetra .728 .612 .728 r .64773 .1599 .65869 .19001 .67928 .17125 .66834 .14085 Mtetra .719 .606 .73 r .66834 .14085 .67928 .17125 .6999 .15291 .68901 .1228 Mtetra .711 .604 .735 r .68901 .1228 .6999 .15291 .72057 .13525 .70976 .10592 Mtetra .703 .605 .743 r .70976 .10592 .72057 .13525 .74132 .11845 .73063 .09031 Mtetra .371 .739 .99 r .06429 .37114 .0779 .37805 .09437 .3768 .08073 .37052 Mtetra .324 .729 .98 r .08073 .37052 .09437 .3768 .11097 .37582 .09729 .37025 Mtetra .27 .713 .962 r .09729 .37025 .11097 .37582 .1277 .37512 .11398 .37031 Mtetra .21 .691 .933 r .11398 .37031 .1277 .37512 .14457 .37467 .13082 .37068 Mtetra .147 .662 .893 r .13082 .37068 .14457 .37467 .16159 .37445 .14781 .37134 Mtetra .083 .627 .844 r .14781 .37134 .16159 .37445 .17878 .37443 .16498 .37224 Mtetra .023 .589 .787 r .16498 .37224 .17878 .37443 .19614 .37457 .18233 .3733 Mtetra 0 .553 .729 r .18233 .3733 .19614 .37457 .21369 .37479 .19988 .37444 Mtetra .066 0 0 r .19988 .37444 .21369 .37479 .23144 .37501 .21765 .37552 Mtetra .09 0 0 r .21765 .37552 .23144 .37501 .2494 .37514 .23565 .37642 Mtetra .096 0 0 r .23565 .37642 .2494 .37514 .26758 .37505 .2539 .37695 Mtetra .082 0 0 r .2539 .37695 .26758 .37505 .28599 .37459 .27241 .3769 Mtetra .046 0 0 r .27241 .3769 .28599 .37459 .30464 .3736 .29119 .37605 Mtetra 0 0 0 r .29119 .37605 .30464 .3736 .32355 .3719 .31026 .37413 Mtetra .31026 .37413 .32355 .3719 .3427 .36928 .3296 .3709 Mtetra .249 .761 .782 r .3296 .3709 .3427 .36928 .36209 .36555 .34921 .36609 Mtetra .409 .86 .873 r .34921 .36609 .36209 .36555 .38173 .36051 .36909 .35946 Mtetra .569 .929 .94 r .36909 .35946 .38173 .36051 .40159 .35397 .3892 .3508 Mtetra .693 .945 .96 r .3892 .3508 .40159 .35397 .42166 .34577 .40951 .33999 Mtetra .767 .915 .938 r .40951 .33999 .42166 .34577 .4419 .3358 .43 .32695 Mtetra .799 .863 .896 r .43 .32695 .4419 .3358 .46229 .32399 .45061 .31172 Mtetra .807 .808 .852 r .45061 .31172 .46229 .32399 .4828 .31036 .47131 .29444 Mtetra .802 .758 .812 r .47131 .29444 .4828 .31036 .50339 .29498 .49205 .27538 Mtetra .792 .716 .78 r .49205 .27538 .50339 .29498 .52403 .27801 .5128 .25487 Mtetra .78 .681 .755 r .5128 .25487 .52403 .27801 .54468 .2597 .53352 .23335 Mtetra .767 .653 .737 r .53352 .23335 .54468 .2597 .56533 .24035 .5542 .21131 Mtetra .754 .631 .724 r .5542 .21131 .56533 .24035 .58596 .22032 .57484 .18924 Mtetra .742 .614 .717 r .57484 .18924 .58596 .22032 .60656 .19998 .59544 .16762 Mtetra .73 .602 .713 r .59544 .16762 .60656 .19998 .62715 .17972 .61604 .14687 Mtetra .72 .594 .714 r .61604 .14687 .62715 .17972 .64773 .1599 .63665 .12732 Mtetra .71 .59 .719 r .63665 .12732 .64773 .1599 .66834 .14085 .65732 .1092 Mtetra .702 .591 .728 r .65732 .1092 .66834 .14085 .68901 .1228 .67808 .09262 Mtetra .695 .595 .741 r .67808 .09262 .68901 .1228 .70976 .10592 .69897 .07759 Mtetra .688 .604 .757 r .69897 .07759 .70976 .10592 .73063 .09031 .72002 .064 Mtetra .282 .708 .969 r .05036 .36488 .06429 .37114 .08073 .37052 .06673 .36508 Mtetra .213 .683 .941 r .06673 .36508 .08073 .37052 .09729 .37025 .08322 .36571 Mtetra .135 .647 .896 r .08322 .36571 .09729 .37025 .11398 .37031 .09985 .36677 Mtetra .052 .601 .835 r .09985 .36677 .11398 .37031 .13082 .37068 .11662 .36822 Mtetra 0 .547 .76 r .11662 .36822 .13082 .37068 .14781 .37134 .13355 .37001 Mtetra .103 0 0 r .13355 .37001 .14781 .37134 .16498 .37224 .15067 .37208 Mtetra .163 0 0 r .15067 .37208 .16498 .37224 .18233 .3733 .16798 .37432 Mtetra .207 0 0 r .16798 .37432 .18233 .3733 .19988 .37444 .18552 .3766 Mtetra .234 0 0 r .18552 .3766 .19988 .37444 .21765 .37552 .2033 .37873 Mtetra .242 0 0 r .2033 .37873 .21765 .37552 .23565 .37642 .22134 .3805 Mtetra .23 0 0 r .22134 .3805 .23565 .37642 .2539 .37695 .23967 .38165 Mtetra .196 0 0 r .23967 .38165 .2539 .37695 .27241 .3769 .25831 .38188 Mtetra .134 0 0 r .25831 .38188 .27241 .3769 .29119 .37605 .27726 .38086 Mtetra .033 0 0 r .27726 .38086 .29119 .37605 .31026 .37413 .29653 .37824 Mtetra 0 0 0 r .29653 .37824 .31026 .37413 .3296 .3709 .31613 .37368 Mtetra .32 .805 .774 r .31613 .37368 .3296 .3709 .34921 .36609 .33603 .36686 Mtetra .54 .926 .895 r .33603 .36686 .34921 .36609 .36909 .35946 .35622 .35752 Mtetra .709 .962 .943 r .35622 .35752 .36909 .35946 .3892 .3508 .37665 .34549 Mtetra .795 .923 .922 r .37665 .34549 .3892 .3508 .40951 .33999 .39728 .33073 Mtetra .822 .856 .873 r .39728 .33073 .40951 .33999 .43 .32695 .41806 .31332 Mtetra .821 .79 .823 r .41806 .31332 .43 .32695 .45061 .31172 .43892 .29352 Mtetra .809 .734 .782 r .43892 .29352 .45061 .31172 .47131 .29444 .45982 .27172 Mtetra .793 .689 .75 r .45982 .27172 .47131 .29444 .49205 .27538 .4807 .24845 Mtetra .776 .654 .728 r .4807 .24845 .49205 .27538 .5128 .25487 .50153 .22433 Mtetra .761 .627 .712 r .50153 .22433 .5128 .25487 .53352 .23335 .5223 .20002 Mtetra .746 .606 .702 r .5223 .20002 .53352 .23335 .5542 .21131 .54299 .17616 Mtetra .732 .591 .698 r .54299 .17616 .5542 .21131 .57484 .18924 .56363 .15331 Mtetra .72 .58 .698 r .56363 .15331 .57484 .18924 .59544 .16762 .58424 .13194 Mtetra .709 .575 .703 r .58424 .13194 .59544 .16762 .61604 .14687 .60487 .11234 Mtetra .699 .575 .712 r .60487 .11234 .61604 .14687 .63665 .12732 .62555 .09466 Mtetra .691 .58 .725 r .62555 .09466 .63665 .12732 .65732 .1092 .64633 .07888 Mtetra .685 .589 .743 r .64633 .07888 .65732 .1092 .67808 .09262 .66725 .06486 Mtetra .679 .604 .764 r .66725 .06486 .67808 .09262 .69897 .07759 .68833 .05238 Mtetra .675 .622 .788 r .68833 .05238 .69897 .07759 .72002 .064 .70958 .04114 Mtetra .149 .645 .913 r .03604 .35952 .05036 .36488 .06673 .36508 .05231 .36079 Mtetra .05 .592 .847 r .05231 .36079 .06673 .36508 .08322 .36571 .06869 .36262 Mtetra 0 .523 .759 r .06869 .36262 .08322 .36571 .09985 .36677 .0852 .36498 Mtetra .151 0 0 r .0852 .36498 .09985 .36677 .11662 .36822 .10186 .36785 Mtetra .234 0 0 r .10186 .36785 .11662 .36822 .13355 .37001 .11869 .37114 Mtetra .298 0 0 r .11869 .37114 .13355 .37001 .15067 .37208 .13572 .37474 Mtetra .342 0 0 r .13572 .37474 .15067 .37208 .16798 .37432 .15296 .3785 Mtetra .366 0 0 r .15296 .3785 .16798 .37432 .18552 .3766 .17046 .38221 Mtetra .372 0 0 r .17046 .38221 .18552 .3766 .2033 .37873 .18824 .38558 Mtetra .361 0 0 r .18824 .38558 .2033 .37873 .22134 .3805 .20633 .38828 Mtetra .329 0 0 r .20633 .38828 .22134 .3805 .23967 .38165 .22477 .38992 Mtetra .273 0 0 r .22477 .38992 .23967 .38165 .25831 .38188 .24358 .39005 Mtetra .178 0 0 r .24358 .39005 .25831 .38188 .27726 .38086 .26277 .3882 Mtetra .024 0 0 r .26277 .3882 .27726 .38086 .29653 .37824 .28236 .38389 Mtetra 0 0 0 r .28236 .38389 .29653 .37824 .31613 .37368 .30232 .37671 Mtetra .509 .911 .829 r .30232 .37671 .31613 .37368 .33603 .36686 .32263 .3663 Mtetra .736 .978 .919 r .32263 .3663 .33603 .36686 .35622 .35752 .34325 .35248 Mtetra .83 .924 .896 r .34325 .35248 .35622 .35752 .37665 .34549 .36411 .33524 Mtetra .844 .838 .839 r .36411 .33524 .37665 .34549 .39728 .33073 .38513 .31477 Mtetra .831 .762 .786 r .38513 .31477 .39728 .33073 .41806 .31332 .40625 .29154 Mtetra .81 .702 .746 r .40625 .29154 .41806 .31332 .43892 .29352 .42738 .26616 Mtetra .788 .657 .718 r .42738 .26616 .43892 .29352 .45982 .27172 .44846 .23946 Mtetra .768 .623 .699 r .44846 .23946 .45982 .27172 .4807 .24845 .46945 .21232 Mtetra .75 .597 .687 r .46945 .21232 .4807 .24845 .50153 .22433 .49033 .18562 Mtetra .734 .578 .681 r .49033 .18562 .50153 .22433 .5223 .20002 .51109 .16014 Mtetra .719 .566 .68 r .51109 .16014 .5223 .20002 .54299 .17616 .53177 .13652 Mtetra .706 .559 .685 r .53177 .13652 .54299 .17616 .56363 .15331 .55241 .11516 Mtetra .695 .557 .694 r .55241 .11516 .56363 .15331 .58424 .13194 .57305 .09623 Mtetra .686 .562 .709 r .57305 .09623 .58424 .13194 .60487 .11234 .59374 .07968 Mtetra .679 .573 .729 r .59374 .07968 .60487 .11234 .62555 .09466 .61454 .0653 Mtetra .674 .59 .753 r .61454 .0653 .62555 .09466 .64633 .07888 .63548 .05273 Mtetra .67 .612 .781 r .63548 .05273 .64633 .07888 .66725 .06486 .65657 .0416 Mtetra .668 .637 .81 r .65657 .0416 .66725 .06486 .68833 .05238 .67785 .03149 Mtetra .666 .663 .837 r .67785 .03149 .68833 .05238 .70958 .04114 .6993 .02209 Mtetra 0 .524 .787 r .02127 .3554 .03604 .35952 .05231 .36079 .03737 .3581 Mtetra .166 0 0 r .03737 .3581 .05231 .36079 .06869 .36262 .05358 .36153 Mtetra .276 0 0 r .05358 .36153 .06869 .36262 .0852 .36498 .06991 .36568 Mtetra .361 0 0 r .06991 .36568 .0852 .36498 .10186 .36785 .08639 .37047 Mtetra .42 0 0 r .08639 .37047 .10186 .36785 .11869 .37114 .10305 .37578 Mtetra .457 0 0 r .10305 .37578 .11869 .37114 .13572 .37474 .11992 .38144 Mtetra .474 0 0 r .11992 .38144 .13572 .37474 .15296 .3785 .13705 .38718 Mtetra .476 0 0 r .13705 .38718 .15296 .3785 .17046 .38221 .15448 .39266 Mtetra .463 0 0 r .15448 .39266 .17046 .38221 .18824 .38558 .17225 .39743 Mtetra .434 0 0 r .17225 .39743 .18824 .38558 .20633 .38828 .19043 .40094 Mtetra .383 0 0 r .19043 .40094 .20633 .38828 .22477 .38992 .20905 .4026 Mtetra .298 0 0 r .20905 .4026 .22477 .38992 .24358 .39005 .22815 .40171 Mtetra .152 0 0 r .22815 .40171 .24358 .39005 .26277 .3882 .24774 .39763 Mtetra 0 0 0 r .24774 .39763 .26277 .3882 .28236 .38389 .26782 .38974 Mtetra .485 .887 .743 r .26782 .38974 .28236 .38389 .30232 .37671 .28834 .37761 Mtetra .781 .991 .886 r .28834 .37761 .30232 .37671 .32263 .3663 .30926 .36103 Mtetra .867 .91 .858 r .30926 .36103 .32263 .3663 .34325 .35248 .33048 .34009 Mtetra .86 .804 .795 r .33048 .34009 .34325 .35248 .36411 .33524 .35189 .31526 Mtetra .832 .723 .744 r .35189 .31526 .36411 .33524 .38513 .31477 .37339 .28731 Mtetra .804 .663 .708 r .37339 .28731 .38513 .31477 .40625 .29154 .39486 .25731 Mtetra .778 .62 .684 r .39486 .25731 .40625 .29154 .42738 .26616 .41622 .22648 Mtetra .755 .588 .67 r .41622 .22648 .42738 .26616 .44846 .23946 .43741 .19608 Mtetra .735 .565 .663 r .43741 .19608 .44846 .23946 .46945 .21232 .45841 .16723 Mtetra .717 .549 .661 r .45841 .16723 .46945 .21232 .49033 .18562 .47925 .1408 Mtetra .702 .54 .666 r .47925 .1408 .49033 .18562 .51109 .16014 .49995 .11735 Mtetra .689 .538 .676 r .49995 .11735 .51109 .16014 .53177 .13652 .52059 .09706 Mtetra .679 .543 .692 r .52059 .09706 .53177 .13652 .55241 .11516 .54122 .07981 Mtetra .672 .555 .715 r .54122 .07981 .55241 .11516 .57305 .09623 .56192 .06521 Mtetra .667 .576 .743 r .56192 .06521 .57305 .09623 .59374 .07968 .58272 .05275 Mtetra .664 .603 .776 r .58272 .05275 .59374 .07968 .61454 .0653 .60365 .04188 Mtetra .663 .633 .81 r .60365 .04188 .61454 .0653 .63548 .05273 .62475 .03207 Mtetra .663 .664 .841 r .62475 .03207 .63548 .05273 .65657 .0416 .64601 .02293 Mtetra .663 .691 .866 r .64601 .02293 .65657 .0416 .67785 .03149 .66745 .01414 Mtetra .663 .711 .883 r .66745 .01414 .67785 .03149 .6993 .02209 .68906 .00551 Mtetra 0 g .68874 0 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .03716 .25514 m 0 .48963 L s 0 .48963 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .68874 0 m .03716 .25514 L s .03716 .25514 m .68874 0 L s .23689 .17693 m .24136 .18173 L s [(1)] .22795 .16733 .93182 1 Mshowa .45343 .09214 m .4575 .09728 L s [(2)] .44528 .08186 .79278 1 Mshowa .68874 0 m .69233 .00549 L s [(3)] .68156 -0.01098 .65374 1 Mshowa .125 Mabswid .07572 .24004 m .07856 .24276 L s .11507 .22463 m .11787 .22739 L s .15504 .20898 m .1578 .21178 L s .19564 .19308 m .19837 .19592 L s .27881 .16052 m .28145 .16344 L s .3214 .14384 m .32399 .1468 L s .36469 .12689 m .36724 .12989 L s .40869 .10966 m .41119 .1127 L s .49891 .07433 m .5013 .07746 L s .54517 .05622 m .5475 .05939 L s .59221 .0378 m .59448 .04101 L s .64006 .01906 m .64227 .02231 L s gsave .29165 .07573 -70.3112 -16.5625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 16.562500 moveto 460.000000 16.562500 lineto 460.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 16.562500 lineto closepath clip newpath 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (x) show 69.000000 12.812500 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Courier grestore % End of Graphics MathPictureEnd \ \>"], "NumberedFigure", ImageSize->{288, 233.563}, ImageMargins->{{68, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgC5003ok>C58NcTa@00oncTaB7/iC5003ok>C58NcTa@00oncTaB7/iC50039k>C50P0005G/icTaNcTa@0005C/icT aNcTa@1Ck>C5003;k>C500<0003/icTa@040000k>C5k>C50000E>cTa@00bNcT a@800007k>C51@0004W/icTaNcTa@19k>C5003Dk>C500<0003/icTa@030000k>C5k>C504W/icTaNcTa@19k>C5003=k>C50P0000C/iC50038k>C50`0000?/icTa@00a^cTa@800003k>C50jVf hP030000k>C5000004o/icTaNcTa@0004k/ik>C5002nk>C50`000003k>C50000ZK3M00JY/=d4 ZKKR00D0002Y]^;/icTa@800003k>C50ZVYe`NY/=d3ZKKR00FZZMH0002Z ZMJZZMK/iC5 0000C>cTa@00]^cTa@<00004k>C51jVYe`FY/=d2Zj??0jZYeP040000ZZWFZZWFZZWF0^cTa@030000 k>C5k>C504W/icTa@BYX/l7ZJWG0ZV`g@F[Xll2ZZWF00@0002ZZMJZZMJZZMH2 k>C500<0003/icTa@000>cTaNcTa@JYX/l7ZJWG1j^Sc`>ZZMH0 10000:ZYeZZYeZZYeP;/icTaNcTa@18k>C5001Qk>C50P000003k>C50000000004W/iYV/H6ZJ;?1:VYe`>[WC500<0003/iC5000002K/iC51JVJaPJYX/l3ZJWG1:^L a`N[Xll2ZZWF00<0002/WlV/WlT00ZbOb@;/icTaNcTa@17k>C5001Sk>C500<0003/iC5k>C501c/iC5001Qk>C50P000003k>C50000000002K/icTaNcTa@0Hk>C50`00 00K/in2:VJaPBYX/l2[9O01j^La`B[Xll3[I[300>/WlT0002/WlT01:bOb@?/icT aNcTa@15k>C5002=k>C500<0003/iC500<0003/iC5k>C504G/icTaNcTa@0001?/icTa@JZTkh8ZI[61ZbG`0N[WcTaNcTa@14k>C5002C50P0001;/inZY>n 00FZTkh5ZI[60ZfB^PN/Ul05Zic700>_U[j]V/>]V/<01JfJ``030000[9o9[9o900:/WlT2/9[11>cT a@030000k>C5k>C504?/in1:VJaPB]T[X6[9O00j^La`B_U[h6 [I[300<0002/WlV/WlT01K2J`@?/icTaNcTa@13k>C5002Kk>C50P000003k>C50000k>C5 00W/i[WC5002Hk>C50`0000g/iC5k>C5047/in00>_SkF]T[Z]T[X01JfB^PF/Ul02/9Bi1jnF_P>]V/<2/IRm00<0002aV;f`V/401K2J `@G/icTaNcTa@11k>C5002Ck>C50`0000o/i]`>ZTkh4[hne1jfB^P>/Ul04 /9Bi1jnF_P06[I[3/IRm/IRm/IRm0000/IRm1k2J`@G/icTaNcTa@10k>C5002Ak>C50P00 017/i]`03ZY>n[hne[hne00>_SkD7[I:j00>/Ul2`U;V`U;T01;2D^@N_U[h4/IRm00<0 002aV;faV;d01[2J`@G/icTaNcTa@10k>C5002>k>C50`000003k>C50000k>C500o/i]`N_SkD6[I:j2;2D^@F_U[h00k>G^[6H_K6H_@02/IRm00<0002aV;faV;d01K2J`@03/iZn k>C5k>C500C/icTaNcTa@0ok>C5002;k>C50`0001C/i ]`03/Hja[hne[hne00F_SkD5[I:j00>bTkJ`U;V`U;T01[2D^@>_U[h4/iNj0k6H_@030000/IRm/IRm 00>`V/44/iZn1^cTa@030000k>C5k>C503k/i]`>aS[46 [hne0jfB^PBbTkH8/9Bi00>_U[jcUkZcUkX00k>G^P>aV;d01@000;6H_K6H_K6H_K2J`@05/iZn1NcT a@800007k>C5100003G/i]`BaS[47[hne00>]T[ZbTkJb TkH00k:C]PR`U;T7/iNj0[6H_@040000/IRm/IRm/IRm1k>J_PK/icTaNcTa@04k>C500<0 003/icTa@8000000ncTa@000>cTa@0Ek>C51[29[@N]Rk400jb>]k6>/K6>/@03 /Hja1jn?]@NbTkH6/9Bi00>eUkRcUkZcUkX01K>G^P:aV;d010000;6H_K6H_KJJ_0NcV[h7k>C500<0 003/icTa@030000k>C5k>C503G/i/@F_SkD0 0kFC/k:C][:C]P05/Y>f1K2D^@>eUkP6/iNj0[6H_@030000]YZl]YZl00:fV[`7/iZn1^cTa@030000 k>C5k>C500G/icTaNcTa@0dk>C5001ok>C50P0001_/i:Z[29[K29[@05/8V]1Zf; /@03]8n_/Hja/Hja00FaS[44[hne0kFC/`JbTkH3/9Bi1KFG^0NcUkX00k6H_@000;JJ_003]YZl1k>J _PO/icTaNcTa@02k>C500@0003/iC5001lk>C50`0001c/i/@>_SkD4]I>c1k:C]P03/9Bi]INh]INh00BeUkP7/iNj0[JJ_0030000]YZl]YZl 00:fV[`5/iZn00>gWKk/iC5k>C500;/iC51;>:ZPN`RJd2[H^a1KB?[`NaS[400jn?]KFC/kFC/`03]I>c1k:C]PNeUkP5/iNj0[RK^P:fV[`0 0`000;JJ_;JJ_002]YZl0k>J_PBgWKh5k>C50`0003c/i]Rk6dSjndSjl01;B?[`NaS[47]I>c1K:C]P03^9Rf]INh]INh00JeUkP3/iNj1;RK ^P03]YZl0000]YZl00BfV[`00k>J_[NM_[NM_P03]ifn2>cTa@030000k>C5k>C503W/iC51K>:ZPN`RJd8]8n_1K6>/@03^9Bb]I>c]I>c00FeTk<4/Y>f0kRH]PNeUkP0 0k>G^[RK^[RK^P04^9^j00>fV[`0002fV[`01;JJ_0NgWKh8k>C500<0003/i>cTa@00ENcT a@030000k>C5k>C501[/ihT:jdSjndSjl01[B?[`BaS[43^9Bb1[FC /`>bTkH4^9Rf1kFG^0NhVkX00kJJ_0000;JJ_003]YZl00>iWkfgWKjgWKh01KNM_PS/icT aNcTa@0hk>C5001Ek>C500<0003/icTa@80000Uk>C500>gS:VcRZZcRZX01K>:ZPB`RJd3 ^92^1kB?[`>aS[44^9Bb1kFC/`03/Y>f^9Rf^9Rf00BhV;H5]INh00>jW;ZhVkZhVkX01KRK^P03]YZl 0000]YZl00:fV[`3^Inm1kNM_PS/icTaNcTa@0gk>C5001Ek>C500<0003/iC50[NjW;X7^9^j00<0 002fV[biWkd01;VO_@NgWKh9k>C500<0003/iC5k>C501?/igS:T6/hZZ0k29[@BhT:h8]8n_00>aS[6hU;:hU;801;RD/PFeTk<00kZJ][RH][RH]P05 ^9Rf0kFG^0BjW;X7^9^j00<0002iWkfiWkd01;VO_@FgWKh2^Z?11ncTa@<0000hk>C5001Dk>C50P00 01;/i`RJfhT:jhT:h01;R@[PNdSjl7^9Bb1;FC/`>jV[H7^9Rf00>e UkRjW;ZjW;X01;ZL^PJhVkX00`000;VO_KVO_@04^Inm1;NM_PBjXl49k>C500<0003/iC51KNc1;ZJ]PNhV;H7 ^Ybj1KRK^P03^j6n0000^Inm00JiWkd00kNM_[ZS`KZS`@04^Z?12NcTa@030000k>C5k>C503G/ikTjjhT:jhT:h01KR@[PFdSjl2^iNb2;RD/P03]I>c^YZf^YZf 00BjV[H5^9Rf00>lWkZjW;ZjW;X01KZL^P>hVkX3^j6n00<0002iWkfiWkd01KVO_@NjXl4:k>C500<0 003/icTa@00H>cTa@<0000`k>C51kN^1[R@[P>dSjl5^iNb1kRD/PNjV[H4 ^9Rf0kbO^PNjW;X00kRK^[^Q_[^Q_P02^j6n00<0002iWkfiWkd01;VO_@03_:G2^Z?1^Z?100FjXl4; k>C500<0003/iC500>lT:VgS:VgS:T01KN^1kR@ [P03]8n_^iNb^iNb00BkUk86^9Bb00>mWKNjV[JjV[H01KZJ]P>hV;H4_9nj1kZL^PFkXKh00`000;^Q _[VO_@03^Inm0kbU`PNjXl4:k>C500<0003/iC50[b@Z@NgS:T3 /hZZ1;^C[PNhT:h7^iNb1KRD/P>mWKL7^YZf00>hV;JlWkZlWkX01;bO^PFjW;X00kfT_k^Q_[^Q_P03 ^j6n00<0002kXKjiWkd00[VO_@BlYL87^Z?12NcTa@030000k>C5000003C/ilT:T7]hbY00>cRZZkTjjkTjh00k^C[PJhT:h00kjK/k^G/[^G/P05^iNb1;RD/PBmWKL7^YZf1kbO ^PBjW;X3_JBo1;^Q_P040000^j6n^j6n^Inm1[bU`PFjXl42_JS52ncTa@030000k>C5k>C5037/iC5k>C503;/i^^i>^00BkTjh5^92^0[jK /`NkUk82^9Bb1KfM]`JjV[H00knR_;bO^[bO^P05_9nj0kZL^PBmY;l4^j6n00<0002kXKjkXKh01kbU `P>jXl44_JS52ncTa@030000k>C5k>C5037/iNcTa@FlT:T7]hbY1k^C[PBhT:h3 _Y^c1k^G/P03^9Bb_Ifg_Ifg00FmWKL4^YZf0knR_0NlWkX00kZL^[fT_kfT_`04_JBo0k^Q_P040000 ^j6n_ZS3_ZS31kbU`P03^Z?1_JS5_JS500BmZC500<0003/icTa@00DNcTa@<0000j k>C51[b@Z@JgS:T00knH[k^C[[^C[P05^i>^0kR@[PBnVk<7^iNb2;fM]`>jV[H4_j:l1kbO^PNmY;l3 ^j6n00@0002nZ<>nZ<>nZ<<7_:G21kfXa@c/icTaNcTa@0_k>C5001?k>C50P0003g/ioV:l6^i>^0[R@[PJnVk<5^iNb00?1XKVmWKNmWKL01[fM]`>jV[H5_j:l1KbO^P03`:O1 _JBo_JBo00JmY;l00k^Q_[jX``000004_ZS31KbU`P:n[C5001C50`00 0003k>C50000k>C503_/i^00>hT:jnVk>nVk<01;jK/`BkUk83`J6i2;fM ]`03^YZf_j:l_j:l00BoX[`4_9nj0l2W`@NmY;l2_ZS300<0002nZ<>nZ<<00[jX``>lYL84_Zc71kfX a@c/icTaNcTa@0Jk>C50P0001;/icTa@03`IJ[_92Y_92Y00JlT:T3 ]hbY1;nH[`NkTjh7_Y^c0k^G/PC1XKT8_Ifg1knR_0>lWkX4`:O11[fT_`;0[lYL:n[cTa@030000k>C5k>C501S/icTaNcTa@00 017/i^00?2X;JnVk>nVk<01[jK/`03^iNb `J6i`J6i00C1XKT6_Ifg00?2YkjoX[boX[`01[nR_003_9nj`:O1`:O100C0Yl44_JBo0l2/a@:nZ<<0 0`000;jX`kjX``02_ZS31kj/a`>mZcTa@030000k>C5k>C501S/icTaNcTa@0B k>C50015k>C50P0004C/i^0l:P]PNnVk<7`J6i1KfM ]`?2Ykh7_j:l1l2W`@>mY;l5`:c500>nZ<<0002nZ<<00[jX``03`:o9_Zc7_Zc700Jn[cTa@030000k>C5k>C501K/icTa@12 k>C51<6FZ`NlT:T8_iR_0k^C[PC2X;H6_Y^c00?4Ykc1XKW1XKT01L6Q^@>mWKL5`ZNn1[nR_003`Zc4 `:O1`:O100K0Yl400kfT_l2/aL2/a@04`:c500>nZ<<0002nZ<<01<2_b@Nn[C5k>C501K/icTaNcTa@0Bk>C50010k>C50P0004O/i^1L:P]PBnVk<3a:Nl1l6Q^@03_Ifg`ZNn`ZNn00C2Ykh5_j:l0l:/a0O0Yl48`:c500<0 0030[lW0[lT00l2_b@Fn[C5000mk>C50`0004W/ikTjk2X;K2X;H01<:P]P>nVk<4a:Nl1l6Q^@O2Ykh3_j:l1L:/a0G0Yl42 `[382<2/a@030000`:o9`:o900?0[lT4_Zc71;ncc@Nn[l/=k>C500<0003/iC5k>C500008ncTa@00>^cTa@<0001;k>C51l6FZ`BlT:T3a9nb2;nH[`O2X;H3_Y^c1LBW_0G1XKT2 a:g21l:W_P03_j:l`Zc4`Zc400C2[<@4`:O11<:`b0K0[n[C5k>C500G/icTaNcTa@0Rk>C5000hk>C50P00 00;/icTaNcTa@18k>C500?7WZo1UZ_1UZ/01L6FZ`>lT:T4a9nb1knH[`03aZNj`Z2f`Z2f 00K2X;H00kjK/lBW_C500<0003/iC5k>C5 027/iC5k>C5k>C5000000;/icTaNcTa@0Qk>C5000ck>C50P00057/icTaNcTa@02k>C50P0002C/ioV:l6 aZNj1<:P]P?7[/47a:Nl2o/ld4_kWD1knfd@c/icTa@00000Yk>C5000^k>C50P0005C/in^mL>k>C500<0 003/iC51lNN[`C1UZ/3bJRg1lBO/PS6YkX3`Z2f1LN^`@C4Yk`3 akC71/B]`P;6^cTaNcTa@0Vk>C5000Yk>C50P0005S/ik>C500<0003/iC52C500<0003/icTa@009ncT a@80001Hk>C500?=ZKG7WZo7WZl01lNN[`03`IJ[bJRgbJRg00C9Z;L3a9nb1<^`_`O6YkX00lZgalN^ `LN^`@06ajk12oeP000000000000K2^M46 `KcE00<00031]m71]m401[nnf0>o^M@4_[oK1;jke`>m`Md=k>C50P0002K/icT a@00001Gk>C50/fY]@S7WZl7bJRg0lBO/PG;/;l5aZNj0lZga`K7[/42bKc>1lNda`S6^cTaNcTa@0Sk>C5000Pk>C50P0000C/iC5k>C505?/inbJRgbJRg00K9Z;L00lBO//^`_l^`_`04bk2o0lJW^PG:]lL5ajk10lVlcPK7]oeP?2^M44`L7I1L6le@03_l;L0000_l;L00Fo_]P3_/?N1[jof`Nm`Md? k>C500<0003/iC5k>C500000ncTa@030000k>C5k>C500;/icTaNcTa@1Ak>C51n1lVX]`S;/;l00lJW^/ZgalZga`04b[O70lN^`@K9_

oeP07`koF1l71f@;1_=D4_l;L00<0002o_]Ro _]P00[nnf0Bn`mh4_[oK0kc4h0Nm`Md>k>C500<0003/iC5k>C5 00000ncTa@800004k>C500<0003/icTa@G=ZKD4aij_10/Nda`K7`=<3a[S=0lG3f0<00002aKcB104_L7M0k[5hPk/icTaNcTa@0Qk>C5000Ok>C500@0 003/iC500<0003/icTa@030000k>C5k>C504k/io ePC1a]h4`L7I0kk7h@No`]`00`000;k3g[k3gP05_/?N1kc4h0>m`Md4^/GR3NcTa@80000Sk>C5000O k>C500@0003/iC500<0003/ik>C51/fY]@?7WZl6ck>n0lVX ]`G?^lP4bk2o0lg2c`K:]lL2blKF1/VlcP?7bM/7al3C0P0000K5`mP7`lGL00?3_mK1a]k1a]h01L76 gP;1`MT5_/OQ1;o2g0:lb><00`000;k3g[k3gP03_/?N0k_8i0Nla>07^/GR3^cTa@030000k>C5k>C5 023/icTa@800008k>C500<0003/in00?9Z;O?^lS?^lP01186`lGL2<76gPNnan43_l;L1;c8h`040000_/?N_/?N_/?N1;_8i0Fla>03^LSU1[[5 hPo/icTaNcTa@0Ok>C5000Uk>C500<0003/iC5k>C504S/i1lO9f`<00004 aL_O0lG3f0G2c>84`lGL0ko<00`000;_8i;_8i005^lST0[c4h0Fib>D4 ^/GR0kS8iPk/icTaNcTa@0Ok>C5000Uk>C50P0000_/icTaNcTa@16k>C50mBi _PK=ZKD2e@3`LKN1Kg< iP>nan44^lcW1Kc8h`03^LcX0000^LcX00Jkb>@8^LSU0[[5hPBhb>H?k>C500<0003/iC5k>C500_/icTaNcTa@14k>C51=Bi_PG=ZKD3efPK=`/l2b]7O1/_6eP;6d^<01LO9f`00000000000od^P7`/cR2;o< i0Rmc>H6^lcW0kc8h`Bic>P010000;_8i;_8i;_8i0BgbnT7^LSU1kS8iPk/iC500<0003/ic]X3cL;?1L[A g`?;a]H2a];S0`0000?7bM/5`]?V0lG;g`Fod^P4`/cR0kcBjPFoc>@3^]7[1Kghd>`6^lcW1kW< j0030000]l_Y]l_Y00FgbnT3^LSU1;K;j@Bhb>H3]L[Z3^cTa@030000k>C5k>C501g/icTaNcTa@0=k>C500<0003/ic]X2 cL;?1/[Ag`;;a]H300001mc>H4^=3/0k_k@030000]l_Y]l_Y00FgbnT6]/_Y0kS8iPFeb^X>k>C500<0003/icTa@004^cT a@800004k>C50P0000?/iC5k>C500k/icTaNcTa@0ok>C52=Bi _P03cJVeefPO:dMl200001LKBh`>nf^h5`]?V0k_I k`Nod^P8_=;Z2;[Aj`Nhd>`7]lo/0kWec^d00`000;O;jKO;j@02]l_Y1;C=k@JfbnT8]L[Z3^cT a@030000k>C5k>C501_/icTaNcTa@0000[/icTaNcTa@02k>C50P00 017/icTaNcTa@0mk>C52MBi_PSD`lT7d/[B0lcLi@G>c]X3amgY0l[Ag`<00003`]c/0lKB h`Fnf^h3`]?V1K_Ik`>od^P5^=O`0kcBjPBfeO04^]7[1;CCl0Bhd>`3/m;`1kO?k0Jec^d00`000;C= kKC=k@05]d5]L[Z0k;cTaNcTa@0Kk>C5000Ak>C500@0003/iC500<0003/iC5k>C5017/icTaNcTa@0kk>C50]c= b`OD^Kh2f=KF1]C3b@;Bfml5d/[B1LcLi@?>c]X4amgY0`000003b]7O`]c/`]c/00C2g>`8_][^2;_I k`Rheo07]]G`1kCCl0>hd>`5/m;`0kO?k0BbdO04]Lk]0[7?l0030000]d=k>C50P0000S/iC5k>C500002^cTa@030000k>C5k>C5 00;/iC5k>C503W/ighO@5_][^0kCNm@FkfNl3/m_e1KSGl0>afO@4]]G`0k3Gm0Nddo08/m;`1[;A l0>ec^d3/Lo`00<0002aco2dcNd00[C=k@B`c^l6/lc]2;;cTaNcTa@06k>C500<0 003/icTa@004NcTa@040000k>C5k>C500002^cTa@030000k>C5k>C500;/icT aNcTa@0Ck>C500<0003/inf^h5]=ke0k_Ik`BcfoD3^=O`1K7Im0>feO05/=Od0kCCl0B_e?<4/m;`1:oC l`JbdO06/Lo`00<0002aco2`c^l01K3>k`>cc>d5/l=k>C500<0003/iC5000Bk>C50P0000[/icTa@80000Ek>C500<0003/i[`0lcLi@04_^Ob0000000000000[kWlP?7gNT6^^Cd2;OQm0Rdg_D7/m_e2;7I m0R`eo@7[mCc1joCl`>bdO04[]7b1;7?l0:^d?800`000:k@l[3>k`05/l>k>C500<0 003/iC5k>C500004^cTa@009>cTa@030000k>C5k>C501G/icT aNcTa@0dk>C52=c=b`OHe]H3bnc/0m;Kg`K4j_0300001[kWlPFji?@5[>Gi0kOQm0B/hOT4]=ke1:_N n@>cfoD5Zm_h0k7Im0F[fOL3/=Od1:_Gm`>_e?<4ZmGf1joCl`N^dO86[]3b00@0002`c^n`c^n`c^l4 [Loa1;3=k`B]c_46[lc_3^cTa@030000k>C5k>C500;/icTa@00000Bk>C5000Sk>C500<0 003/iC5k>C503;/iGi1jcQn@R[g_T8Zm_h2:_Im`N[eoL7ZmGf0joCl`B[doD3[]7b1:_Am0F^d?800`000:k@ lZg?l@06[Loa1jg>l@>_c>l4[Lga2ncTa@<00005k>C50P0001;/iC50]gXf`KLcL/4e>cU0]SFePG;k>`4/O7e00C4j_00000000000005[ngh1ZgYn@BNi_`4[>Gi1:7S o0>/hOT6Xn3l1jCMn`>[foP5YM[j0j_Im`BVf?T3ZmOg1JKFn0J[eOH7Zm?e1j_Am0>^d?82Zm3c00<0 002[d?>]co400Zg?l@B[co<7[Lka1Zg=l@k/icTaNcTa@0Fk>C5000Sk>C500<0003/iC5k>C502g/iD5bnc/0k7am@<00005[ngh1Y_YnPRNi_`8 XN?l1J?Po0FLgOd6Y=gk2:GJnPNVf?T8Y]Kh1ZODm`>[doD5Ym;f1Z_Am0F[d?<00`000:_@lj_?l`05 Zloc1:g>l@B[c_86[Lga3NcTa@030000k>C5k>C501K/iC5k>C5 02_/iD5]OKa0[7am@<00006Uncg1I_YnPJ>i?`8U>;m29WPo@RLgOd7Wm_l1j7I n`>Vf?T5X]Oj0jKFn0BSeOT6YmCg2:OBmPJXdOH3Zm3c0ZS@m@030000Z=3eZloc00F[co<7Zlkb0jg= l@B[cO8=k>C500<0003/iC5k>C501c/icTaNcTa@0Z k>C51]gXf`KDk>D3]OKa0Y7]l0<000000i7]l9O/miO/m`03Uncg1XKUm`F>i?`5Qmom0iCRo@F?g_h3 VN3m1ICMoP>LgOd4V=_n0ioKo0FKfOd6XMWk2:;GnPJSeOT3YmCg1JCCn0>Wd_H4YM;g1ZSAmPBXd?D0 0`000:S@mJ_?l`02Zloc1JS>m0J[c_87Zlgb3NcTa@030000k>C5k>C501C/icT a@800003k>C5100000C/icTaNcTa@0Mk>C500<0003/icTa@GMj=/6_?[[0kGf l@05TNg`000000000000TNg`00Iihnl3Q^Gg27gOn@R7god8Smkn29CMoPNHfoh8VmWm1igGo0>ReoX4 WmGk1Z?En@RTdoP6YM;g0jSAmPBUd?H4Z=3e00<0002Xd?FXc_@01jS>m0JXcO<3Zlgb1:WC5k>C500002>cTa@030000k>C5k>C500C/icTa@8VYNTI k>C500<0003/iXc_@4Y/kd1ZS=l`JYc?8=k>C500<0003/iC5k>C500002NcTa@030000k>C5k>C500?/icTaNcTa@05k>C51BJUj@A6000Bk>C500<0 003/iOeO/4WM?k1Z7CnPRRd_P6Xm7h0jG@mPBTcoL3Y/oe00<0 002VcoFVcoD01jK>m0>XcO<4Ylgd1ZWcTaNcTa@0Bk>C5000?k>C500@0003/iC500<0003/iC514Ren08f[_08J`00202<`P;/icT aNcTa@0Qk>C51VcoD00jC>mP000:C>mP02Y m0JWcO@3ZLcb1:OcTaNcTa@0Bk>C5000?k>C500@0003/iC500@0 003/iC500<0003/icTa@D2jM@0000000000S6hf@<00002mP040000YcTa@030000k>C5k>C5017/iC50P0000g/iQdOT4Wm3i1Z;@n0JRc_L4YWc?<4Y/cc2^cTa@030000k>C5000001;/icTaNcTa@0>k>C51Fk1oPAV`?h= N@001Ul000ML0005>P00138000DR000010H007cS_WcS_WcS_PA9`?83000015[7n@EHb?L8Ilcl1FS> n`Mcd?h7O=;o1WoCo`N6dol7Rm?o1XkDo`NBdoh6UM;m1YSCo0NJd_/3W=;k19c@nPJNdOT6Wm3i0j;@ n0BQcoP6X/kg0j?>mP040000XlkfXlkfXlkf0jG=m@BTcOD6Y/cd1ZKcTaNcTa@0@ k>C5000Qk>C500<0003/im`:Sc_H010000:?> mZ?>mZ?>mPNTcOD6YLcd1ZKcTaNcTa@0?k>C5000Qk>C50P0001C/icTaNcTa@0>k>C50002k>C500<0003/icTa@030000k>C5k>C501C/i n0NPc_L3X/kg1:7=m`:RcOH010000:;=mZ;=mZ;=mPJSc?D3YLcd1:C;m0JUbo@:k>C50P00013/icTa@00000001_/icTa@00000Fk>C51X73o@Ala?h5PRc?H0002R c?H00j;C500<0003/iC5k>C5 00006^cTa@80000Hk>C51hO3n`B3a?`5PoPJ;coh7S/om1Y7>o@JBcod6ULkl1YK?n`JHc_X6 V/oj29_>n@JMcOP6W/gh1Yo=m`>QcOL4XLcf00>Rc?H0002Rc?H00j;C5k>C500g/icTaNcTa@0000O/icTa@800004k>C50P0000G/icTaNcTa@0Ik>C51XO3n`B3a?`6Q/Gl1X?5o@Aoa_h4PlOm0`0000F0aoh4OLSo1h;9oPF0b_l7 Q<[n1H?;o`F2c?l7Q/cn1HK=o`J:cOh6R/kn1hk>o@NAcO`5TLkm1iC>o0FEc_`7Ulkk1IS>nPNJc_X3 Vlki19c=n@JMcOP6W/ch1Yo=m`JQc?H2X/cf00<0002QboJQboH00Z7;mPJSboD6Xl_d0jC;m0BTb_@: k>C500<0003/icTa@000ncTa@040000k>C5k>C500001^cTa@040000k>C5k>C500002>cT a@040000k>C5k>C500000ncTa@<0000Lk>C51H_3nPF9a?/5Q/Gl1hS5o0>6a_d3000018?7o@J6aod5 Qo0JFcO/6 Ulkk1YW=nPJJc_X7WC500<0003/iC50004k>C50P0000O/icTaNcTa@0000[/icTaNcTa@02k>C500<0003/iC500@0003/iC5000=k>C500@0003/iC500@0 003/icTa@B;`oX6SLCj1X_5n`<00003SMc?P4WL_g1Yk;m`JOboH6X<_f00>Qb_D0002Qb_D00j7:m@>RboD4X/[d1Z?:m0JSbO<: k>C500<0003/iC50NcTa@003NcTa@040000k>C5k>C500002>cTa@040000 k>C5k>C500000ncTa@030000k>C5k>C5023/i>a?X200000Xk4nPFbO`6S/[l1Y3:n`F@bo`7T/_k1I;Qb_D6X/[d0j?: m0BRbO@5XlWc2ncTa@030000k>C5k>C500C/iC50P0000C/icTaNcTa@0Qk>C51Ho3n@B@a?T300001Hk4nPF@aOT5S/Gj1Hg6n`N>a_X5SLOk1Hc8o0J>b?/5 SLWl1ho9n`F>bO`6TLWk1Y3:n`JBb_/6T/_k2iC;nPNFboX5Ul_j1YS;n@JIboT6V/_h1Y_;n0JLboL3 WL_g19g:m`JNboL6Wl[f1Z3:mP030000XLWeXLWe00>QbOD6X/[d1Z;9m0JSbO<:k>C500<0003/icTa@030000k>C5k>C500;/iQbODC5000Ok>C500<0003/iC50`000003k>C5UcTa@030000k>C5k>C500S/icTaNcTa@0Ok>C50`0000K/icTaNcTa@08 k>C5000Ok>C500<0003/icTa@<0000:k>C51YK3mPFE`oH5UPbOD3XcT a@030000k>C5k>C500O/iC51IK3mPFG`oH5U/?f1YG4m`JFa?L5 ULGg1YK5m`JEaOP4UcTaNcTa@07k>C5000Ok>C500<0003/iC51YS2m@BG`oH5U/?f1iO3 mPFFa?L6UlCf1IK5m`JGaOL5U/Gg1IG6n0JGa_L5U/Kh1YO6m`JGaoP6VC500<0 003/icTa@800004k>C50P0000G/iC5k>C501G/iC5k>C500O/icTaNcTa@0000_/icTaNcTaNcTa@<0000Bk>C50`0001_/iC500<0003/iC5k>C500002>cTa@D00002k>C500<0003/iC52YW2m0JI`o@5VQao<9X/Oc0j;6lPJSao84k>C500<0 003/iC5k>C500002>cTa@040000k>C5k>C500000ncTa@80000= k>C50`0002?/iQao<01:77l`JRao<6 X/Kb0Z?7lPBSa_83k>C500<0003/iC5k>C500002NcTa@030000 k>C5000000?/icTaNcTa@09k>C50`0002O/iMaoD4WLKe1Ig7m@JNa_@6 W/Od1Io6m0JOao@6XcTa@030000 k>C5k>C500K/iC500<0003/iC52i_2 l`FJ`_@5Vl?c49[3m16Ja?D6VlCe1I[5mA6KaOD6VlKe1Ic5mAJLa_D6WLKe0ig7m@VNa_@;WlKd1Yo6 l`JPa_<:XLKc00<0002Qa_>Qa_<01:76l`JRa_<5X/Kb1Z?6lP?/icTaNcTa@06k>C5000M k>C50`0000G/iC500<0003/iC5k>C5 00;/icTa@^L`_85Vl;c2Y_3l`^K`o@@VlCd1Yc4m0JKa?@5WQa_801J76lP^Ra_86XlKb00?/ iC500000080000hk>C51Ig1lP^L`_85W<;c1I_3l`JL`o<5 Vl?d1Yc3l`FKa?@FWC5k>C500K/icTa@FM`O86WL;b19c2 lP^L`_C5k>C500K/icTaNcTa@0kk>C51Ig1l@FM`_85W<;b1Yg2lPFL`_<6WL;b1Ic3l`JM`o<6WcTaNcTa@06k>C5000Ok>C50P0003c/iC5k>C500K/icTaNcTa@0jk>C51Ig1l@JN`O4FWL;b2ig3lPFM`o<5WL?b1Ig3 la2Ma?<6W/Cc1Yg4la2Na?<6W/Gc5Yo5l`^PaO8EXLGb00<0002QaO:RaO801j;5lPg/icT aNcTa@05k>C5000Rk>C500<0003/i^cTaA6N`O45WL;b1Yk2lPFM`_86W/;b1Ig3lPFN`o85 WL?b1Ig3l`JN`o<5WLCc8Ik4l`JOa?<5WlGc1Yo4lPJOaO<;XRaO800`000:;5lZ;5lP05 X/Gb3ncTa@030000k>C5k>C500G/icTaNcTa@0kk>C549k1l@JN`_45W/;b1Ik2 l@^N`_85W/?b1Ig3lPFN`o86W/?c1Ik3lPJNa?<5W/Cb1Yk4l`FOa?86W/Cc1Io4lPJOa?<;WlCb1Z34 lPFPaO86XRaO800`000:;5l^cTa@0Ck>C500<0003/icTa@80000l k>C51Yo1l0FN`O45Wl7a5Yk2l@BN`_8QW/?b1Ik4lPJO`o8LWlCb5Z34lPFQa?86XLGb1J74l@JQaO83 k>C500<0003/iC5k>C500G/icTaNcTa@0kk>C52Yo1 l0^O`O45W/;a1Io2l@FN`_4;W/;b1Ik3lPJO`o85W/?b1Yo3lPFN`o8AWl?b49o4lQJPa?8;XLCb2j74 l@W/icTaNcTa@0Ak>C500<0003/iC5k>C503_/iC5k>C5017/icTaNcTa@05k>C5000Xk>C500<0003/incTa@FO`O06X<7`2Yo1 l0FO`O4PWl;a1Io3lPJO`o45Wl?b1Yo3l@FO`o86XC5k>C5013/icTaNcTa@05k>C5000Yk>C50P0003c/iC5k>C5013/icTaNcTa@04 k>C5000[k>C500<0003/incTa@nP`O05Wl7`1J31l0FO`_46X<;`1Io2l@JP`_45Wl;a1J32 l@JO`_45X<;a6j33l@JQ`o45XC500<0003/iC5k>C5 00C/icTaNcTa@0kk>C51J70kaZP`O0;X<;`8:32lA2P`o4PXL?a8ncTa@030000 k>C5k>C500o/icTaNcTa@04k>C5000]k>C500<0003/incTa@BQ`>lPX<7`2j32 l0FP`_46X<;`4:32l@FQ`_46XcTaNcTa@0>k>C500<0003/icT a@00;^cTa@80000kk>C51J70k`JQ`Nl5X<7`1Z71l0FP`O05XL7`1J31l0JQ`O05X<;`1Z72l0FP`_05 XL;`1J32l@JQ`_05XL;a1Z72l0FQ`o45XL?`1Z73l@FQ`o06XL?a;NcTa@030000k>C5k>C500g/icTaNcTa@04k>C5000`k>C500<0003/iNcTa@JQ`>l;XL7_7j71l2^Q`_05XL?`1Z72 l0FQ`o0bk>C500<0003/iC5k>C500C/icTaNcTa@0j k>C52j70k`ZQ`Nl5XL7`1Z71kaFQ`O0`XL;`=ncTa@030000k>C5k>C500c/icTaNcTa@04 k>C5000bk>C500<0003/i^cTa@^Q`>lJXL7_5J71l2NQ`_0kk>C500<0003/icT a@030000k>C5k>C500?/icTa@BQ`>l6X/3_8:71k`FQ`O05XL7_1J71l1FQ`_06 X/;`2J72l3k/icTaNcTa@0;k>C500<0003/iC5k>C5 03[/iC500<0003/iC5k>C500?/icTaNcTa@0j k>C52Z;0kP^R`>lZX/7_1J;2l0FR`^l:X/;`AncTa@030000k>C5k>C500[/icTaNcTa@03 k>C5000gk>C500<0003/i^cTaA2R`>h5X/3_;j;1k`BR`^l6X/;`C>cTa@030000k>C5k>C5 00W/icTaNcTa@03k>C5000hk>C500<0003/i^cTaAFR`>h^X/7_1J;2ke;/icTaNcTa@08k>C500<0003/iNcTa@80000kk>C56j;0kRRR`NmFk>C500<0 003/icTa@030000k>C5k>C500?/icTaNcTa@0jk>C51J;0kPFS`>hE X/3^7Z;1ke_/icTaNcTa@08k>C500<0003/icTa@030000k>C5k>C5 03[/ih:X/3^1J;1k`FR`Nh:X/7_H>cTa@030000k>C5k>C500O/icT aNcTa@02k>C5000mk>C500<0003/i^cTaAnS`>h5X/3^1J?1kPFR`Nh5X/7_I>cTa@030000 k>C5k>C500O/icTaNcTa@02k>C5000nk>C50P0003_/iC500<0 003/iC5k>C500;/icTaNcTa@0jk>C58j?0kW?/icTaNcTa@05k>C500<0003/iC5k>C503[/icTaNcTa@04k>C500<0003/iC5k>C503[/iilk>C500<0003/icTa@030000k>C5k>C500;/incT a@FS_nd;Xl3]1:?0kX7/icTaNcTa@03k>C500<0003/iC5k>C503W/if5k>C500<0003/iC5k>C5007/icTaNcTa@0ik>C52jBokHW/icTaNcTa@03k>C500<0003/iC5k>C503[/iC5k>C500;/icTaNcTa@01 k>C50018k>C50P0003_/icTaNcTa@2@k>C500D0003/iC5k>C503S/icTaNcTa@2Ak>C500@0003/iC5001;k>C500<0 003/iC5k>C5097/icTaNcTa@0000?/icT aNcTa@0fk>C500<0003/iC5000000?/iC5k>C509?/icTa@000002k>C5001?k>C500<0003/iC5k>C5 09C/icTa@030000k>C5k>C503;/icTaNcTa@2Dk>C50P0000;/icTaNcTa@0`k>C500<0003/iC5001Bk>C50P00033/icTaNcTa@2Ak>C5100000C/icTaNcTa@0]k>C500<0003/iC5001Ek>C500<0003/icTa@030000k>C5k>C508W/icTa@00E^cT a@030000k>C5k>C502_/icTaNcTa@25k>C51000013/iC5k>C5087/icTa@00FNcTa@030000k>C5k>C502S/icTaNcTa@1mk>C51000 01S/icTaNcTa@0Wk>C500<0003/iC5001Kk>C500<0 003/iC5k>C507K/icTa@80000Vk>C500<0003/iC5001Nk>C500<0003/iC5k>C506k/iC5k>C502;/icTaNcTa@1Zk>C5100002_/icT aNcTa@0Qk>C500<0003/iC5001Qk>C50P00027/icTaNcTa@1S k>C50`0003?/icTaNcTa@0Nk>C500<0003/iC5001T k>C500<0003/iC5k>C505_/i^cTa@00INcTa@030000k>C5k>C5 01c/icTaNcTa@1Gk>C5100003k/icTa@030000k>C5k>C505?/icTa@030000k>C5k>C501W/icTaNcTa@1?k>C5100004K/icTaNcTa@0Hk>C500<0003/iC5001Zk>C500<0003/iC5k>C504S/iC5k>C501K/icTaNcTa@14 k>C51000057/iC5k>C5043/iC5k>C501?/icTaNcTa@0lk>C5100005W/icTaNcTa@0Bk>C500<0 003/i>cTa@@0001Mk>C5001`k>C500<0003/iC5k>C503C/iC500<0003/icTa@@0001Uk>C5001ck>C500<0003/iC5k>C502k/icTa@030000k>C5k>C500c/icT aNcTa@0Zk>C5100006c/icTaNcTa@0;k>C500<0003/iC5001fk>C50P0000_/icTaNcTa@0Rk>C5100007C/icTaNcTa@08 k>C500<0003/iC5001ik>C500<0003/iC5k>C5 01[/icTa@00N^cTa@030000k>C5k>C500K/icTaNcTa@0Gk>C50`00083/iC5k>C501?/iC5k>C500?/icTaNcTa@0?k>C5100008O/icTaNcTa@02k>C500<0003/iC5001ok>C500D0003/iC50020k>C50P000003k>C5 0000k>C500C/iC5003ok>C58NcTa@00oncTaB7/iC5003ok>C58NcTa@00oncTaB7/iC50000\ \>"], ImageRangeCache->{{{232.063, 519.063}, {301.625, 69.0625}} -> {-0.976231, \ 0.253153, 0.00372585, 0.00372585}}], Cell[TextData[{ "Solution of the fractional diffusion equation (1.3.16) in the series \ representation (1.3.18). The fractional exponent is ", Cell[BoxData[ \(TraditionalForm\`q = 3/2\)]], ". " }], "SmallText"], Cell[TextData[{ "To determine the asymptotic behavior of the derived Fox's H-function we \ calculate the asymptotic expansion for large ", Cell[BoxData[ \(TraditionalForm\`t \[Rule] \[Infinity]\)]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"rhoasymptotic", "=", RowBox[{ RowBox[{ RowBox[{"Asymptotic", "[", FractionBox[ RowBox[{ SubsuperscriptBox[ StyleBox["\[ScriptCapitalH]", FontSize->16], \(1, 1\), \(1, 0\)], "[", RowBox[{\(\(x\^\(2/q\)\ D\_0\%\(\(-1\)/q\)\)\/t\), "|", GridBox[{ {\(\({}\)\(|\)\), \({{1, 1}}\)}, {\(\({{1, 2\/q}}\)\(|\)\), \({}\)} }]}], "]"}], \(q\ x\)], "]"}], "//", "PowerExpand"}], "//", "Simplify"}]}]], "Input"], Cell[BoxData[ \(\(2\^\(1\/\(\(-2\) + q\)\)\ \[ExponentialE]\^\(4\^\(1\/\(\(-2\) + q\)\)\ \ \((\(-2\) + q)\)\ q\^\(q\/\(2 - q\)\)\ t\^\(q\/\(\(-2\) + q\)\)\ \ x\^\(-\(2\/\(\(-2\) + q\)\)\)\ D\_0\%\(1\/\(\(-2\) + q\)\)\)\ q\^\(\(4 - 3\ q\ \)\/\(\(-4\) + 2\ q\)\)\ t\^\(q\/\(\(-4\) + 2\ q\)\)\ x\^\(\(1 - \ q\)\/\(\(-2\) + q\)\)\ D\_0\%\(1\/\(\(-4\) + 2\ q\)\)\)\/\(\@\[Pi]\ \ \@\(\(-1\) + 2\/q\)\)\)], "Output"] }, Open ]], Cell[TextData[{ "This formula reduces to the standard Gaussian case if we choose here ", Cell[BoxData[ \(TraditionalForm\`q = 1\)]], ". In ", StyleBox["Mathematica", FontSlant->"Italic"], " we get" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(gauss\ = rhoasymptotic /. q \[Rule] 1\)], "Input"], Cell[BoxData[ \(\[ExponentialE]\^\(-\(x\^2\/\(4\ t\ D\_0\)\)\)\/\(2\ \@\[Pi]\ \@t\ \ \@D\_0\)\)], "Output"] }, Open ]], Cell["\<\ The calculation of the asymptotic mean square deviation provides\ \>", "Text"], Cell[BoxData[ \(\(SetOptions[Integrate, GenerateConditions \[Rule] False];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\[LeftAngleBracket]\((r)\)\^2\[RightAngleBracket] = \ \(meanSquareDisplacement\ = \(2 \(\[Integral]\_0\%\[Infinity]\((\(x\^2\) rhoasymptotic)\) \[DifferentialD]x\) // PowerExpand\) // Simplify\)\)], "Input"], Cell[BoxData[ \(Pattern::"nodef" \(\(:\)\(\ \)\) "No default setting found for \!\(Abs\) in position \!\(1\) when length \ is \!\(1\)."\)], "Message"], Cell[BoxData[ \(Pattern::"nodef" \(\(:\)\(\ \)\) "No default setting found for \!\(Abs\) in position \!\(1\) when length \ is \!\(1\)."\)], "Message"], Cell[BoxData[ FractionBox[ RowBox[{\(2\^\(1\/\(\(-2\) + q\)\)\), " ", \(\@\(\(-1\) + 2\/q\)\), " ", \(q\^\(-q\)\), " ", \(\((2\^\(q\/\(\(-2\) + q\)\) - 4\^\(1\/\(\(-2\) + q\)\)\ q)\)\^\(\(-\(5\/2\)\) + q\)\), " ", \(t\^q\), " ", RowBox[{ StyleBox["\[CapitalGamma]", FontSlant->"Italic"], "[", \(5\/2 - q\), "]"}], " ", \(D\_0\)}], \(\@\[Pi]\)]], "Output"] }, Open ]], Cell[TextData[{ "which in fact is proportional to ", Cell[BoxData[ \(TraditionalForm\`t\^q\)]] }], "Text"], Cell[TextData[{ " ", Cell[BoxData[ \(TraditionalForm\`\[LeftAngleBracket]\(r(t)\)\^2\[RightAngleBracket] \ \[Tilde] t\^q\)]], "." }], "NumberedEquation", CellTags->"eq-24"], Cell[TextData[{ "The standard Gaussian behavior follows by choosing ", Cell[BoxData[ \(TraditionalForm\`q = 1\)]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(meanSquareDisplacement /. q \[Rule] 1\)], "Input"], Cell[BoxData[ \(2\ t\ D\_0\)], "Output"] }, Open ]], Cell[TextData[{ "The result shows that the mean square displacement (", ButtonBox["1.3.19", ButtonData:>"eq-24", ButtonStyle->"Hyperlink"], ") follows a power law proportional to ", Cell[BoxData[ \(TraditionalForm\`t\^q\)]], ". Thus, under the condition ", Cell[BoxData[ \(TraditionalForm\`1 < q < 2\)]], ", we conclude that the solution (", ButtonBox["1.3.17", ButtonData:>"eq-22a", ButtonStyle->"Hyperlink"], ") of the anomalous fractional diffusion equation (", ButtonBox["1.3.16", ButtonData:>"eq-18", ButtonStyle->"Hyperlink"], ") describes enhanced intermediate transport phenomena. This result is \ based on the initial condition ", Cell[BoxData[ \(TraditionalForm\`\[Rho](x, t = 0) = \(\(\[Rho]\_0\)(x)\ = \ \[Delta](x)\)\)]], ". " }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], " Conclusions" }], "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"Conclusions"], Cell[TextData[{ "We demonstrated that ", StyleBox["Mathematica", FontSlant->"Italic"], " is able to handle fractional derivatives if the operations are defined in \ an appropriate way. We implemented with a minimal amount of functions the \ Riemann-Liouville and the Weyl calculi. The achievement of both calculi allow \ us to calculate fractional integrals and fractional derivatives. We also \ demonstrated by several examples that the calculation of either fractional \ derivatives or integrals result into special functions. These functions can \ be collected in a common function known as Fox-H function. As applications we \ discussed two physical examples. We applied the fractional calculus to \ formulate anomalous relaxation and diffusion. We solved the fractional \ relaxation equation and the fractional diffusion equation in ", StyleBox["1+1", FontSlant->"Italic"], "-dimensions by means of the Laplace-Mellin transform technique. All the \ calculations presented in this notebook are supported by the package ", StyleBox["FractionalCalculus", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], "." }], "Text"], Cell[TextData[{ StyleBox["Acknowledgement", FontWeight->"Bold"], ": I acknowledge the worke and the many discussions with N. \ S\[UDoubleDot]dland." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ CounterBox["Section"], " References" }], "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}], Cell["\<\ [1] S.F. Lacroix, Trait\[EAcute] du Calcul Diff\[EAcute]rentiel et du Calcul \ Int\[EAcute]gral, 2nd ed., Vol.3, 409-410. Courcier, Paris (1819).\ \>", "SmallText", CellTags->"Lacroix-1819"], Cell["\<\ [2] K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New \ York, (1974).\ \>", "SmallText", CellTags->"Oldham-1974"], Cell["\<\ [3] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and \ Fractional Differential Equations, John Wiley & Sons, Inc., New York, (1993).\ \ \>", "SmallText", CellTags->"Miller-1993"], Cell["\<\ [4] G.F.B. Riemann, Gesammelte Werke, 353-366, Teubner, Leipzig, (1892).\ \>", "SmallText", CellTags->"Riemann-1892"], Cell[TextData[{ "[5] J. Liouville, M\[EAcute]moiresur le calcul des diff\[EAcute]rentielles \ \[AGrave] indices quelconques, J. \[CapitalEAcute]cole Polytech., ", StyleBox["13", FontWeight->"Bold"], ", 71-162, (1832)." }], "SmallText", CellTags->"Liouville-1832a"], Cell[TextData[{ "[6] H. Weyl, Bemerkungen zum Begriff des Differentialquotienten \ gebrochener Ordnung, Vierteljahresschr. Naturforsch. Ges. Z\[UDoubleDot]rich, \ ", StyleBox["62", FontWeight->"Bold"], ", 296-302, (1917)." }], "SmallText", CellTags->"Weyl-1917"], Cell["\<\ [7] H.T. Davis, The Theory of Linear Operators, Principia Press, Bloomington, \ Ind., (1936).\ \>", "SmallText", CellTags->"Davis-1936"], Cell[TextData[{ "[8[ W.G. Gl\[ODoubleDot]ckle and T.F. Nonnenmacher, Fractional Integral \ Operators and Fox Functions in the Theory of Viscoelasticity, Macromolecules, \ ", StyleBox["24", FontWeight->"Bold"], ", 6426-6434, (1991). " }], "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1991"], Cell[TextData[{ "[9] C. Fox, The G and H Functions as Symmetrical Fourier Kernels, Trans. \ Am. Math. Soc., ", StyleBox["98", FontWeight->"Bold"], ", 395-429, (1961)." }], "SmallText", CellTags->"Fox-1961"], Cell[TextData[{ "[10] W.G. Gl\[ODoubleDot]ckle and T.F. Nonnenmacher, Fox function \ representation of non-Debye relaxation processes, J. Stat. Phys., ", StyleBox["71", FontWeight->"Bold"], ", 741-757, (1993)." }], "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1993a"], Cell[TextData[{ "[11] W.R. Schneider and W. Wyss, Fractional Diffusion and Wave Equations, \ J. Math. Phys. ", StyleBox["30", FontWeight->"Bold"], ", 134-144, (1989)." }], "SmallText", CellTags->"Schneider-1989"], Cell["\<\ [12] R. Zwanzig, Time-Correlation Functions and Transport Coefficients in \ Statistical Mechanics, Ann. Rev. Phys. Chem. 16, 67-102, (1965).\ \>", "SmallText", CellTags->"Zwanzig-1965"], Cell[TextData[{ "[13] W.G. Gl\[ODoubleDot]ckle and T.F. Nonnenmacher, Fractional Relaxation \ and the Time-Temperature Superposition Principle, Rheol. Acta, ", StyleBox["30", FontWeight->"Bold"], ", 337-343, (1994)." }], "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1994"], Cell[TextData[{ "[14] B.L.J. Braaksma, Asymptotic Expansions and Analytic Continuations for \ a Class of Barnes-Integrals, Compos. Math. ", StyleBox["15", FontWeight->"Bold"], ", 239-341 , (1964)." }], "SmallText", CellTags->"Braaksma-1964"], Cell["\<\ [15] B.J. West and W. Deering, Fractal physiology for physicists: \ L\[EAcute]vy statistics, Phys. Rep. 246, 1-100, (1994).\ \>", "SmallText", CellTags->"West-1994"], Cell[TextData[{ "[16] W. Wyss, The Fractional Diffusion Equation, J. Math. Phys., ", StyleBox["27", FontWeight->"Bold"], ", 2782-2785, (1986)." }], "SmallText", CellTags->"Wyss-1986"], Cell[TextData[{ "[17] B. O'Shaugnessy and I. Procaccia, Analytical Solutions for Diffusion \ on Fractal Objects, Phys. Rev. Lett., ", StyleBox["54", FontWeight->"Bold"], ", 455-458, (1985)." }], "SmallText", CellTags->"Schaugnessy-1985"], Cell[TextData[{ "[18] A. Compte, Stochastic foundations of fractional dynamics, Phys. Rev. \ E, ", StyleBox["53", FontWeight->"Bold"], ", 4191-4193, (1996)" }], "SmallText", CellTags->"Compte-1996"], Cell[TextData[{ "[19] B.J. West, P. Grigolini, R. Metzler, and T.F. Nonnenmacher, \ Fractional diffusion and L\[EAcute]vy stable processes,Phys. Rev. E, ", StyleBox["55", FontWeight->"Bold"], ", 99-106, (1997)." }], "SmallText", CellTags->"West-1997"], Cell["\<\ [20] J. Podlubny, Fractional Differential Equations, Academic Press, San \ Diego, (1999).\ \>", "SmallText", CellTags->"Podlubny-1999"] }, Open ]] }, Open ]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, AutoGeneratedPackage->Automatic, ScreenStyleEnvironment->"Presentation", WindowSize->{815, 667}, WindowMargins->{{2, Automatic}, {Automatic, 0}}, Visible->True, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, InputAliases->{"notation"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongLeftRightArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "notation>"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongRightArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "notation<"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongLeftArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "symb"->RowBox[ {"Symbolize", "[", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], "]"}], "infixnotation"->RowBox[ {"InfixNotation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], ",", "\[Placeholder]"}], "]"}], "addia"->RowBox[ {"AddInputAlias", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], ",", "\[Placeholder]"}], "]"}], "pattwraper"->TagBox[ "\[Placeholder]", NotationPatternTag, TagStyle -> "NotationPatternWrapperStyle"], "madeboxeswraper"->TagBox[ "\[Placeholder]", NotationMadeBoxesTag, TagStyle -> "NotationMadeBoxesWrapperStyle"]}, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of all cells in \ a given style. Make modifications to any definition using commands in the Format menu. \ \>", "Text"], Cell["\<\ Below is a PICT header for use with all WWMC notebooks. Copy and paste this cell at the top of your notebook. \ \>", "Text"], Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg05eMG@2l_;`0jn_[0>c/k031`L407QhN0000000L71`0QXJ60<[:bP3[jn/0gmoO0:^[ Z`1ADE420000000;06UYJ@3GemL0e=CD055AD@0000009BDU030080oooo00<0Hf=S0000002n_[h00`3oool01@0K6a/0O7al 0?ooo`3oool0WinO00<0000000<0QHF50?ooo`3oool00`3oool01P1IFET0F5QH0?ooo`3oool0/K6a 075aL@80oooo00<0h^;R01XJ6P1mOGd01@3oool01`1iNGT0>3Ph0?ooo`3oool0X:2P00000024Q8@0 0`3oool00`1SHf<01@D50;fm_@040?ooo`030=cLg00G5aL0m?Cd00@0oooo00<0nMOM0=L7;P3E02@0 1@3F02L01@3E0240f0/`0=L4:`3F02H0eP0W0080e`@Z00@0e`D/0=H1:03F02L0eP0W0P3G12X30=H0 9`090=D08@3H2c00e`@[0=H09P3F02L0e`L]0=D08P3G0bX0eP3P0oOgm0?ooo`3oool0alO7 09BDU037alL0=3@d09bLW0020?ooo`030>KViP2FUYH0^[Zj0080oooo00<0oOgm024Q8@1gMgL00P3o ool00`1EEED0H61P0?ooo`020?ooo`030?Shn00J6QX0N7Qh0080oooo00D0Z:RX01`L700L71`00000 07moO`020?ooo`050<30`01KFe/0GemO01XJ6P1NGUh00P3oool01`3Jf]X0k>c/0?ooo`3_knl0@d=3 00000021PH400P3oool01@30`<00Fe]K065QH@0V9RH0@T920080oooo00<0T92@034a<@3kno/00`3o ool04@1FEUH0 GemO0?ooo`3oool0o_kn0;6a/@2HV9P0_Kfm01hN7P3/k>`0oooo0?[jnP1iNGT0FEUI 071?E@3A0R40eP0V00@0eP0W00`0e@0O0>=CK@3d^L@0fado0=D08`3D01d0iF1g0>ELM@3/QYP0fQTl 0=D08`3D01d20>IQN@0I0=@07@3F02L0e@0O0>=CK@3d^L@0fado0=D08`3D01d0jG>80>f>X03aZKL0 fADi0=D08`3E0200gRi>0?Fob@3YN8d0eP8T0=H09P3E0200gBm?0?G0bP3^UJH0ePDW0=H09@090=H0 9`0F0=H09@3G0bX0kYFU0=XH>`3E02<0eP0W0=D08@3M;dl0jWjB0=D08P3F02H0eP0W0=@07@3TFG80 iEae0=@07P3F02L0e00O0>AJL`3c]l80i5Yc0=@07`@0eP0W00<0/@0P000000000000oP0000000`0? 3`l000000000003J00000000200000003`2>SXh0oooo0?ooo`34a<@02`/;0000000<30`08R8R0>CT i03oool0o?cl04aCT0?oo o`3bl_80oooo0?Shn00J6QX0N7Qh0P3oool01@3inOT0k^k^0>7Qh@000000Ng]k0080oooo00D0k^k^ 0=;BdP35aLD00000061PH0050?ooo`040=?Cd`0d=3@000000820P080oooo00D0k^k^0=;BdP34a<@0 000004E5A@020?ooo`080:6QX@32`/80oooo0>c/k03kno/0oooo06EUI@2h^;P20?ooo`0<09:BTP00 0000000001XJ6P0F5QH0kno_0?ooo`3no_h0f][J0=;BdP24AE40`00E103F02L03@3F02@0e`d`0?G4 c@3O=eH0e@4T0=H09`3D01/0ifb20?6Y]P3d_LL0fQPk0=D08`3D01`00P3YL8H06@3D01`0eP0T0=L= <03eaAJL`3ieM`0lkG10=L4:@3F02D0e00L0>b8VP3_UjL0mKo90=TC =`3E02<0e00L0>fAXP3XLHL0l:Bb0>51G`3D01l02@3F02L05P3F02D0e`^1 U@3D01l40=H09`030;408000000000000?h0000000<03`l?000000000000fP00000000P0000000@0 Vi^K0?ooo`3oool0YJFU0`0000001@0@4100l?3`0?ooo`3jn_X03Ph02[Zj/0moOg0?oo o`3Zj^X04aS0?gm o@3oool0JFUY0IWO`3e`l`0m/SA0=TE>@3E02<0 e00L0080j6j301T0e00L0=D08`3I4cL0ml[B0=P=YmT@3D01`0 eP0V0=@07P3^UJH0jWfA0>MXOP3G22d0e@0U0=@07P3_VZX0he=]0>jFYP3SCf/0e00N00T0eP0W01H0 eP0U0=L1:03aY[@0fQ/n0=D08`3F02@0f0/`0?:/^@3b[k/0i5E_0=@07P3E0240gS1@0?>g`@3d^lD0 fQLl0=D08`3D01/0iEYd0?_Xk03UFg@0e00K103F02L00`2a020000000000003n0000000300l?3`00 000000000=X0000000080000000905IFEP3oool0oooo0?KfmP1eMGD0ATI608Z:RP0g=cL0^KVi0080 oooo00@0bl_;05YJFP2:RXX0n?Sh0P3oool00`0i>CT0M7Ad0?ooo`020?ooo`070?;blP0l?3`0a/K6 0?ooo`3hn?P06QXJ07QhN0020?ooo`050;Ng]`14A4@0ADE500X:2P1mOGd00P3oool01@2d];@0>c/k 03/k>`000000HV9R0080oooo00<0/[:b01hN7P3Shn<00P3oool01@0e=CD0M7Ad0?ooo`3oool0];Bd 0080>c/k00<00P8204I6AP3oool00`3oool01P1OGel0SHf=0?ooo`3oool0FEUI0861P@80oooo00d0 g]kN05YJFP1;Bd/0TY:B01lO7`3/k>`0oooo0?[jnP1OGel0>SXj04/]<`3=01/0eP0V00<0eP0W00d0 eP0V0=D18@3ZNi00lk>n0=TF>@3E02<0e00L0>M]P`3WJX40kiVX0=XL?`3E02<0e00L0080j6n401T0 e00L0=H09P3E0B40jW^@0?>c_P3I5ST0e@0S0=H0903G12X0n=3G0>AJM03D01`0eP0W0=@07@3RBfL0 mlWA0>YhS@3F0RD0eP0V0=@07P3QAV<0mlWB0?:_^`3H3S00e@0T00T0eP0W01H0e@0S0=XH?03fbM80 fQPk0=D08`3F02D0eP@W0>j@X@3c]l80gRi>0=D08@3E02<0fQTk0?:^^`3aYK<0e``^0=D0903D01`0 i5Uc0?O@f03TFG<0e00L103F02L00`2a020000000000003n0000000300l?3`00000000000=X00000 00080000000300H61P2k^k/0oooo00@0oooo00<08bSX04U9 B@1bLW800P3oool01@3^k^h0d];B0=CDe00_;bl0FUYJ0080oooo00L0mOGe0>KViP3oool0oooo0>7Q h@0=3@d0NWYj0080oooo00D0kno_0=;BdP3De=@0c/k03oool0o_kn0=_Kf`3AdM40f;Fl0=L5 ;03E02@40=H09`040=H09@3F02L0gS9A0=P:<080eP0U00H0fADh0=XF>@3K7T00e`D[0=H09P3F02D2 0=XE>@070=H09@3F02L0eP0U0=H09`3N0=XH?03E02<:0=H09`0:0=H09@3H3340gS1@ 0=L3:P3F02H0eP0W0=D08`3I53P0gBU:0=D08`80eP0W00X0e@0T0=`RA03J6ch0e@0T0=H09`3F02H0 e`@[0=dZB`3G12/0eP0V103F02L00`2a020000000000003n0000000300l?3`00000000000=X00000 00090000000;01`0UiNG00T92@000000NGUi0?gmo@3lo?`0`L7100d=3@030`<0f][J0?gmo@3emOD0410@07al O03oool0oOgm00<0oooo00@0BTY:06UYJ@3moOd0oOgm0`3oool0100b[ZjP02 0?gmo@80oooo00L0n=?J0=P1:03D01l0eP0Q0=L08`3G0280e@0R0080e`0R00`0e00I0=D0803G0280 e@0R0=D07P3F01h0e`0J0=P07`3G0280e@0R0=D07P3G01h20=D08P0?0=P08@3G0240eP0J0=D0803E 0280e`0R0=L08`3E01/0e@0O0=P08P3H0240e@0R0=D08@3D01X0e@0N0080e`0R00T0e@0R0=D08@3F 01P0e`0L0=D08P3H0240f00P0=L08P3E02800P3F02820=D08P80f00P00T0f00Q0=D0803D01T0e`0Q 0=H08P3E0280f00R0=H07`3F01X00P3E0280103H0240e`0S0=H06P3G01/30=D08P060=H0803D01X0 e@0P0=P08@3H0200f00Q0P3E02800`2b01`000000000003n0000000300l?3`00000000000=X00000 000;0000000<04E5A@2c/k<0_[jn071`L0061PH08R8R05IFEP1]KFd0K6a/05UIF@1=CDd09BDU0P00 00004`0n?Sh0SHf=0;jn_P2DU9@0>3Ph000000010@40>c/k09ZJVP2OWil0H61P01`L701`L700XZ:R 0:2PX02FUYH0N7Qh07IfMP1lO7`00P2PX:006`2NWYh0HF5Q09FEU@1_Kfl0MWIf0::RXP2CTi<0L71` 0451@@0_;bl03@d=000000051@D0MWIf0::RXP2?Shl0?clo04a1HL02X:401G>d00MeIK07=CF01PADT0Le=H07IIGP1F:340=@D<04dP:01eFEh0 M5QM04DL900e1@h0KdiD07MGG@1F=cd0DRP_07IHG@0307EDFP0/06I9CP1OA4P0MUEK079>E00f31<0 BB0W07ELH@1C9Bd0<`/B06]9C`1fEE/0L51F07EDF@1fEE/0Kd]B02l<4P0Z2@h0DBD]07IIGP1fEEX0 F3m306i?E01gEU/0HDA903D53P1;7RH0MEUN07IIGP1F:340=@D=02h83`1D5B00PeUQ08iVK@1_CeD0 KTmD07IEFP1dEe`0?A`R02X93@0o7B<0MEQM07IEFP1G?T;o00000040000000<03`l?000000000000 fP00000000/0000000H0N7Qh0?gmo@3moOd0]kNg0000002c/`00000000000000 000ag]k@3moOd0lo?c018B4P38b3P00<0oooo00@0o_kn0>_[j`2VYZH0 6QXJ0P0000002P18B4P0o_kn0?gmo@3YjNT000000492@P3lo?`0oooo0>o_k`0820P2000000030;no _`3oool0oooo0080C4a<103oool01P3moOd0fMWI07EeM@00000030`<0>k^kP80oOgm0P3oool08P39 bl/0KWEc0:ji]`2V];401PD505ADE02__;X0HV9R0000002LZ:H0[kZh0828Q`29TY00[kZh0:>]Z`17 BDP0S@2_^[P0Yk6`05QNG@2W/K00[kZh06E/JP000000:b/[0:jj^02_^kT0>SXj0000002? VYP0[kZh06ieL`0m@3l20:nj^080/;^i0180VZBR05eSHP2_^[P0[;Ne01LH600m@3l0[kZh07MnO@00 0000Qi2>0:nj^02=UY@0OXF40:nj^02Z]K<0AdY9030bSX0WJJU0:nj^02`^kT0Z[Fc08F=R`80[kZh00<0HFMV 02`^;P1NHf800P2_^[P00`1UK6/000000000003n0000000300l?3`00000000000=X00000000:0000 000700D51@3Fe]H0oooo0?ooo`3/k>`051@D0;Ng]`020?ooo`050?KfmP0X:2P0000000h>3P3De=@0 0`3oool02P3bl_80oooo0?ooo`3oool0FUYJ00@4103`l?00oooo0>SXj02:RXX20?ooo`030CT0?ooo`3no_h0lO7a00<0oooo00@0bSX0N7Qh0?ooo`020?ooo`0405mOG`00000000000;Rh^080oooo0P1EEED2 0?ooo`030?Win@3dm?@0oooo0080oooo01@0KFe]00820P3`l?00oooo0?knoP3SP2b/[80MgMg03dm?@H0/[:b0240Xj>S02DU 9@2XZ:P0/[:b08>3P`00000051@D0:b/[02b/[80FU]K0000001bLW80/[:b09>CT`0_;bl0[jn_0;:b /P2VYZH0QhN707emO@0j>SX0[Jf]0;:b/P1=CDd0FEUI0;:b/P2_[jl0:b/[07UiN@2b/[80S8b<034a <@2`/;001@2b/[80302][Jd092@T08J6QP2b/[80Z:RX00P92@0A4Q80[:b/0;:b/P1oOgl04aT Y080/[:b00@0[Zj^0:n_[`1VIVH0U9BD1P2b/[800`19BDT000000000003n0000000300l?3`000000 00000=X00000000:0000000703dm?@3no_h0oooo0?ooo`3moOd0E5AD0=cLg0030?ooo`0308Z:RP00 0000KVi^0080oooo00@0i>CT04Y:BP0_;bl0ZJVY0P3oool01@3:b/X04ac/k03oool0oOgm0080 oooo00@0l?3`0410@0000000PH610P3oool02P2e]KD0@41003lo?`0Q8B40kNg]0?ooo`3inOT0BTY: 05UIF@3_knl20?ooo`0303hn?P071`L0i>CT00<0oooo00<0Ng]k0:6QX@3oool00P3oool01035aLD0 0@410000002h^;P20?ooo`80EEEE0P3oool00`31`L40c/ 0?ooo`3kno/0P82006QXJ00_;bl020P80:2PX02b/[80Jf][08B4Q0020;:b/P0@06UYJ@23Ph<0/[:b 07inOP0410@0T92@0;:b/P2][Jd0LG5a0:ZZZP2b/[80Rh^;00P8202IVIT0/[:b09bLW0800`<30180 WIfM0;:b/P2CTi<0GUiN096AT@2b/[80YZJV02DU9@2VYZH0/[:b09BDU018B4P0@T9200P8202>SXh0 /[:b07YjNP1gMgL20;:b/P0F07MgM`1dM7@0/[:b09>CT`020P80OWin0;:b/P2a/K40MgMg0:6QX@2b /[80WinO00@4101`L700/[:b0;2`/00S8b<00@4109ZJVP2b/[80U9BD03Ti>@80/[:b00D0UiNG02XZ :P0[:b/0<30`05EEE@020;: b/P0508>3P`2>SXh0/[:b0;6a/@0[:b/0o`0000010000000300l?3`00 000000000=X00000000:0000000=0:RXZ03oool0i>CT0k^kP0P8200jn_[0?oo o`3no_h0oOgm0?ooo`3moOd0_Kfm01DE5@1jNWX00P3oool02P2GUiL000000000000<30`0lO7a0?oo o`3hn?P07QhN0000002j^[X20?ooo`0?06m_K`1JFUX0oooo0?KfmP2l_;`0oooo0@3Xj>P40?ooo`0K08F5Q@000000Lg=c0;:b/P2JVYX0YJFU0:n_[`2XZ:P0YJFU09>C T`2b/[80P82000000012@T80/[:b0:n_[`0g=cL0WYjN0;:b/P1^KVh0000008:2PP2b/[80[:b/01300D0/[:b00<0[jn_034a<@2@T900102b/[805@0J6QX0FEUI0;:b/P2UYJD0VYZJ0:n_ [`2XZ:P0ZZZZ08n?S`2b/[80Ti>C0000000];Bd0/[:b0;6a/@16ATH0QhN70;:b/P24Q8@0000005UI F@020;:b/P0903/k>`000000Ph>30;:b/P2SXj<0BDU90;2`/02b/[80KFe]00<0000000P04A4A0:>S X`2b/[80Hf=S069RHP2b/[80Z:RX00l?3ol000000@0000000`0?3`l000000000003J000000002@00 00001@0F5QH0k^k^0?ooo`2ZZZX0MGEe00<0oooo00H0Shn?08Z:RP3oool0o_kn03Xj>P1kNg/20?oo o`040=3@d00O7al02`/;08:2PP80oooo00L0g=cL01TI6@3/k>`0oooo0>o_k`0c7Qh@02 0?ooo`0605=CD`2a/K40oooo0>?Sh`1ADE40no_k0P3oool01`35aLD0HV9R0?ooo`3oool0PH610000 002g]kL00P3oool205EEE@80oooo00l0^KVi00`<301]KFd0o_kn0?ooo`3Kfm/08B4Q0>_[j`3oool0 o?cl0:BTY02DU9@0ATI600000010@4000`2b/[800`2@T900KVi^0;:b/P020;:b/P0D0820P0000000 1@D509FEU@2b/[80Q8B40:FUY@2b/[80D51@00820P1YJFT0/[:b0;6a/@0bC00<30`000000Q8B40;:b/P2;Rh/0W9bL0;:b/P1SHf<00`<304=3 @`2a/K40/[:b05QHF0020P80JFUY0;:b/P2^[Zh0@41009jNWP2b/[80VIVI01TI6@0000008B4Q0000 001IFET0/[:b0:6QX@28R8P0/[:b08Z:RP010@40o`0000010000000300l?3`00000000000=X00000 00090000000605eMG@3oool0oooo0820P00/;2`0o_kn0P3oool01`1HF5P0E5AD0?ooo`3oool0YZJV 01`L703bl_800P3oool00`3Vi^H0c/k>0?ooo`020?ooo`0708R8R0051@D0kno_0?ooo`3emOD0MgMg 0=GEe@020?ooo`05065QH@1_Kfl0oooo0?ooo`2LW9`00P0000001P0?3`l0l?3`0?ooo`3moOd0d=3@ 0>g]k@80oooo00L0fm_K03De=@3alO40oooo0;jn_P0>3Ph0hN7Q0080oooo00L0V9RH020P803inOT0 oooo0=oOg`0<30`0/k>c0080oooo0P1EEED20?ooo`030>k^kP3@d=00oooo0080oooo00/0RXZ:00<3 0`3_knl0oooo0?_kn`29RHT0Lg=c059BDP0000004Q8B0:JVYP020;:b/P030820P00S8b<0[Jf]0080 /[:b00@0P820000000000000B4Q80`2b/[80102`/;00?Cdm07MgM`2IVIT20;:b/P0;09ZJVP1aLG40 Fe]K0;:b/P2_[jl0;bl_02@T902][Jd0/[:b05ADE01LG5`00P2b/[801@1YJFT0D51@03Hf=P061PH0 V9RH0080/[:b00<0UYJF01TI6@2SXj<00P2b/[80102CTi<01@D50000000d=3@40;:b/P0804E5A@1J FUX0TI6A0;6a/@2b/[80XZ:R07emO@1fMWH20;:b/P0>0410@01ADE40/[:b0;:b/P2MWId0O7al0:2P X00E5AD03Ph>0:FUY@2b/[80/K6a0;:b/P1]KFgo00000080000000<03`l?000000000000fP000000 00P0000000L020P80=?Cd`3oool0oooo05YJFP010@40jNWY0080oooo00P0;Bd]02HV9P3oool0oooo 0?knoP0N7Qh0Fe]K0?7al@D0oooo00@0/;2`010@400;2`/0no_k1@3oool00`3Cdm<04Q8B0820P002 0?ooo`050:>SX`0000000000010@403kno/01@3oool00`3Lg=`0?clo092@T0020?ooo`0309NGU`00 0000[jn_0080oooo00<0K6a/0000003Ogml00P3oool0101LG5`0/k>c0?ooo`3oool205UIF@H0oooo 00@0];Bd01LG5`0:2PX0no_k103oool01038bSX`061PH00P8209JFUP2g]kL0^[Zj04=3@`00000000<30`0000002`/;0:ZZZP<0]KFe00D0^;Rh 08>3P`000000000003`l?0020820P00604aCT`20P8008B4Q0000000E5AD0Ng]k07moO`1n OWh09bLWo`0000020000000300/;2`00000000000=X00000001X0000000301hN7P0?3`l03`l?0?l0 3`l?@@0?3`l00`0N7Qh000000000003J00000000o`00003o000008X00000003o00000?l00000RP00 00000?l00000o`00002:00000000 \ \>"], "WWMCHeader", ShowCellBracket->False, CellMargins->{{0, 0}, {0, 0}}, Evaluatable->False, CellFrameMargins->4, ImageSize->{648, 25}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, Background->GrayLevel[0]], Cell[CellGroupData[{ Cell["Style Environment Names", "Section"], Cell[StyleData[All, "Working"], PageWidth->WindowWidth, ScriptMinSize->9], Cell[StyleData[All, "Presentation"], PageWidth->WindowWidth, ScriptMinSize->12, FontSize->16], Cell[StyleData[All, "Condensed"], PageWidth->WindowWidth, ScriptMinSize->8, FontSize->11], Cell[StyleData[All, "Printout"], PageWidth->PaperWidth, ScriptMinSize->5, FontSize->10, PrivateFontOptions->{"FontType"->"Outline"}] }, Closed]], Cell[CellGroupData[{ Cell["Notebook Options", "Section"], Cell["\<\ The options defined for the style below will be used at the Notebook level. \ \>", "Text"], Cell[StyleData["Notebook", "Presentation"], PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], None, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], None, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, CellBracketOptions->{"Color"->RGBColor[0.66717, 0.187915, 0.232395]}, CellElementSpacings->{"ClosedGroupTopMargin"->20}, CellFrameLabelMargins->6, StyleMenuListing->None, Background->RGBColor[0.924025, 0.891524, 0.771649]], Cell[StyleData["Notebook", "Printout"], PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], None, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], None, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, CellElementSpacings->{"ClosedGroupTopMargin"->20}, CellFrameLabelMargins->6, StyleMenuListing->None, Background->None] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headings", "Section"], Cell[CellGroupData[{ Cell[StyleData["Title"], CellMargins->{{40, Inherited}, {20, 40}}, CellGroupingRules->{"TitleGrouping", 0}, PageBreakBelow->False, CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subtitle", 0}, {"Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->36, FontWeight->"Bold"], Cell[StyleData["Title", "Presentation"], ShowCellBracket->False, CellMargins->{{0, 100}, {0, 0}}, CellFrameMargins->{{30, 100}, {10, 20}}, AutoIndent->False, LineSpacing->{0, 44}, FontSize->40, FontColor->GrayLevel[1], Background->RGBColor[0.812512, 0, 0]], Cell[StyleData["Title", "Condensed"], CellMargins->{{8, 10}, {4, 8}}, FontSize->20], Cell[StyleData["Title", "Printout"], CellFrame->{{0, 0}, {0.25, 0}}, CellMargins->{{10, 10}, {12, 30}}, CellFrameMargins->2, FontSize->26] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], CellMargins->{{40, Inherited}, {20, 15}}, CellGroupingRules->{"TitleGrouping", 10}, PageBreakBelow->False, CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->24], Cell[StyleData["Subtitle", "Presentation"], ShowCellBracket->False, CellMargins->{{98, 0}, {20, 0}}, CellFrameMargins->{{10, 4}, {4, 6}}, AutoIndent->False, LineSpacing->{0, 34}, FontSize->30, FontColor->GrayLevel[1], Background->RGBColor[0.500008, 0, 0]], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{40, 10}, {1, 0}}, FontSize->18] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["Author"], CellMargins->{{100, Inherited}, {20, 0}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Author", "Presentation"], CellFrame->{{0, 0}, {2, 0}}, ShowCellBracket->False, CellMargins->{{98, 0}, {60, 10}}, CellFrameMargins->{{4, 4}, {2, 8}}, LineSpacing->{1, 0}, FontSize->22, FontColor->GrayLevel[0]], Cell[StyleData["Author", "Condensed"], CellMargins->{{8, 10}, {8, 8}}, FontSize->12], Cell[StyleData["Author", "Printout"], CellMargins->{{40, 10}, {60, 8}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], CellMargins->{{12, Inherited}, {10, 20}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{24, 10}, {10, 20}}, LineSpacing->{1, 0}, FontSize->24, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {8, 12}}, FontSize->12, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {8, 10}}, FontSize->14, FontColor->GrayLevel[0]] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellDingbat->"\[FilledSquare]", CellMargins->{{25, Inherited}, {8, 24}}, CellGroupingRules->{"SectionGrouping", 30}, PageBreakBelow->False, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->16, FontWeight->"Bold"], Cell[StyleData["Section", "Presentation"], CellFrame->{{0, 0}, {0, 2}}, CellDingbat->None, CellMargins->{{40, 22}, {0, 30}}, CellFrameMargins->{{99, 0}, {1, 4}}, CellFrameColor->RGBColor[0.708598, 0.00158694, 0.047715], CellFrameLabelMargins->{{4, 4}, {0, 2}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Section", "Condensed"], CellMargins->{{18, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Section", "Printout"], CellFrame->{{0, 0}, {0, 0.5}}, CellDingbat->None, CellMargins->{{10, 0}, {4, 22}}, CellFrameMargins->3, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellMargins->{{22, Inherited}, {8, 20}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellFrame->{{0, 0}, {0, 2}}, CellMargins->{{40, 22}, {0, 30}}, CellFrameMargins->{{0, 0}, {0, 2}}, CellFrameColor->GrayLevel[1], LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Subsection", "Printout"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{10, 0}, {0, 22}}, CellFrameMargins->3, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 18}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, CounterIncrements->"Subsubsection", FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{99, 60}, {0, 26}}, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{40, 0}, {0, 25}}, FontSize->11] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Rule"], CellMargins->{{10, Inherited}, {8, 18}}, PageBreakBelow->False], Cell[StyleData["Rule", "Presentation"], CellFrame->{{0, 0}, {3, 0}}, CellMargins->{{99, 60}, {0, 40}}, CellFrameMargins->False, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Rule", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Rule", "Printout"], CellMargins->{{10, 0}, {7, 14}}, FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{12, 10}, {7, 7}}, TextJustification->1, LineSpacing->{1, 3}, CounterIncrements->"Text"], Cell[StyleData["Text", "Presentation"], CellMargins->{{99, 22}, {10, 10}}, TextAlignment->Left, TextJustification->1, LineSpacing->{1, 3}, FontFamily->"Arial", FontSize->16], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["Text", "Printout"], CellMargins->{{40, 2}, {6, 6}}, TextJustification->1] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{12, 10}, {6, 6}}, LineSpacing->{1, 3}, CounterIncrements->"SmallText", FontFamily->"Helvetica", FontSize->9], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{119, 22}, {10, 10}}, LineSpacing->{1, 5}, FontSize->12, FontColor->RGBColor[0.0899214, 0.182635, 0.460777]], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{50, 2}, {5, 5}}, TextJustification->0.5, FontSize->7] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MathCaption"], CellFrame->{{4, 0}, {0, 0}}, CellMargins->{{47, 62}, {0, 14}}, CellFrameMargins->5, CellFrameColor->RGBColor[0, 0.2, 1], TextJustification->1, Hyphenation->True, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, FontColor->RGBColor[0, 0, 0.6]], Cell[StyleData["MathCaption", "Presentation"], CellFrame->{{4, 0}, {0, 0}}, CellMargins->{{105, 22}, {0, 14}}, CellFrameMargins->5, CellFrameColor->RGBColor[0, 0.2, 1], Hyphenation->True, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, FontFamily->"Arial", FontSize->16, FontColor->RGBColor[0, 0, 0.6]], Cell[StyleData["MathCaption", "Printout"], CellMargins->{{34, 62}, {0, 14}}, CellFrameColor->GrayLevel[0.700008], FontSize->10, FontColor->GrayLevel[0]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output to the kernel. Be careful when modifying, renaming, or removing these styles, because the front end associates special meanings with these style names. Some attributes for these styles are actually set in FormatType Styles (in the last section of this stylesheet). \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{45, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{99, 45}, {0, 10}}, CellFrameMargins->12, LineSpacing->{1, 0}, FontSize->16, FontColor->GrayLevel[1], Background->RGBColor[0.28748, 0.378042, 0.556527], ButtonBoxOptions->{ButtonMinHeight->0.125, ButtonMargins->9, Background->RGBColor[0.665293, 0.0723888, 0.101137]}], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}], Cell[StyleData["Input", "Printout"], CellFrame->True, CellMargins->{{40, 0}, {0, 6}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->9, Background->GrayLevel[0.849989]] }, Open ]], Cell[StyleData["InputOnly"], CellMargins->{{99, Inherited}, {Inherited, Inherited}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["InputWord"], CellMargins->{{99, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"InputGrouping", AutoItalicWords->{}, FormatType->InputForm, FontWeight->"Bold"], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{47, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Output"], Cell[StyleData["Output", "Presentation"], CellMargins->{{99, 45}, {10, 0}}, CellFrameMargins->12, LineSpacing->{1, 0}, FontSize->16, Background->RGBColor[0.978958, 0.959915, 0.622477]], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}], Cell[StyleData["Output", "Printout"], CellFrame->True, CellMargins->{{40, 0}, {6, 0}}, FontSize->9] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{99, 45}, {Inherited, Inherited}}, CellFrameMargins->12, LineSpacing->{1, 0}, FontColor->RGBColor[0.694072, 0.204471, 0.227802], Background->RGBColor[0.963821, 0.948333, 0.891249]], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Message", "Printout"], CellMargins->{{40, Inherited}, {Inherited, Inherited}}, FontSize->8, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{99, 45}, {0, 0}}, CellFrameMargins->{{12, 12}, {2, 2}}, LineSpacing->{1, 0}, Background->GrayLevel[1]], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Print", "Printout"], CellMargins->{{50, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None], Cell[StyleData["Graphics", "Presentation"], CellMargins->{{99, 45}, {10, 0}}, Background->RGBColor[0.978958, 0.959915, 0.622477]], Cell[StyleData["Graphics", "Condensed"], ImageMargins->{{38, Inherited}, {Inherited, 0}}, Magnification->0.6], Cell[StyleData["Graphics", "Printout"], CellFrame->True, CellMargins->{{40, 0}, {0, -1}}, ImageMargins->{{40, Inherited}, {Inherited, 0}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12, FontColor->GrayLevel[0]], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontSize->7, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Definition"], CellMargins->{{12, 10}, {7, 7}}, PageBreakBelow->False, TextJustification->1, LineSpacing->{1, 3}, CounterIncrements->"Definition", FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "StrikeThrough"->False}], Cell[StyleData["Definition", "Presentation"], CellMargins->{{99, 22}, {10, 10}}, LineSpacing->{1, 0}, FontSize->18, FontColor->RGBColor[0.500008, 0, 0]], Cell[StyleData["Definition", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Definition", "Printout"], CellMargins->{{40, 2}, {7, 14}}, FontSize->11, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Theorem"], CellMargins->{{12, 10}, {7, 7}}, PageBreakBelow->False, TextJustification->1, LineSpacing->{1, 3}, CounterIncrements->"Theorem", FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "StrikeThrough"->False}], Cell[StyleData["Theorem", "Presentation"], CellMargins->{{99, 22}, {10, 10}}, LineSpacing->{1, 0}, FontSize->18, FontColor->RGBColor[0.500008, 0, 0]], Cell[StyleData["Theorem", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Theorem", "Printout"], CellMargins->{{40, 2}, {7, 14}}, FontSize->11, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Example"], CellMargins->{{12, 10}, {7, 7}}, PageBreakBelow->False, TextJustification->1, LineSpacing->{1, 3}, CounterIncrements->"Theorem", FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "StrikeThrough"->False}], Cell[StyleData["Example", "Presentation"], CellMargins->{{99, 22}, {10, 10}}, LineSpacing->{1, 0}, FontSize->16, FontColor->RGBColor[0.500008, 0.250004, 0]], Cell[StyleData["Example", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Example", "Printout"], CellMargins->{{40, 2}, {7, 14}}, FontSize->11, FontColor->GrayLevel[0]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{99, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{10, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], CellMargins->{{99, Inherited}, {Inherited, 10}}, LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}], Cell[StyleData["DisplayFormula", "Printout"], CellMargins->{{10, Inherited}, {Inherited, Inherited}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, or between Notebooks. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line help system. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnsLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard ButtonFunctions, for use in palette buttons. \ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder objects in palette templates. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Placeholder->True, StyleMenuListing->None, FontSlant->"Italic", FontColor->RGBColor[0.890623, 0.864698, 0.384756], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], Placeholder->PrimaryPlaceholder, StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "Condensed"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles of most cells. If a cell's FormatType matches the name of one of the styles defined below, then that style is applied between the cell's style and its own options. This is particularly true of Input and Output. \ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an inline cell within another. \ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]], Cell[CellGroupData[{ Cell["Expression Annotation Styles", "Section"], Cell["\<\ The cells below define styles that are used to effect the display of certain types of objects in typeset expressions. For example, \"UnmatchedBracket\" style defines how unmatched bracket, curly bracket, and parenthesis characters are displayed (typically by coloring them to make them stand out). \ \>", "Text"], Cell[StyleData["UnmatchedBracket"], FontColor->RGBColor[0.760006, 0.330007, 0.8]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Automatic Numbering", "Section"], Cell["\<\ The following styles are useful for numbered equations, figures, etc. They automatically give the cell a FrameLabel containing a reference to a particular counter, and also increment that counter. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["NumberedEquation"], CellMargins->{{110, 10}, {0, 10}}, CellFrameLabels->{{None, Cell[ TextData[ {"(", CounterBox[ "Title"], ".", CounterBox[ "Section"], ".", CounterBox[ "NumberedEquation"], ")"}]]}, {None, None}}, DefaultFormatType->DefaultInputFormatType, CounterIncrements->"NumberedEquation", FormatTypeAutoConvert->False], Cell[StyleData["NumberedEquation", "Presentation"], CellMargins->{{99, 22}, {0, 10}}, FontFamily->"Arial", FontSize->16], Cell[StyleData["NumberedEquation", "Printout"], CellMargins->{{85, 5}, {0, 10}}, FontSize->10] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["NumberedFigure"], CellMargins->{{55, 145}, {2, 10}}, CellHorizontalScrolling->True, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Figure ", CounterBox[ "Title"], ".", CounterBox[ "Section"], ".", CounterBox[ "NumberedFigure"]}], FontWeight -> "Bold"], None}}, CounterIncrements->"NumberedFigure", FormatTypeAutoConvert->False], Cell[StyleData["NumberedFigure", "Printout"], FontSize->10] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["NumberedTable"], CellMargins->{{99, 145}, {2, 10}}, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Table ", CounterBox[ "Title"], ".", CounterBox[ "Section"], ".", CounterBox[ "NumberedTable"]}], FontWeight -> "Bold"], None}}, TextAlignment->Center, CounterIncrements->"NumberedTable", FormatTypeAutoConvert->False], Cell[StyleData["NumberedTable", "Printout"], CellMargins->{{65, 5}, {Inherited, Inherited}}, TextAlignment->Center, FontSize->10] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["NumberedExample"], CellMargins->{{12, 10}, {7, 7}}, PageBreakBelow->False, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Example: (", CounterBox[ "Title"], ".", CounterBox[ "Section"], ".", CounterBox[ "NumberedExample"], ")"}], FontWeight -> "Bold"], None}}, TextJustification->1, LineSpacing->{1, 3}, CounterIncrements->"Theorem", FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "StrikeThrough"->False}], Cell[StyleData["NumberedExample", "Presentation"], CellMargins->{{99, 22}, {10, 10}}, LineSpacing->{1, 0}, FontSize->16, FontColor->RGBColor[0.500008, 0.250004, 0]], Cell[StyleData["NumberedExample", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["NumberedExample", "Printout"], CellMargins->{{40, 2}, {7, 14}}, FontSize->11, FontColor->GrayLevel[0]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Tables", "Section"], Cell[CellGroupData[{ Cell[StyleData["SingleRowTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnAlignments->{Left}}], Cell[StyleData["SingleRowTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["SingleRowTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnWidths->{0.34, 0.64}, ColumnAlignments->{Left, Center}}], Cell[StyleData["2ColumnTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["2ColumnTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnEvenTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnWidths->0.49, ColumnAlignments->{Left, Center}}], Cell[StyleData["2ColumnEvenTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["2ColumnEvenTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnWidths->{0.28, 0.28, 0.43}, ColumnAlignments->{Left, Center}}], Cell[StyleData["3ColumnTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["3ColumnTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["4ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnWidths->0.25, ColumnAlignments->{Left, Center}}], Cell[StyleData["4ColumnTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["4ColumnTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["5ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnWidths->0.2, ColumnAlignments->{Left, Center}}], Cell[StyleData["5ColumnTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["5ColumnTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["6ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnWidths->0.16, ColumnAlignments->{Left, Center}}], Cell[StyleData["6ColumnTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["6ColumnTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["7ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnWidths->0.14, ColumnAlignments->{Left, Center}}], Cell[StyleData["7ColumnTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["7ColumnTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["8ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->2, ColumnWidths->0.12, ColumnAlignments->{Left, Center}}], Cell[StyleData["8ColumnTable", "Printout"], CellMargins->{{2, 0}, {0, 8}}], Cell[StyleData["8ColumnTable", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Miscellaneous Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Commentary"], CellFrame->{{2, 0}, {0, 0}}, CellMargins->{{36, 10}, {7, 7}}, PageBreakBelow->False, CellFrameMargins->8, CellFrameColor->RGBColor[0, 0.2, 1], LineSpacing->{1, 3}, ParagraphSpacing->{0, 8}, FontSlant->"Italic"], Cell[StyleData["Commentary", "Printout"], CellMargins->{{36, 0}, {6, 6}}, CellFrameColor->GrayLevel[0.8], FontSize->10], Cell[StyleData["Commentary", "EnhancedPrintout"], CellMargins->{{36, 0}, {6, 6}}, CellFrameColor->GrayLevel[0.8], FontFamily->"Palatino", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ItemizedText"], CellMargins->{{20, 4}, {0, 4}}, LineSpacing->{1, 3}, ParagraphSpacing->{0, 4}, ParagraphIndent->-21, CounterIncrements->"ItemizedText"], Cell[StyleData["ItemizedText", "Printout"], ParagraphIndent->-18, FontSize->11], Cell[StyleData["ItemizedText", "EnhancedPrintout"], ParagraphIndent->-18, FontFamily->"Palatino", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ItemizedTextNote"], CellMargins->{{41, 4}, {0, 4}}, LineSpacing->{1, 3}, ParagraphSpacing->{0, 4}, CounterIncrements->"Text"], Cell[StyleData["ItemizedTextNote", "Printout"], CellMargins->{{38, 4}, {0, 4}}, FontSize->11], Cell[StyleData["ItemizedTextNote", "EnhancedPrintout"], CellMargins->{{38, 4}, {0, 4}}, FontFamily->"Palatino", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["IndentedText"], CellMargins->{{20, 4}, {0, 6}}, LineSpacing->{1, 3}, ParagraphSpacing->{0, 8}, CounterIncrements->"Text"], Cell[StyleData["IndentedText", "Printout"], FontSize->11], Cell[StyleData["IndentedText", "EnhancedPrintout"], FontFamily->"Palatino", FontSize->10] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Emphasis Boxes and Pictures", "Section"], Cell[CellGroupData[{ Cell[StyleData["DefinitionBox"], CellFrame->0.5, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.3, 0.7}, ColumnAlignments->{Left}}], Cell[StyleData["DefinitionBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[1]], Cell[StyleData["DefinitionBox", "EnhancedPrintout"], CellMargins->{{2, 4}, {0, 8}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DefinitionBox3Col"], CellFrame->0.5, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.2, 0.3, 0.5}, ColumnAlignments->{Left}}], Cell[StyleData["DefinitionBox3Col", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[1]], Cell[StyleData["DefinitionBox3Col", "EnhancedPrintout"], CellMargins->{{2, 4}, {0, 8}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DefinitionBox4Col"], CellFrame->0.5, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.15, 0.35, 0.15, 0.35}, ColumnAlignments->{Left}}], Cell[StyleData["DefinitionBox4Col", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[1]], Cell[StyleData["DefinitionBox4Col", "EnhancedPrintout"], CellMargins->{{2, 4}, {0, 8}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DefinitionBox5Col"], CellFrame->0.5, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->0.2, ColumnAlignments->{Left}}], Cell[StyleData["DefinitionBox5Col", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[1]], Cell[StyleData["DefinitionBox5Col", "EnhancedPrintout"], CellMargins->{{2, 4}, {0, 8}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DefinitionBox6Col"], CellFrame->0.5, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.13, 0.24, 0.13, 0.13, 0.24, 0.13}, ColumnAlignments->{Left}}], Cell[StyleData["DefinitionBox6Col", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[1]], Cell[StyleData["DefinitionBox6Col", "EnhancedPrintout"], CellMargins->{{2, 4}, {0, 8}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TopBox"], CellFrame->{{0.5, 0.5}, {0, 0.5}}, CellMargins->{{11, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakBelow->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.31, 0.62}, ColumnAlignments->{Left}}], Cell[StyleData["TopBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, Background->GrayLevel[1]], Cell[StyleData["TopBox", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 8}}, FontFamily->"Palatino", Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MiddleBox"], CellFrame->{{0.5, 0.5}, {0, 0}}, CellMargins->{{11, 4}, {0, -7}}, CellHorizontalScrolling->True, PageBreakAbove->False, PageBreakBelow->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.31, 0.62}, ColumnAlignments->{Left}}], Cell[StyleData["MiddleBox", "Printout"], CellMargins->{{2, 0}, {0, 2}}, Background->GrayLevel[1]], Cell[StyleData["MiddleBox", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 4}}, FontFamily->"Palatino", Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MiddleSpacedBox"], CellFrame->{{0.5, 0.5}, {0, 0}}, CellMargins->{{11, 4}, {0, -7}}, CellHorizontalScrolling->True, PageBreakAbove->False, PageBreakBelow->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.31, 0.62}, ColumnAlignments->{Left}, RowMinHeight->1.2}], Cell[StyleData["MiddleSpacedBox", "Printout"], CellMargins->{{2, 0}, {0, 0}}, Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->1.8}], Cell[StyleData["MiddleSpacedBox", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 0}}, FontFamily->"Palatino", Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->1.8}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["BottomBox"], CellFrame->{{0.5, 0.5}, {0.5, 0}}, CellMargins->{{11, 4}, {0, -7}}, CellHorizontalScrolling->True, PageBreakAbove->False, PageBreakBelow->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.31, 0.62}, ColumnAlignments->{Left}, RowMinHeight->1.2}], Cell[StyleData["BottomBox", "Printout"], CellMargins->{{2, 0}, {0, -5}}, FontSize->10, Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->2.2}], Cell[StyleData["BottomBox", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, -5}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->2.2}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TopSpanBox"], CellFrame->{{0.5, 0.5}, {0, 0.5}}, CellMargins->{{11, 4}, {-2, 8}}, CellHorizontalScrolling->True, PageBreakBelow->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.9, 0.03}, ColumnAlignments->{Left}}], Cell[StyleData["TopSpanBox", "Printout"], CellMargins->{{2, 0}, {-2, 8}}, FontSize->10, Background->GrayLevel[1]], Cell[StyleData["TopSpanBox", "EnhancedPrintout"], CellMargins->{{2, 0}, {-4, 8}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MiddleSpanBox"], CellFrame->{{0.5, 0.5}, {0, 0}}, CellMargins->{{11, 4}, {-3, -8}}, CellHorizontalScrolling->True, PageBreakAbove->False, PageBreakBelow->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.9, 0.03}, ColumnAlignments->{Left}, RowMinHeight->1.2}], Cell[StyleData["MiddleSpanBox", "Printout"], CellMargins->{{2, 0}, {-5, 0}}, FontSize->10, Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->1.8}], Cell[StyleData["MiddleSpanBox", "EnhancedPrintout"], CellMargins->{{2, 0}, {-7, 0}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->1.8}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Picture"], CellMargins->{{12, Inherited}, {0, 8}}, CellHorizontalScrolling->True], Cell[StyleData["Picture", "Printout"], CellMargins->{{2, Inherited}, {0, 8}}], Cell[StyleData["Picture", "EnhancedPrintout"], CellMargins->{{2, Inherited}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Caption"], CellMargins->{{12, 4}, {0, 2}}, PageBreakAbove->False, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["Caption", "Printout"], CellMargins->{{2, 4}, {2, 4}}, FontSize->7], Cell[StyleData["Caption", "EnhancedPrintout"], CellMargins->{{2, 4}, {2, 4}}, FontFamily->"Futura", FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Contents and Index", "Section"], Cell[CellGroupData[{ Cell[StyleData["ContentsTitle"], CellMargins->{{10, 4}, {0, 18}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->26, FontWeight->"Bold"], Cell[StyleData["ContentsTitle", "Printout"], CellMargins->{{2, 0}, {0, 18}}, PageBreakBelow->False, FontSize->18], Cell[StyleData["ContentsTitle", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 18}}, PageBreakBelow->False, FontFamily->"Futura", FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ContentsSection"], CellMargins->{{20, 4}, {3, 18}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->12, FontWeight->"Bold"], Cell[StyleData["ContentsSection", "Printout"], CellMargins->{{12, 0}, {3, 18}}, PageBreakBelow->False, FontSize->11], Cell[StyleData["ContentsSection", "EnhancedPrintout"], CellMargins->{{12, 0}, {3, 18}}, PageBreakBelow->False, FontFamily->"Futura", FontSize->11] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["Contents"], CellMargins->{{21, 4}, {0, 8}}, StyleMenuListing->None], Cell[StyleData["Contents", "Printout"], CellMargins->{{13, 0}, {0, 8}}], Cell[StyleData["Contents", "EnhancedPrintout"], CellMargins->{{13, 0}, {0, 8}}, FontFamily->"Palatino", FontSize->11] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Index"], CellMargins->{{21, 4}, {0, 0}}, ParagraphIndent->-48, StyleMenuListing->None], Cell[StyleData["Index", "Printout"], CellMargins->{{13, 0}, {0, 0}}, FontSize->10], Cell[StyleData["Index", "EnhancedPrintout"], CellMargins->{{13, 0}, {0, 0}}, FontFamily->"Palatino", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["IndexSubentry"], CellMargins->{{36, 4}, {0, 0}}, ParagraphIndent->-48, StyleMenuListing->None], Cell[StyleData["IndexSubentry", "Printout"], CellMargins->{{24, 0}, {0, 0}}, FontSize->10], Cell[StyleData["IndexSubentry", "EnhancedPrintout"], CellMargins->{{24, 0}, {0, 0}}, FontFamily->"Palatino", FontSize->10] }, Closed]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Notation Package Styles", "Section", GeneratedCell->True, CellTags->"NotationPackage"], Cell["\<\ The cells below define certain styles needed by the Notation package. These \ styles serve to make visible otherwise invisible tagboxes.\ \>", "Text", GeneratedCell->True, CellTags->"NotationPackage"], Cell[StyleData["NotationTemplateStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[1, 1, 0.850004], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"], Cell[StyleData["NotationPatternWrapperStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[1, 0.900008, 0.979995], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"], Cell[StyleData["NotationMadeBoxesWrapperStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[0.900008, 0.889998, 1], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"] }, Closed]] }] ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{ "Top"->{ Cell[1739, 51, 55, 1, 74, "Title", CellTags->"Top"]}, "Introduction"->{ Cell[3650, 133, 168, 6, 55, "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"Introduction"]}, "Leibnit's Question"->{ Cell[478725, 7942, 363, 10, 64, "MathCaption", CellTags->"Leibnit's Question"]}, "The Riemann Liouville and Weyl Calculus"->{ Cell[487671, 8230, 222, 6, 65, "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"The Riemann Liouville and Weyl Calculus"]}, "Riemann and Liouville Calculus"->{ Cell[488264, 8248, 189, 10, 59, "Subsection", CellTags->"Riemann and Liouville Calculus"]}, "Cauchy's integral formula"->{ Cell[491940, 8364, 119, 2, 42, "Text", CellTags->"Cauchy's integral formula"]}, "Riemann fractional integral"->{ Cell[493026, 8397, 426, 10, 38, "NumberedEquation", CellTags->"Riemann fractional integral"]}, "Liouville fractional integral"->{ Cell[493455, 8409, 1047, 29, 131, "Text", CellTags->"Liouville fractional integral"]}, "Riemann-Liouville fractional integral"->{ Cell[494505, 8440, 499, 9, 54, "NumberedEquation", CellTags->"Riemann-Liouville fractional integral"]}, "eq-3.2.10"->{ Cell[496374, 8487, 519, 14, 55, "NumberedEquation", CellTags->"eq-3.2.10"]}, "Properties of Riemann-Liouville Operators"->{ Cell[499858, 8574, 247, 11, 46, "Subsubsection", CellTags->"Properties of Riemann-Liouville Operators"]}, "Linearity"->{ Cell[500602, 8597, 188, 13, 63, "Rule", CellTags->"Linearity"], Cell[543481, 9983, 152, 10, 63, "Rule", CellTags->"Linearity"]}, "Composition Rule"->{ Cell[503214, 8686, 202, 13, 63, "Rule", CellTags->"Composition Rule"], Cell[546336, 10078, 166, 10, 63, "Rule", CellTags->"Composition Rule"]}, "Examples of the Riemann-Liouville Operator"->{ Cell[509675, 8900, 97, 1, 46, "Subsubsection", CellTags->"Examples of the Riemann-Liouville Operator"]}, "hier gehts weiter"->{ Cell[516167, 9111, 766, 19, 130, "Text", CellTags->"hier gehts weiter"]}, "Weyl Calculus"->{ Cell[536190, 9741, 149, 8, 59, "Subsection", CellTags->"Weyl Calculus"]}, "Weyl-Plus operator"->{ Cell[536791, 9765, 516, 14, 44, "NumberedEquation", CellTags->"Weyl-Plus operator"]}, "Weyl-Minus operator"->{ Cell[537356, 9783, 457, 12, 41, "NumberedEquation", CellTags->"Weyl-Minus operator"]}, "eq-4.2.3"->{ Cell[538616, 9821, 285, 8, 40, "NumberedEquation", CellTags->"eq-4.2.3"]}, "eq-4.2.4"->{ Cell[538977, 9833, 316, 9, 37, "NumberedEquation", CellTags->"eq-4.2.4"]}, "Properties of the Weyl Operator"->{ Cell[543193, 9969, 164, 7, 46, "Subsubsection", CellTags->"Properties of the Weyl Operator"]}, "Examples"->{ Cell[551669, 10262, 118, 7, 46, "Subsubsection", CellTags->"Examples"]}, "Anomalous Relaxation"->{ Cell[559880, 10561, 161, 8, 59, "Subsection", CellTags->"Anomalous Relaxation"]}, "eq-3"->{ Cell[560245, 10577, 397, 13, 30, "NumberedEquation", CellTags->"eq-3"]}, "eq-4"->{ Cell[560895, 10602, 418, 10, 51, "NumberedEquation", CellTags->"eq-4"]}, "eq-5"->{ Cell[561497, 10622, 348, 10, 42, "NumberedEquation", CellTags->"eq-5"]}, "eq-6"->{ Cell[562798, 10656, 184, 4, 31, "NumberedEquation", CellTags->"eq-6"]}, "eq-7"->{ Cell[563126, 10669, 302, 9, 38, "NumberedEquation", CellTags->"eq-7"]}, "eq-8"->{ Cell[564733, 10716, 321, 6, 40, "NumberedEquation", CellTags->"eq-8"]}, "eq-9"->{ Cell[566150, 10757, 258, 4, 37, "NumberedEquation", CellTags->"eq-9"]}, "eq-10"->{ Cell[567808, 10815, 214, 6, 37, "NumberedEquation", CellTags->"eq-10"]}, "Anomalous Diffusion"->{ Cell[619791, 12540, 123, 5, 59, "Subsection", CellTags->"Anomalous Diffusion"]}, "eq-11"->{ Cell[622114, 12605, 193, 4, 30, "NumberedEquation", CellTags->"eq-11"]}, "eq-12"->{ Cell[622732, 12624, 299, 8, 32, "NumberedEquation", CellTags->"eq-12"]}, "eq-14"->{ Cell[623760, 12662, 393, 10, 42, "NumberedEquation", CellTags->"eq-14"]}, "eq-15"->{ Cell[624371, 12681, 327, 9, 34, "NumberedEquation", CellTags->"eq-15"]}, "eq-16"->{ Cell[624962, 12703, 300, 8, 35, "NumberedEquation", CellTags->"eq-16"]}, "eq-17"->{ Cell[625599, 12725, 358, 9, 43, "NumberedEquation", CellTags->"eq-17"]}, "eq-18"->{ Cell[626448, 12753, 387, 11, 41, "NumberedEquation", CellTags->"eq-18"]}, "eq-22a"->{ Cell[634354, 13014, 527, 14, 68, "NumberedEquation", CellTags->"eq-22a"]}, "eq-24"->{ Cell[775030, 16505, 186, 7, 30, "NumberedEquation", CellTags->"eq-24"]}, "Conclusions"->{ Cell[776392, 16560, 166, 6, 65, "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"Conclusions"]}, "Lacroix-1819"->{ Cell[778064, 16609, 203, 4, 41, "SmallText", CellTags->"Lacroix-1819"]}, "Oldham-1974"->{ Cell[778270, 16615, 148, 4, 41, "SmallText", CellTags->"Oldham-1974"]}, "Miller-1993"->{ Cell[778421, 16621, 213, 5, 62, "SmallText", CellTags->"Miller-1993"]}, "Riemann-1892"->{ Cell[778637, 16628, 129, 3, 41, "SmallText", CellTags->"Riemann-1892"]}, "Liouville-1832a"->{ Cell[778769, 16633, 276, 7, 41, "SmallText", CellTags->"Liouville-1832a"]}, "Weyl-1917"->{ Cell[779048, 16642, 274, 8, 62, "SmallText", CellTags->"Weyl-1917"]}, "Davis-1936"->{ Cell[779325, 16652, 148, 4, 41, "SmallText", CellTags->"Davis-1936"]}, "Gl\[ODoubleDot]ckle-1991"->{ Cell[779476, 16658, 301, 8, 62, "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1991"]}, "Fox-1961"->{ Cell[779780, 16668, 218, 7, 41, "SmallText", CellTags->"Fox-1961"]}, "Gl\[ODoubleDot]ckle-1993a"->{ Cell[780001, 16677, 278, 7, 62, "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1993a"]}, "Schneider-1989"->{ Cell[780282, 16686, 224, 7, 41, "SmallText", CellTags->"Schneider-1989"]}, "Zwanzig-1965"->{ Cell[780509, 16695, 197, 4, 62, "SmallText", CellTags->"Zwanzig-1965"]}, "Gl\[ODoubleDot]ckle-1994"->{ Cell[780709, 16701, 283, 7, 62, "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1994"]}, "Braaksma-1964"->{ Cell[780995, 16710, 253, 7, 62, "SmallText", CellTags->"Braaksma-1964"]}, "West-1994"->{ Cell[781251, 16719, 177, 4, 41, "SmallText", CellTags->"West-1994"]}, "Wyss-1986"->{ Cell[781431, 16725, 195, 6, 41, "SmallText", CellTags->"Wyss-1986"]}, "Schaugnessy-1985"->{ Cell[781629, 16733, 249, 7, 62, "SmallText", CellTags->"Schaugnessy-1985"]}, "Compte-1996"->{ Cell[781881, 16742, 210, 7, 41, "SmallText", CellTags->"Compte-1996"]}, "West-1997"->{ Cell[782094, 16751, 263, 7, 62, "SmallText", CellTags->"West-1997"]}, "Podlubny-1999"->{ Cell[782360, 16760, 147, 4, 41, "SmallText", CellTags->"Podlubny-1999"]} } *) (*CellTagsIndex CellTagsIndex->{ {"Top", 856322, 19277}, {"Introduction", 856406, 19280}, {"Leibnit's Question", 856577, 19284}, {"The Riemann Liouville and Weyl Calculus", 856715, 19287}, {"Riemann and Liouville Calculus", 856928, 19291}, {"Cauchy's integral formula", 857063, 19294}, {"Riemann fractional integral", 857188, 19297}, {"Liouville fractional integral", 857330, 19300}, {"Riemann-Liouville fractional integral", 857472, 19303}, {"eq-3.2.10", 857603, 19306}, {"Properties of Riemann-Liouville Operators", 857739, 19309}, {"Linearity", 857872, 19312}, {"Composition Rule", 858045, 19317}, {"Examples of the Riemann-Liouville Operator", 858259, 19322}, {"hier gehts weiter", 858399, 19325}, {"Weyl Calculus", 858504, 19328}, {"Weyl-Plus operator", 858614, 19331}, {"Weyl-Minus operator", 858737, 19334}, {"eq-4.2.3", 858850, 19337}, {"eq-4.2.4", 858951, 19340}, {"Properties of the Weyl Operator", 859075, 19343}, {"Examples", 859196, 19346}, {"Anomalous Relaxation", 859307, 19349}, {"eq-3", 859411, 19352}, {"eq-4", 859506, 19355}, {"eq-5", 859601, 19358}, {"eq-6", 859696, 19361}, {"eq-7", 859790, 19364}, {"eq-8", 859884, 19367}, {"eq-9", 859978, 19370}, {"eq-10", 860073, 19373}, {"Anomalous Diffusion", 860183, 19376}, {"eq-11", 860287, 19379}, {"eq-12", 860383, 19382}, {"eq-14", 860479, 19385}, {"eq-15", 860576, 19388}, {"eq-16", 860672, 19391}, {"eq-17", 860768, 19394}, {"eq-18", 860864, 19397}, {"eq-22a", 860962, 19400}, {"eq-24", 861060, 19403}, {"Conclusions", 861162, 19406}, {"Lacroix-1819", 861330, 19410}, {"Oldham-1974", 861432, 19413}, {"Miller-1993", 861533, 19416}, {"Riemann-1892", 861635, 19419}, {"Liouville-1832a", 861741, 19422}, {"Weyl-1917", 861844, 19425}, {"Davis-1936", 861942, 19428}, {"Gl\[ODoubleDot]ckle-1991", 862055, 19431}, {"Fox-1961", 862166, 19434}, {"Gl\[ODoubleDot]ckle-1993a", 862278, 19437}, {"Schneider-1989", 862396, 19440}, {"Zwanzig-1965", 862501, 19443}, {"Gl\[ODoubleDot]ckle-1994", 862616, 19446}, {"Braaksma-1964", 862732, 19449}, {"West-1994", 862833, 19452}, {"Wyss-1986", 862930, 19455}, {"Schaugnessy-1985", 863034, 19458}, {"Compte-1996", 863140, 19461}, {"West-1997", 863239, 19464}, {"Podlubny-1999", 863340, 19467} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1739, 51, 55, 1, 74, "Title", CellTags->"Top"], Cell[1797, 54, 147, 5, 100, "Subtitle"], Cell[1947, 61, 142, 7, 230, "Author"], Cell[CellGroupData[{ Cell[2114, 72, 124, 2, 46, "Subsubsection"], Cell[2241, 76, 217, 6, 65, "Text"], Cell[2461, 84, 80, 2, 71, "Input", InitializationCell->True], Cell[2544, 88, 81, 2, 71, "Input", InitializationCell->True], Cell[2628, 92, 79, 2, 71, "Input", InitializationCell->True], Cell[2710, 96, 390, 6, 232, "Input", InitializationCell->True], Cell[3103, 104, 32, 0, 42, "Text"], Cell[CellGroupData[{ Cell[3160, 108, 84, 2, 71, "Input", InitializationCell->True], Cell[3247, 112, 69, 1, 70, "Print"], Cell[3319, 115, 101, 2, 70, "Print"] }, Open ]], Cell[CellGroupData[{ Cell[3457, 122, 84, 2, 71, "Input", InitializationCell->True], Cell[3544, 126, 57, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[3650, 133, 168, 6, 55, "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"Introduction"], Cell[3821, 141, 372, 8, 87, "Text"], Cell[4196, 151, 288581, 4733, 165, 288431, 4729, "GraphicsData", "Bitmap", \ "Graphics"], Cell[292780, 4886, 102, 3, 42, "Text"], Cell[292885, 4891, 185837, 3049, 189, 185687, 3045, "GraphicsData", "Bitmap", \ "Graphics"], Cell[478725, 7942, 363, 10, 64, "MathCaption", CellTags->"Leibnit's Question"], Cell[479091, 7954, 147, 3, 64, "Text"], Cell[479241, 7959, 113, 5, 40, "MathCaption"], Cell[479357, 7966, 569, 13, 112, "Text"], Cell[479929, 7981, 261, 5, 86, "Text"], Cell[480193, 7988, 562, 16, 110, "Text"], Cell[480758, 8006, 185, 2, 41, "NumberedEquation"], Cell[480946, 8010, 352, 9, 64, "Text"], Cell[481301, 8021, 204, 5, 41, "NumberedEquation"], Cell[481508, 8028, 761, 18, 130, "Text"], Cell[482272, 8048, 204, 5, 41, "NumberedEquation"], Cell[482479, 8055, 444, 11, 109, "Text"], Cell[CellGroupData[{ Cell[482948, 8070, 60, 1, 56, "Input"], Cell[483011, 8073, 196, 3, 115, "Message"], Cell[483210, 8078, 60, 1, 66, "Output"] }, Open ]], Cell[483285, 8082, 573, 14, 133, "Text"], Cell[483861, 8098, 50, 1, 54, "Input"], Cell[483914, 8101, 204, 4, 121, "Input"], Cell[484121, 8107, 48, 1, 54, "Input"], Cell[484172, 8110, 282, 5, 86, "Text"], Cell[CellGroupData[{ Cell[484479, 8119, 67, 1, 64, "Input"], Cell[484549, 8122, 67, 1, 78, "Output"] }, Open ]], Cell[484631, 8126, 151, 5, 42, "Text"], Cell[CellGroupData[{ Cell[484807, 8135, 60, 1, 56, "Input"], Cell[484870, 8138, 78, 1, 70, "Output"] }, Open ]], Cell[484963, 8142, 97, 2, 42, "Text"], Cell[CellGroupData[{ Cell[485085, 8148, 65, 1, 56, "Input"], Cell[485153, 8151, 171, 3, 55, "Output"] }, Open ]], Cell[485339, 8157, 454, 14, 86, "Text"], Cell[485796, 8173, 1838, 52, 262, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[487671, 8230, 222, 6, 65, "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"The Riemann Liouville and Weyl Calculus"], Cell[487896, 8238, 343, 6, 108, "Text"], Cell[CellGroupData[{ Cell[488264, 8248, 189, 10, 59, "Subsection", CellTags->"Riemann and Liouville Calculus"], Cell[488456, 8260, 600, 10, 152, "Text"], Cell[489059, 8272, 221, 6, 41, "NumberedEquation"], Cell[489283, 8280, 55, 0, 42, "Text"], Cell[489341, 8282, 288, 7, 41, "NumberedEquation"], Cell[489632, 8291, 561, 13, 111, "Text"], Cell[490196, 8306, 232, 6, 34, "NumberedEquation"], Cell[490431, 8314, 605, 16, 111, "Text"], Cell[491039, 8332, 232, 6, 33, "NumberedEquation"], Cell[491274, 8340, 329, 12, 45, "Text"], Cell[491606, 8354, 331, 8, 34, "NumberedEquation"], Cell[491940, 8364, 119, 2, 42, "Text", CellTags->"Cauchy's integral formula"], Cell[492062, 8368, 289, 7, 39, "NumberedEquation"], Cell[492354, 8377, 73, 1, 42, "Text"], Cell[492430, 8380, 335, 8, 38, "NumberedEquation"], Cell[492768, 8390, 255, 5, 64, "Text"], Cell[493026, 8397, 426, 10, 38, "NumberedEquation", CellTags->"Riemann fractional integral"], Cell[493455, 8409, 1047, 29, 131, "Text", CellTags->"Liouville fractional integral"], Cell[494505, 8440, 499, 9, 54, "NumberedEquation", CellTags->"Riemann-Liouville fractional integral"], Cell[495007, 8451, 773, 19, 135, "Text"], Cell[495783, 8472, 588, 13, 131, "Text"], Cell[496374, 8487, 519, 14, 55, "NumberedEquation", CellTags->"eq-3.2.10"], Cell[496896, 8503, 352, 11, 86, "Text"], Cell[497251, 8516, 1266, 24, 263, "Text"], Cell[498520, 8542, 590, 11, 262, "Input"], Cell[499113, 8555, 720, 15, 176, "Text"], Cell[CellGroupData[{ Cell[499858, 8574, 247, 11, 46, "Subsubsection", CellTags->"Properties of Riemann-Liouville Operators"], Cell[500108, 8587, 491, 8, 130, "Text"], Cell[500602, 8597, 188, 13, 63, "Rule", CellTags->"Linearity"], Cell[500793, 8612, 328, 6, 86, "Text"], Cell[501124, 8620, 379, 7, 32, "NumberedEquation"], Cell[501506, 8629, 430, 13, 88, "Text"], Cell[501939, 8644, 164, 3, 77, "Input"], Cell[502106, 8649, 145, 3, 64, "Text"], Cell[502254, 8654, 179, 3, 100, "Input"], Cell[502436, 8659, 379, 10, 89, "Text"], Cell[502818, 8671, 258, 7, 36, "NumberedEquation"], Cell[503079, 8680, 132, 4, 42, "Text"], Cell[503214, 8686, 202, 13, 63, "Rule", CellTags->"Composition Rule"], Cell[503419, 8701, 240, 8, 42, "Text"], Cell[503662, 8711, 301, 6, 35, "NumberedEquation"], Cell[503966, 8719, 22, 0, 42, "Text"], Cell[503991, 8721, 130, 4, 42, "Text"], Cell[504124, 8727, 264, 5, 32, "NumberedEquation"], Cell[504391, 8734, 322, 12, 64, "Text"], Cell[504716, 8748, 267, 6, 100, "Input"], Cell[504986, 8756, 130, 5, 42, "Text"], Cell[505119, 8763, 392, 6, 32, "NumberedEquation"], Cell[505514, 8771, 51, 0, 42, "Text"], Cell[505568, 8773, 234, 4, 31, "NumberedEquation"], Cell[505805, 8779, 354, 11, 64, "Text"], Cell[506162, 8792, 275, 7, 40, "NumberedEquation"], Cell[506440, 8801, 205, 8, 42, "Text"], Cell[506648, 8811, 181, 3, 32, "NumberedEquation"], Cell[506832, 8816, 98, 5, 42, "Text"], Cell[506933, 8823, 185, 3, 32, "NumberedEquation"], Cell[507121, 8828, 191, 6, 64, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[507349, 8839, 46, 1, 46, "Subsubsection"], Cell[507398, 8842, 938, 22, 201, "Text"], Cell[508339, 8866, 1299, 29, 227, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[509675, 8900, 97, 1, 46, "Subsubsection", CellTags->"Examples of the Riemann-Liouville Operator"], Cell[509775, 8903, 666, 19, 108, "Text"], Cell[CellGroupData[{ Cell[510466, 8926, 74, 1, 58, "Input"], Cell[510543, 8929, 53, 1, 75, "Output"] }, Open ]], Cell[510611, 8933, 684, 10, 196, "Text"], Cell[CellGroupData[{ Cell[511320, 8947, 62, 1, 54, "Input"], Cell[511385, 8950, 53, 1, 75, "Output"] }, Open ]], Cell[511453, 8954, 104, 3, 42, "Text"], Cell[CellGroupData[{ Cell[511582, 8961, 65, 1, 54, "Input"], Cell[511650, 8964, 53, 1, 75, "Output"] }, Open ]], Cell[511718, 8968, 165, 3, 64, "Text"], Cell[511886, 8973, 1235, 27, 243, "Text"], Cell[CellGroupData[{ Cell[513146, 9004, 50, 1, 54, "Input"], Cell[513199, 9007, 108, 2, 54, "Output"] }, Open ]], Cell[513322, 9012, 223, 6, 64, "Text"], Cell[CellGroupData[{ Cell[513570, 9022, 74, 1, 56, "Input"], Cell[513647, 9025, 174, 4, 74, "Output"] }, Open ]], Cell[513836, 9032, 313, 9, 64, "Text"], Cell[514152, 9043, 401, 9, 109, "Text"], Cell[CellGroupData[{ Cell[514578, 9056, 58, 1, 54, "Input"], Cell[514639, 9059, 92, 1, 54, "Output"] }, Open ]], Cell[514746, 9063, 120, 3, 64, "Text"], Cell[CellGroupData[{ Cell[514891, 9070, 91, 1, 54, "Input"], Cell[514985, 9073, 93, 1, 54, "Output"] }, Open ]], Cell[515093, 9077, 564, 13, 130, "Text"], Cell[515660, 9092, 55, 1, 54, "Input"], Cell[CellGroupData[{ Cell[515740, 9097, 84, 1, 56, "Input"], Cell[515827, 9100, 325, 8, 74, "Output"] }, Open ]], Cell[516167, 9111, 766, 19, 130, "Text", CellTags->"hier gehts weiter"], Cell[516936, 9132, 58, 1, 54, "Input"], Cell[CellGroupData[{ Cell[517019, 9137, 110, 2, 56, "Input"], Cell[517132, 9141, 573, 15, 74, "Output"] }, Open ]], Cell[517720, 9159, 273, 8, 65, "Text"], Cell[517996, 9169, 265, 6, 41, "NumberedEquation"], Cell[518264, 9177, 99, 2, 42, "Text"], Cell[CellGroupData[{ Cell[518388, 9183, 92, 1, 56, "Input"], Cell[518483, 9186, 541, 14, 103, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[519061, 9205, 92, 1, 56, "Input"], Cell[519156, 9208, 516, 14, 103, "Output"] }, Open ]], Cell[519687, 9225, 213, 5, 64, "Text"], Cell[519903, 9232, 255, 6, 64, "Text"], Cell[CellGroupData[{ Cell[520183, 9242, 114, 2, 56, "Input"], Cell[520300, 9246, 558, 13, 114, "Output"] }, Open ]], Cell[520873, 9262, 246, 6, 64, "Text"], Cell[CellGroupData[{ Cell[521144, 9272, 127, 2, 56, "Input"], Cell[521274, 9276, 1018, 25, 182, "Output"] }, Open ]], Cell[522307, 9304, 170, 5, 42, "Text"], Cell[522480, 9311, 492, 8, 130, "Text"], Cell[CellGroupData[{ Cell[522997, 9323, 74, 1, 58, "Input"], Cell[523074, 9326, 53, 1, 75, "Output"] }, Open ]], Cell[523142, 9330, 178, 5, 42, "Text"], Cell[CellGroupData[{ Cell[523345, 9339, 79, 1, 58, "Input"], Cell[523427, 9342, 53, 1, 80, "Output"] }, Open ]], Cell[523495, 9346, 203, 6, 64, "Text"], Cell[523701, 9354, 78, 2, 42, "Text"], Cell[CellGroupData[{ Cell[523804, 9360, 105, 2, 56, "Input"], Cell[523912, 9364, 746, 17, 74, "Output"] }, Open ]], Cell[524673, 9384, 88, 2, 42, "Text"], Cell[CellGroupData[{ Cell[524786, 9390, 110, 2, 56, "Input"], Cell[524899, 9394, 573, 15, 74, "Output"] }, Open ]], Cell[525487, 9412, 454, 9, 108, "Text"], Cell[CellGroupData[{ Cell[525966, 9425, 77, 1, 56, "Input"], Cell[526046, 9428, 290, 6, 74, "Output"] }, Open ]], Cell[526351, 9437, 215, 6, 64, "Text"], Cell[CellGroupData[{ Cell[526591, 9447, 107, 2, 56, "Input"], Cell[526701, 9451, 340, 8, 74, "Output"] }, Open ]], Cell[527056, 9462, 65, 0, 42, "Text"], Cell[CellGroupData[{ Cell[527146, 9466, 87, 1, 56, "Input"], Cell[527236, 9469, 1467, 34, 185, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[528740, 9508, 92, 1, 56, "Input"], Cell[528835, 9511, 541, 14, 103, "Output"] }, Open ]], Cell[529391, 9528, 372, 10, 86, "Text"], Cell[CellGroupData[{ Cell[529788, 9542, 213, 5, 56, "Input"], Cell[530004, 9549, 1373, 33, 226, "Output"] }, Open ]], Cell[531392, 9585, 86, 2, 42, "Text"], Cell[CellGroupData[{ Cell[531503, 9591, 294, 7, 56, "Input"], Cell[531800, 9600, 1568, 41, 161, "Output"] }, Open ]], Cell[533383, 9644, 134, 5, 44, "Text"], Cell[CellGroupData[{ Cell[533542, 9653, 79, 1, 76, "Input"], Cell[533624, 9656, 35, 1, 54, "Output"] }, Open ]], Cell[533674, 9660, 147, 3, 64, "Text"], Cell[CellGroupData[{ Cell[533846, 9667, 77, 1, 76, "Input"], Cell[533926, 9670, 198, 4, 92, "Output"] }, Open ]], Cell[534139, 9677, 402, 10, 86, "Text"], Cell[CellGroupData[{ Cell[534566, 9691, 125, 2, 60, "Input"], Cell[534694, 9695, 1017, 28, 176, "Output"] }, Open ]], Cell[535726, 9726, 415, 9, 109, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[536190, 9741, 149, 8, 59, "Subsection", CellTags->"Weyl Calculus"], Cell[536342, 9751, 446, 12, 86, "Text"], Cell[536791, 9765, 516, 14, 44, "NumberedEquation", CellTags->"Weyl-Plus operator"], Cell[537310, 9781, 43, 0, 42, "Text"], Cell[537356, 9783, 457, 12, 41, "NumberedEquation", CellTags->"Weyl-Minus operator"], Cell[537816, 9797, 797, 22, 115, "Text"], Cell[538616, 9821, 285, 8, 40, "NumberedEquation", CellTags->"eq-4.2.3"], Cell[538904, 9831, 70, 0, 42, "Text"], Cell[538977, 9833, 316, 9, 37, "NumberedEquation", CellTags->"eq-4.2.4"], Cell[539296, 9844, 927, 24, 135, "Text"], Cell[540226, 9870, 152, 4, 54, "Input"], Cell[540381, 9876, 19, 0, 42, "Text"], Cell[540403, 9878, 112, 2, 54, "Input"], Cell[540518, 9882, 115, 3, 42, "Text"], Cell[540636, 9887, 722, 17, 141, "Text"], Cell[541361, 9906, 479, 13, 39, "NumberedEquation"], Cell[541843, 9921, 259, 9, 42, "Text"], Cell[542105, 9932, 292, 7, 39, "NumberedEquation"], Cell[542400, 9941, 192, 6, 49, "Text"], Cell[542595, 9949, 402, 11, 42, "NumberedEquation"], Cell[543000, 9962, 168, 3, 64, "Text"], Cell[CellGroupData[{ Cell[543193, 9969, 164, 7, 46, "Subsubsection", CellTags->"Properties of the Weyl Operator"], Cell[543360, 9978, 118, 3, 42, "Text"], Cell[543481, 9983, 152, 10, 63, "Rule", CellTags->"Linearity"], Cell[543636, 9995, 114, 3, 42, "Text"], Cell[543753, 10000, 380, 6, 36, "NumberedEquation"], Cell[544136, 10008, 726, 20, 113, "Text"], Cell[544865, 10030, 126, 2, 77, "Input"], Cell[544994, 10034, 19, 0, 42, "Text"], Cell[545016, 10036, 132, 2, 77, "Input"], Cell[545151, 10040, 120, 3, 42, "Text"], Cell[545274, 10045, 128, 2, 77, "Input"], Cell[545405, 10049, 19, 0, 42, "Text"], Cell[545427, 10051, 135, 2, 77, "Input"], Cell[545565, 10055, 331, 7, 87, "Text"], Cell[545899, 10064, 313, 7, 40, "NumberedEquation"], Cell[546215, 10073, 118, 3, 42, "Text"], Cell[546336, 10078, 166, 10, 63, "Rule", CellTags->"Composition Rule"], Cell[546505, 10090, 226, 5, 64, "Text"], Cell[546734, 10097, 341, 5, 37, "NumberedEquation"], Cell[547078, 10104, 412, 14, 87, "Text"], Cell[547493, 10120, 240, 5, 100, "Input"], Cell[547736, 10127, 70, 0, 42, "Text"], Cell[547809, 10129, 243, 5, 100, "Input"], Cell[548055, 10136, 68, 0, 42, "Text"], Cell[548126, 10138, 313, 7, 37, "NumberedEquation"], Cell[548442, 10147, 487, 14, 74, "Text"], Cell[548932, 10163, 175, 5, 37, "NumberedEquation"], Cell[549110, 10170, 123, 5, 43, "Text"], Cell[549236, 10177, 89, 1, 54, "Input"], Cell[549328, 10180, 19, 0, 42, "Text"], Cell[549350, 10182, 90, 1, 54, "Input"], Cell[549443, 10185, 107, 3, 42, "Text"], Cell[549553, 10190, 349, 9, 86, "Text"], Cell[549905, 10201, 296, 7, 40, "NumberedEquation"], Cell[550204, 10210, 227, 6, 65, "Text"], Cell[550434, 10218, 240, 5, 100, "Input"], Cell[550677, 10225, 145, 4, 44, "Text"], Cell[550825, 10231, 197, 4, 100, "Input"], Cell[551025, 10237, 142, 4, 42, "Text"], Cell[551170, 10243, 341, 7, 40, "NumberedEquation"], Cell[551514, 10252, 118, 5, 42, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[551669, 10262, 118, 7, 46, "Subsubsection", CellTags->"Examples"], Cell[551790, 10271, 357, 8, 87, "Text"], Cell[CellGroupData[{ Cell[552172, 10283, 158, 2, 77, "Input"], Cell[552333, 10287, 93, 1, 54, "Output"] }, Open ]], Cell[552441, 10291, 181, 4, 42, "Text"], Cell[CellGroupData[{ Cell[552647, 10299, 46, 1, 54, "Input"], Cell[552696, 10302, 81, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[552814, 10308, 104, 2, 57, "Input"], Cell[552921, 10312, 97, 2, 54, "Output"] }, Open ]], Cell[553033, 10317, 225, 5, 64, "Text"], Cell[CellGroupData[{ Cell[553283, 10326, 121, 2, 59, "Input"], Cell[553407, 10330, 84, 1, 54, "Output"] }, Open ]], Cell[553506, 10334, 264, 8, 65, "Text"], Cell[CellGroupData[{ Cell[553795, 10346, 104, 2, 57, "Input"], Cell[553902, 10350, 455, 10, 83, "Output"] }, Open ]], Cell[554372, 10363, 222, 6, 47, "Text"], Cell[CellGroupData[{ Cell[554619, 10373, 91, 1, 59, "Input"], Cell[554713, 10376, 368, 9, 83, "Output"] }, Open ]], Cell[555096, 10388, 183, 5, 64, "Text"], Cell[CellGroupData[{ Cell[555304, 10397, 103, 2, 57, "Input"], Cell[555410, 10401, 450, 10, 83, "Output"] }, Open ]], Cell[555875, 10414, 19, 0, 42, "Text"], Cell[CellGroupData[{ Cell[555919, 10418, 84, 1, 59, "Input"], Cell[556006, 10421, 391, 9, 83, "Output"] }, Open ]], Cell[556412, 10433, 476, 15, 86, "Text"], Cell[556891, 10450, 55, 1, 54, "Input"], Cell[CellGroupData[{ Cell[556971, 10455, 103, 2, 60, "Input"], Cell[557077, 10459, 325, 8, 91, "Output"] }, Open ]], Cell[557417, 10470, 19, 0, 42, "Text"], Cell[CellGroupData[{ Cell[557461, 10474, 103, 2, 58, "Input"], Cell[557567, 10478, 395, 9, 85, "Output"] }, Open ]], Cell[557977, 10490, 225, 6, 42, "Text"], Cell[558205, 10498, 55, 1, 54, "Input"], Cell[CellGroupData[{ Cell[558285, 10503, 82, 1, 59, "Input"], Cell[558370, 10506, 320, 8, 74, "Output"] }, Open ]], Cell[558705, 10517, 149, 4, 42, "Text"], Cell[CellGroupData[{ Cell[558879, 10525, 87, 1, 59, "Input"], Cell[558969, 10528, 320, 8, 74, "Output"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[559362, 10544, 140, 5, 65, "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}], Cell[559505, 10551, 350, 6, 108, "Text"], Cell[CellGroupData[{ Cell[559880, 10561, 161, 8, 59, "Subsection", CellTags->"Anomalous Relaxation"], Cell[560044, 10571, 198, 4, 64, "Text"], Cell[560245, 10577, 397, 13, 30, "NumberedEquation", CellTags->"eq-3"], Cell[560645, 10592, 247, 8, 64, "Text"], Cell[560895, 10602, 418, 10, 51, "NumberedEquation", CellTags->"eq-4"], Cell[561316, 10614, 178, 6, 42, "Text"], Cell[561497, 10622, 348, 10, 42, "NumberedEquation", CellTags->"eq-5"], Cell[561848, 10634, 947, 20, 196, "Text"], Cell[562798, 10656, 184, 4, 31, "NumberedEquation", CellTags->"eq-6"], Cell[562985, 10662, 138, 5, 42, "Text"], Cell[563126, 10669, 302, 9, 38, "NumberedEquation", CellTags->"eq-7"], Cell[563431, 10680, 698, 18, 130, "Text"], Cell[564132, 10700, 598, 14, 130, "Text"], Cell[564733, 10716, 321, 6, 40, "NumberedEquation", CellTags->"eq-8"], Cell[565057, 10724, 1090, 31, 155, "Text"], Cell[566150, 10757, 258, 4, 37, "NumberedEquation", CellTags->"eq-9"], Cell[566411, 10763, 1077, 34, 152, "Text"], Cell[567491, 10799, 182, 6, 42, "Text"], Cell[567676, 10807, 129, 6, 42, "Text"], Cell[567808, 10815, 214, 6, 37, "NumberedEquation", CellTags->"eq-10"], Cell[568025, 10823, 1375, 41, 178, "Text"], Cell[569403, 10866, 51, 1, 54, "Input"], Cell[CellGroupData[{ Cell[569479, 10871, 162, 3, 57, "Input"], Cell[569644, 10876, 140, 2, 57, "Output"] }, Open ]], Cell[569799, 10881, 113, 5, 42, "Text"], Cell[CellGroupData[{ Cell[569937, 10890, 77, 1, 54, "Input"], Cell[570017, 10893, 176, 3, 70, "Output"] }, Open ]], Cell[570208, 10899, 175, 6, 42, "Text"], Cell[CellGroupData[{ Cell[570408, 10909, 102, 2, 54, "Input"], Cell[570513, 10913, 147, 3, 73, "Output"] }, Open ]], Cell[570675, 10919, 892, 20, 174, "Text"], Cell[CellGroupData[{ Cell[571592, 10943, 108, 2, 54, "Input"], Cell[571703, 10947, 688, 21, 67, "Print"], Cell[572394, 10970, 361, 9, 85, "Output"] }, Open ]], Cell[572770, 10982, 161, 5, 42, "Text"], Cell[CellGroupData[{ Cell[572956, 10991, 88, 1, 54, "Input"], Cell[573047, 10994, 356, 9, 86, "Output"] }, Open ]], Cell[573418, 11006, 168, 6, 42, "Text"], Cell[CellGroupData[{ Cell[573611, 11016, 134, 2, 55, "Input"], Cell[573748, 11020, 356, 8, 85, "Output"] }, Open ]], Cell[574119, 11031, 173, 3, 64, "Text"], Cell[CellGroupData[{ Cell[574317, 11038, 87, 1, 59, "Input"], Cell[574407, 11041, 315, 9, 69, "Output"] }, Open ]], Cell[574737, 11053, 58, 0, 42, "Text"], Cell[574798, 11055, 194, 6, 36, "NumberedEquation"], Cell[574995, 11063, 1195, 26, 207, "Text"], Cell[CellGroupData[{ Cell[576215, 11093, 367, 9, 73, "Input"], Cell[576585, 11104, 216, 6, 69, "Output"] }, Open ]], Cell[576816, 11113, 502, 13, 86, "Text"], Cell[CellGroupData[{ Cell[577343, 11130, 497, 12, 100, "Input"], Cell[577843, 11144, 516, 13, 90, "Output"] }, Open ]], Cell[578374, 11160, 56, 0, 42, "Text"], Cell[CellGroupData[{ Cell[578455, 11164, 480, 11, 100, "Input"], Cell[578938, 11177, 294, 8, 88, "Output"] }, Open ]], Cell[579247, 11188, 166, 5, 42, "Text"], Cell[579416, 11195, 39867, 1323, 248, 24607, 1130, "GraphicsData", \ "PostScript", "NumberedFigure"], Cell[619286, 12520, 204, 8, 42, "SmallText"], Cell[619493, 12530, 261, 5, 86, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[619791, 12540, 123, 5, 59, "Subsection", CellTags->"Anomalous Diffusion"], Cell[619917, 12547, 1631, 40, 240, "Text"], Cell[621551, 12589, 560, 14, 108, "Text"], Cell[622114, 12605, 193, 4, 30, "NumberedEquation", CellTags->"eq-11"], Cell[622310, 12611, 419, 11, 86, "Text"], Cell[622732, 12624, 299, 8, 32, "NumberedEquation", CellTags->"eq-12"], Cell[623034, 12634, 259, 10, 42, "Text"], Cell[623296, 12646, 461, 14, 64, "Text"], Cell[623760, 12662, 393, 10, 42, "NumberedEquation", CellTags->"eq-14"], Cell[624156, 12674, 212, 5, 45, "Text"], Cell[624371, 12681, 327, 9, 34, "NumberedEquation", CellTags->"eq-15"], Cell[624701, 12692, 258, 9, 45, "Text"], Cell[624962, 12703, 300, 8, 35, "NumberedEquation", CellTags->"eq-16"], Cell[625265, 12713, 331, 10, 64, "Text"], Cell[625599, 12725, 358, 9, 43, "NumberedEquation", CellTags->"eq-17"], Cell[625960, 12736, 485, 15, 86, "Text"], Cell[626448, 12753, 387, 11, 41, "NumberedEquation", CellTags->"eq-18"], Cell[626838, 12766, 238, 9, 43, "Text"], Cell[627079, 12777, 51, 1, 54, "Input"], Cell[CellGroupData[{ Cell[627155, 12782, 208, 3, 74, "Input"], Cell[627366, 12787, 490, 12, 74, "Output"] }, Open ]], Cell[627871, 12802, 167, 6, 42, "Text"], Cell[CellGroupData[{ Cell[628063, 12812, 90, 1, 54, "Input"], Cell[628156, 12815, 430, 10, 56, "Output"] }, Open ]], Cell[628601, 12828, 112, 3, 42, "Text"], Cell[CellGroupData[{ Cell[628738, 12835, 352, 5, 124, "Input"], Cell[629093, 12842, 132, 2, 78, "Output"] }, Open ]], Cell[629240, 12847, 92, 2, 42, "Text"], Cell[CellGroupData[{ Cell[629357, 12853, 111, 2, 77, "Input"], Cell[629471, 12857, 147, 3, 79, "Output"] }, Open ]], Cell[629633, 12863, 211, 5, 64, "Text"], Cell[CellGroupData[{ Cell[629869, 12872, 171, 3, 100, "Input"], Cell[630043, 12877, 193, 3, 101, "Output"] }, Open ]], Cell[630251, 12883, 362, 10, 86, "Text"], Cell[630616, 12895, 63, 1, 54, "Input"], Cell[630682, 12898, 62, 0, 42, "Text"], Cell[CellGroupData[{ Cell[630769, 12902, 167, 3, 100, "Input"], Cell[630939, 12907, 850, 26, 80, "Print"], Cell[631792, 12935, 662, 17, 96, "Output"] }, Open ]], Cell[632469, 12955, 97, 2, 42, "Text"], Cell[CellGroupData[{ Cell[632591, 12961, 184, 4, 100, "Input"], Cell[632778, 12967, 679, 16, 96, "Output"] }, Open ]], Cell[633472, 12986, 87, 2, 42, "Text"], Cell[CellGroupData[{ Cell[633584, 12992, 158, 2, 57, "Input"], Cell[633745, 12996, 534, 13, 109, "Output"] }, Open ]], Cell[634294, 13012, 57, 0, 42, "Text"], Cell[634354, 13014, 527, 14, 68, "NumberedEquation", CellTags->"eq-22a"], Cell[634884, 13030, 453, 12, 67, "Text"], Cell[635340, 13044, 679, 14, 137, "NumberedEquation"], Cell[636022, 13060, 86, 2, 42, "Text"], Cell[636111, 13064, 135519, 3331, 273, 101230, 2903, "GraphicsData", \ "PostScript", "NumberedFigure"], Cell[771633, 16397, 222, 6, 62, "SmallText"], Cell[771858, 16405, 219, 5, 64, "Text"], Cell[CellGroupData[{ Cell[772102, 16414, 658, 16, 165, "Input"], Cell[772763, 16432, 413, 6, 128, "Output"] }, Open ]], Cell[773191, 16441, 229, 8, 65, "Text"], Cell[CellGroupData[{ Cell[773445, 16453, 71, 1, 54, "Input"], Cell[773519, 16456, 111, 2, 95, "Output"] }, Open ]], Cell[773645, 16461, 88, 2, 42, "Text"], Cell[773736, 16465, 93, 1, 54, "Input"], Cell[CellGroupData[{ Cell[773854, 16470, 262, 4, 99, "Input"], Cell[774119, 16476, 161, 3, 75, "Message"], Cell[774283, 16481, 161, 3, 75, "Message"], Cell[774447, 16486, 449, 10, 111, "Output"] }, Open ]], Cell[774911, 16499, 116, 4, 42, "Text"], Cell[775030, 16505, 186, 7, 30, "NumberedEquation", CellTags->"eq-24"], Cell[775219, 16514, 135, 4, 42, "Text"], Cell[CellGroupData[{ Cell[775379, 16522, 70, 1, 54, "Input"], Cell[775452, 16525, 44, 1, 54, "Output"] }, Open ]], Cell[775511, 16529, 832, 25, 108, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[776392, 16560, 166, 6, 65, "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}, CellTags->"Conclusions"], Cell[776561, 16568, 1154, 22, 243, "Text"], Cell[777718, 16592, 168, 5, 43, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[777923, 16602, 138, 5, 65, "Section", CounterAssignments->{{"Figure", 0}, {"NumberedEquation", 0}}], Cell[778064, 16609, 203, 4, 41, "SmallText", CellTags->"Lacroix-1819"], Cell[778270, 16615, 148, 4, 41, "SmallText", CellTags->"Oldham-1974"], Cell[778421, 16621, 213, 5, 62, "SmallText", CellTags->"Miller-1993"], Cell[778637, 16628, 129, 3, 41, "SmallText", CellTags->"Riemann-1892"], Cell[778769, 16633, 276, 7, 41, "SmallText", CellTags->"Liouville-1832a"], Cell[779048, 16642, 274, 8, 62, "SmallText", CellTags->"Weyl-1917"], Cell[779325, 16652, 148, 4, 41, "SmallText", CellTags->"Davis-1936"], Cell[779476, 16658, 301, 8, 62, "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1991"], Cell[779780, 16668, 218, 7, 41, "SmallText", CellTags->"Fox-1961"], Cell[780001, 16677, 278, 7, 62, "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1993a"], Cell[780282, 16686, 224, 7, 41, "SmallText", CellTags->"Schneider-1989"], Cell[780509, 16695, 197, 4, 62, "SmallText", CellTags->"Zwanzig-1965"], Cell[780709, 16701, 283, 7, 62, "SmallText", CellTags->"Gl\[ODoubleDot]ckle-1994"], Cell[780995, 16710, 253, 7, 62, "SmallText", CellTags->"Braaksma-1964"], Cell[781251, 16719, 177, 4, 41, "SmallText", CellTags->"West-1994"], Cell[781431, 16725, 195, 6, 41, "SmallText", CellTags->"Wyss-1986"], Cell[781629, 16733, 249, 7, 62, "SmallText", CellTags->"Schaugnessy-1985"], Cell[781881, 16742, 210, 7, 41, "SmallText", CellTags->"Compte-1996"], Cell[782094, 16751, 263, 7, 62, "SmallText", CellTags->"West-1997"], Cell[782360, 16760, 147, 4, 41, "SmallText", CellTags->"Podlubny-1999"] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)