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Log after I corrected the error, error on chap1.tex:1671

Jun 10th, 2017
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  1. This is LuaTeX, Version beta-0.80.0 (TeX Live 2015/Debian) (rev 5238) (format=lualatex 2016.7.20) 10 JUN 2017 12:46
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  895. .................................................
  896. .................................................
  897. . lualatex-math info: "patch-macro"
  898. .
  899. . I'm going to patch macro \@genfrac.
  900. .................................................
  901. .................................................
  902. . lualatex-math info: "patch-macro"
  903. .
  904. . I'm going to patch macro \newmcodes@.
  905. .................................................
  906. .................................................
  907. . lualatex-math info: "patch-macro"
  908. .
  909. . I'm going to patch macro \MT_cramped_internal:Nn.
  910. .................................................
  911. )
  912. .................................................
  913. . LaTeX info: "xparse/define-command"
  914. .
  915. . Defining command \setmathfontface with sig. 'mO{}mO{}' on line 167.
  916. .................................................
  917. .................................................
  918. . LaTeX info: "xparse/define-command"
  919. .
  920. . Defining command \setoperatorfont with sig. 'm' on line 171.
  921. .................................................
  922. .................................................
  923. . LaTeX info: "xparse/define-command"
  924. .
  925. . Defining command \setmathfont with sig. 'O{}mO{}' on line 280.
  926. .................................................
  927. .................................................
  928. . LaTeX info: "xparse/define-command"
  929. .
  930. . Defining command \addnolimits with sig. 'm' on line 523.
  931. .................................................
  932. .................................................
  933. . LaTeX info: "xparse/define-command"
  934. .
  935. . Defining command \removenolimits with sig. 'm' on line 527.
  936. .................................................
  937.  
  938. (/usr/share/texlive/texmf-dist/tex/latex/unicode-math/unicode-math-table.tex)
  939. .................................................
  940. . unicode-math info: "patch-macro"
  941. .
  942. . I'm going to patch macro \plainroot@.
  943. .................................................
  944. .................................................
  945. . unicode-math info: "patch-macro"
  946. .
  947. . I'm going to patch macro \r@@t.
  948. .................................................
  949.  
  950. *************************************************
  951. * unicode-math warning: "mathtools-colon"
  952. *
  953. * I'm going to overwrite the following commands from the `mathtools' package:
  954. *
  955. * \dblcolon, \coloneqq, \Coloneqq, \eqqcolon.
  956. *
  957. * Note that since I won't overwrite the other colon-like commands, using them
  958. * will lead to inconsistencies.
  959. *************************************************
  960. .................................................
  961. . LaTeX info: "xparse/define-command"
  962. .
  963. . Defining command \dblcolon with sig. '' on line 1965.
  964. .................................................
  965. .................................................
  966. . LaTeX info: "xparse/define-command"
  967. .
  968. . Defining command \coloneqq with sig. '' on line 1965.
  969. .................................................
  970. .................................................
  971. . LaTeX info: "xparse/define-command"
  972. .
  973. . Defining command \Coloneqq with sig. '' on line 1965.
  974. .................................................
  975. .................................................
  976. . LaTeX info: "xparse/define-command"
  977. .
  978. . Defining command \eqqcolon with sig. '' on line 1965.
  979. .................................................
  980. )) (./titlesec.sty
  981. Package: titlesec 2016/03/21 v2.10.2 Sectioning titles
  982. \ttl@box=\box45
  983. \beforetitleunit=\skip97
  984. \aftertitleunit=\skip98
  985. \ttl@plus=\dimen180
  986. \ttl@minus=\dimen181
  987. \ttl@toksa=\toks35
  988. \titlewidth=\dimen182
  989. \titlewidthlast=\dimen183
  990. \titlewidthfirst=\dimen184
  991. )
  992. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  993. back to file:(compiling luc: /var/lib/texmf/luatex-cache/generic/fonts/otf/xits
  994. -math.luc)(load luc: /home/jonathan/.texmf-var/luatex-cache/generic/fonts/otf/xi
  995. ts-math.luc)
  996. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  997. back to file:
  998. \g__fontspec_family_xits-math_int=\count188
  999. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1000. back to file:
  1001. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1002. back to file:
  1003. luaotfload | aux : font no 21 (XITSMath) does not define feature smcp for script
  1004. math with language dflt
  1005. luaotfload | aux : no font with id 21
  1006. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1007. back to file:
  1008. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1009. back to file:
  1010. .................................................
  1011. . fontspec info: "defining-font"
  1012. .
  1013. . Font family 'xits-math(0)' created for font 'xits-math' with options
  1014. . [Ligatures=TeX,Renderer=Basic,BoldItalicFont={},ItalicFont={},Script=Math,Size
  1015. Features={{Size=10-},{Size=7-10,Font=xits-math,Style=MathScript},{Size=-7,Font=x
  1016. its-math,Style=MathScriptScript}},Path={~/texmf/},Extension={.otf}].
  1017. .
  1018. . This font family consists of the following NFSS series/shapes:
  1019. . - 'normal' (m/n) with NFSS spec.:
  1020. . <10->"[~/texmf/xits-math.otf]:mode=base;script=math;language=DFLT;+tlig;"<7-10
  1021. >"[~/texmf/xits-math.otf]:mode=base;script=math;language=DFLT;+tlig;+ssty=0;"<-7
  1022. >"[~/texmf/xits-math.otf]:mode=base;script=math;language=DFLT;+tlig;+ssty=1;"
  1023. . - 'small caps' (m/sc) with NFSS spec.:
  1024. .................................................
  1025. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1026. back to file:
  1027. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1028. back to file:
  1029. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1030. back to file:
  1031. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1032. back to file:
  1033. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1034. back to file:
  1035. LaTeX Font Info: Encoding `OT1' has changed to `EU2' for symbol font
  1036. (Font) `operators' in the math version `normal' on input line 49.
  1037. LaTeX Font Info: Overwriting symbol font `operators' in version `normal'
  1038. (Font) OT1/cmr/m/n --> EU2/xits-math(0)/m/n on input line 49.
  1039. LaTeX Font Info: Encoding `OT1' has changed to `EU2' for symbol font
  1040. (Font) `operators' in the math version `bold' on input line 49.
  1041. LaTeX Font Info: Overwriting symbol font `operators' in version `bold'
  1042. (Font) OT1/cmr/bx/n --> EU2/xits-math(0)/bx/n on input line 49.
  1043.  
  1044. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1045. back to file:
  1046. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1047. back to file:
  1048. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1049. back to file:
  1050. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1051. back to file:
  1052. luaotfload | aux : font no 21 (XITSMath) does not define feature smcp for script
  1053. math with language dflt
  1054. luaotfload | aux : no font with id 21
  1055. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1056. back to file:
  1057. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1058. back to file:
  1059. .................................................
  1060. . fontspec info: "defining-font"
  1061. .
  1062. . Font family 'xits-math(1)' created for font 'xits-math' with options
  1063. . [Ligatures=TeX,Renderer=Basic,BoldItalicFont={},ItalicFont={},Script=Math,Size
  1064. Features={{Size=10-},{Size=7-10,Font=xits-math,Style=MathScript},{Size=-7,Font=x
  1065. its-math,Style=MathScriptScript}},Path={~/texmf/},Extension={.otf},Scale=1.00001
  1066. ,FontAdjustment={\fontdimen
  1067. . 8\font =380108.8sp\relax \fontdimen 9\font =314572.8sp\relax \fontdimen
  1068. . 10\font =314572.8sp\relax \fontdimen 11\font =458752sp\relax \fontdimen
  1069. . 12\font =314572.8sp\relax \fontdimen 13\font =262144sp\relax \fontdimen
  1070. . 14\font =262144sp\relax \fontdimen 15\font =180224sp\relax \fontdimen
  1071. . 16\font =163840sp\relax \fontdimen 17\font =0sp\relax \fontdimen 18\font
  1072. . =245760sp\relax \fontdimen 19\font =32768sp\relax \fontdimen 20\font
  1073. . =0pt\relax \fontdimen 21\font =0pt\relax \fontdimen 22\font =163840sp\relax
  1074. . }].
  1075. .
  1076. . This font family consists of the following NFSS series/shapes:
  1077. . - 'normal' (m/n) with NFSS spec.:
  1078. . <10->s*[1.00001]"[~/texmf/xits-math.otf]:mode=base;script=math;language=DFLT;+
  1079. tlig;"<7-10>s*[1.00001]"[~/texmf/xits-math.otf]:mode=base;script=math;language=D
  1080. FLT;+tlig;+ssty=0;"<-7>s*[1.00001]"[~/texmf/xits-math.otf]:mode=base;script=math
  1081. ;language=DFLT;+tlig;+ssty=1;"
  1082. . - 'small caps' (m/sc) with NFSS spec.:
  1083. . and font adjustment code:
  1084. . \fontdimen 8\font =380108.8sp\relax \fontdimen 9\font =314572.8sp\relax
  1085. . \fontdimen 10\font =314572.8sp\relax \fontdimen 11\font =458752sp\relax
  1086. . \fontdimen 12\font =314572.8sp\relax \fontdimen 13\font =262144sp\relax
  1087. . \fontdimen 14\font =262144sp\relax \fontdimen 15\font =180224sp\relax
  1088. . \fontdimen 16\font =163840sp\relax \fontdimen 17\font =0sp\relax \fontdimen
  1089. . 18\font =245760sp\relax \fontdimen 19\font =32768sp\relax \fontdimen 20\font
  1090. . =0pt\relax \fontdimen 21\font =0pt\relax \fontdimen 22\font =163840sp\relax
  1091. .................................................
  1092. LaTeX Font Info: Encoding `OMS' has changed to `EU2' for symbol font
  1093. (Font) `symbols' in the math version `normal' on input line 49.
  1094. LaTeX Font Info: Overwriting symbol font `symbols' in version `normal'
  1095. (Font) OMS/cmsy/m/n --> EU2/xits-math(1)/m/n on input line 49.
  1096. LaTeX Font Info: Encoding `OMS' has changed to `EU2' for symbol font
  1097. (Font) `symbols' in the math version `bold' on input line 49.
  1098. LaTeX Font Info: Overwriting symbol font `symbols' in version `bold'
  1099. (Font) OMS/cmsy/b/n --> EU2/xits-math(1)/bx/n on input line 49.
  1100.  
  1101. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1102. back to file:
  1103. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1104. back to file:
  1105. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1106. back to file:
  1107. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1108. back to file:
  1109. luaotfload | aux : font no 21 (XITSMath) does not define feature smcp for script
  1110. math with language dflt
  1111. luaotfload | aux : no font with id 21
  1112. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1113. back to file:
  1114. luaotfload | load : path lookup of "~/texmf/xits-math.otf" unsuccessful, falling
  1115. back to file:
  1116. .................................................
  1117. . fontspec info: "defining-font"
  1118. .
  1119. . Font family 'xits-math(2)' created for font 'xits-math' with options
  1120. . [Ligatures=TeX,Renderer=Basic,BoldItalicFont={},ItalicFont={},Script=Math,Size
  1121. Features={{Size=10-},{Size=7-10,Font=xits-math,Style=MathScript},{Size=-7,Font=x
  1122. its-math,Style=MathScriptScript}},Path={~/texmf/},Extension={.otf},Scale=0.99999
  1123. ,FontAdjustment={\fontdimen
  1124. . 8\font =43253.76sp\relax \fontdimen 9\font =98304sp\relax \fontdimen 10\font
  1125. . =98304sp\relax \fontdimen 11\font =196608sp\relax \fontdimen 12\font
  1126. . =393216sp\relax \fontdimen 13\font =0pt\relax }].
  1127. .
  1128. . This font family consists of the following NFSS series/shapes:
  1129. . - 'normal' (m/n) with NFSS spec.:
  1130. . <10->s*[0.99999]"[~/texmf/xits-math.otf]:mode=base;script=math;language=DFLT;+
  1131. tlig;"<7-10>s*[0.99999]"[~/texmf/xits-math.otf]:mode=base;script=math;language=D
  1132. FLT;+tlig;+ssty=0;"<-7>s*[0.99999]"[~/texmf/xits-math.otf]:mode=base;script=math
  1133. ;language=DFLT;+tlig;+ssty=1;"
  1134. . - 'small caps' (m/sc) with NFSS spec.:
  1135. . and font adjustment code:
  1136. . \fontdimen 8\font =43253.76sp\relax \fontdimen 9\font =98304sp\relax
  1137. . \fontdimen 10\font =98304sp\relax \fontdimen 11\font =196608sp\relax
  1138. . \fontdimen 12\font =393216sp\relax \fontdimen 13\font =0pt\relax
  1139. .................................................
  1140. LaTeX Font Info: Encoding `OMX' has changed to `EU2' for symbol font
  1141. (Font) `largesymbols' in the math version `normal' on input line 49
  1142. .
  1143. LaTeX Font Info: Overwriting symbol font `largesymbols' in version `normal'
  1144. (Font) OMX/cmex/m/n --> EU2/xits-math(2)/m/n on input line 49.
  1145. LaTeX Font Info: Encoding `OMX' has changed to `EU2' for symbol font
  1146. (Font) `largesymbols' in the math version `bold' on input line 49.
  1147. LaTeX Font Info: Overwriting symbol font `largesymbols' in version `bold'
  1148. (Font) OMX/cmex/m/n --> EU2/xits-math(2)/bx/n on input line 49.
  1149.  
  1150. luaotfload | cache : Lookup cache loaded from /home/jonathan/.texmf-var/luatex-c
  1151. ache/generic/names/luaotfload-lookup-cache.luc.
  1152. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1153. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1154. \g__fontspec_family_LatinModernRoman_int=\count189
  1155. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1156. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-bolditalic.o
  1157. tf"(compiling luc: /var/lib/texmf/luatex-cache/generic/fonts/otf/lmroman10-boldi
  1158. talic.luc)(load luc: /home/jonathan/.texmf-var/luatex-cache/generic/fonts/otf/lm
  1159. roman10-bolditalic.luc)
  1160. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1161. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-bold.otf"
  1162. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1163. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-italic.otf"
  1164. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-regular.otf"
  1165. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-regular.otf"
  1166. luaotfload | aux : font no 24 (LMRoman10-Regular) does not define feature smcp f
  1167. or script latn with language dflt
  1168. luaotfload | aux : no font with id 24
  1169. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-bold.otf"
  1170. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-bold.otf"
  1171. luaotfload | aux : font no 26 (LMRoman10-Bold) does not define feature smcp for
  1172. script latn with language dflt
  1173. luaotfload | aux : no font with id 26
  1174. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-italic.otf"
  1175. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-italic.otf"
  1176. luaotfload | aux : font no 27 (LMRoman10-Italic) does not define feature smcp fo
  1177. r script latn with language dflt
  1178. luaotfload | aux : no font with id 27
  1179. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-bolditalic.otf
  1180. "
  1181. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-bolditalic.otf
  1182. "
  1183. luaotfload | aux : font no 25 (LMRoman10-BoldItalic) does not define feature smc
  1184. p for script latn with language dflt
  1185. luaotfload | aux : no font with id 25
  1186. .................................................
  1187. . fontspec info: "defining-font"
  1188. .
  1189. . Font family 'LatinModernRoman(0)' created for font 'Latin Modern Roman' with
  1190. . options [Ligatures=TeX,Ligatures=TeX].
  1191. .
  1192. . This font family consists of the following NFSS series/shapes:
  1193. . - 'normal' (m/n) with NFSS spec.:
  1194. . <->"LatinModernRoman:mode=node;script=latn;language=DFLT;+tlig;+tlig;"
  1195. . - 'small caps' (m/sc) with NFSS spec.: - 'bold' (bx/n) with NFSS spec.:
  1196. . <->"LatinModernRoman/B:mode=node;script=latn;language=DFLT;+tlig;+tlig;"
  1197. . - 'bold small caps' (bx/sc) with NFSS spec.: - 'italic' (m/it) with NFSS
  1198. . spec.:
  1199. . <->"LatinModernRoman/I:mode=node;script=latn;language=DFLT;+tlig;+tlig;"
  1200. . - 'italic small caps' (m/itsc) with NFSS spec.: - 'bold italic' (bx/it)
  1201. . with NFSS spec.:
  1202. . <->"LatinModernRoman/BI:mode=node;script=latn;language=DFLT;+tlig;+tlig;"
  1203. . - 'bold italic small caps' (bx/itsc) with NFSS spec.:
  1204. .................................................
  1205. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1206. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1207. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1208. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-bolditalic.o
  1209. tf"
  1210. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1211. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-bold.otf"
  1212. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-regular.otf"
  1213. luaotfload | load : Lookup/name: "Latin Modern Roman" -> "lmroman10-italic.otf"
  1214. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-regular.otf"
  1215. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-regular.otf"
  1216. luaotfload | aux : font no 24 (LMRoman10-Regular) does not define feature smcp f
  1217. or script latn with language dflt
  1218. luaotfload | aux : no font with id 24
  1219. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-bold.otf"
  1220. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-bold.otf"
  1221. luaotfload | aux : font no 26 (LMRoman10-Bold) does not define feature smcp for
  1222. script latn with language dflt
  1223. luaotfload | aux : no font with id 26
  1224. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-italic.otf"
  1225. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-italic.otf"
  1226. luaotfload | aux : font no 27 (LMRoman10-Italic) does not define feature smcp fo
  1227. r script latn with language dflt
  1228. luaotfload | aux : no font with id 27
  1229. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-bolditalic.otf
  1230. "
  1231. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-bolditalic.otf
  1232. "
  1233. luaotfload | aux : font no 25 (LMRoman10-BoldItalic) does not define feature smc
  1234. p for script latn with language dflt
  1235. luaotfload | aux : no font with id 25
  1236. .................................................
  1237. . fontspec info: "defining-font"
  1238. .
  1239. . Font family 'LatinModernRoman(1)' created for font 'Latin Modern Roman' with
  1240. . options [Ligatures=TeX,Renderer=Basic].
  1241. .
  1242. . This font family consists of the following NFSS series/shapes:
  1243. . - 'normal' (m/n) with NFSS spec.:
  1244. . <->"LatinModernRoman:mode=base;script=latn;language=DFLT;+tlig;"
  1245. . - 'small caps' (m/sc) with NFSS spec.: - 'bold' (bx/n) with NFSS spec.:
  1246. . <->"LatinModernRoman/B:mode=base;script=latn;language=DFLT;+tlig;"
  1247. . - 'bold small caps' (bx/sc) with NFSS spec.: - 'italic' (m/it) with NFSS
  1248. . spec.: <->"LatinModernRoman/I:mode=base;script=latn;language=DFLT;+tlig;"
  1249. . - 'italic small caps' (m/itsc) with NFSS spec.: - 'bold italic' (bx/it)
  1250. . with NFSS spec.:
  1251. . <->"LatinModernRoman/BI:mode=base;script=latn;language=DFLT;+tlig;"
  1252. . - 'bold italic small caps' (bx/itsc) with NFSS spec.:
  1253. .................................................
  1254. LaTeX Font Info: Overwriting math alphabet `\mathrm' in version `normal'
  1255. (Font) EU2/xits-math(0)/m/n --> EU2/LatinModernRoman(1)/m/n on
  1256. input line 50.
  1257. LaTeX Font Info: Overwriting math alphabet `\mathit' in version `normal'
  1258. (Font) OT1/cmr/m/it --> EU2/LatinModernRoman(1)/m/it on input l
  1259. ine 50.
  1260. LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `normal'
  1261. (Font) OT1/cmr/bx/n --> EU2/LatinModernRoman(1)/bx/n on input l
  1262. ine 50.
  1263. luaotfload | load : Lookup/name: "LatinModernRoman" -> "lmroman10-regular.otf"
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  1584. [][]\EU2/LatinModernRoman(0)/bx/n/24.88 TABLE OF CONTENTS 06/10/2017
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  1599. Chapter 1.
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  2187. 489.
  2188.  
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  2191.  
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  2194. [][]\EU2/LatinModernRoman(0)/m/n/10 It can be seen from the $\EU2/xits-math(0)/
  2195. m/n/10 𝑚 = 1$ \EU2/LatinModernRoman(0)/m/n/10 case of [][]--[][] (which we j
  2196. ust proved) that for $\EU2/xits-math(0)/m/n/10 𝜃 ∈
  2197. []
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  2199. [59]
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  2222. [][]\EU2/LatinModernRoman(0)/m/n/10 Now we seek to prove [][] for $\EU2/xits-ma
  2223. th(0)/m/n/10 |𝑘[] [] 𝜃 − 𝑘[]| ≤ []$ \EU2/LatinModernRoman(0)/m/n/1
  2224. 0 in case (i). We apply Lemma []6[]
  2225. []
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  2264. .
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  2329. Chapter 2.
  2330. ) [73
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  2334. ]
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  2342. (./app.tex
  2343. Appendix A.
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  2415. 35.
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  2432. 1.
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  2436. 3.
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  2440. 3.
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  2458.  
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  2461. [][]\EU2/LatinModernRoman(0)/m/n/10 To prove [][], first let $\EU2/xits-math(0)
  2462. /m/n/10 𝑡 ≥ 0$ \EU2/LatinModernRoman(0)/m/n/10 without loss of gener-ality
  2463. . Then $\EU2/xits-math(0)/m/n/10 𝑡[] =
  2464. []
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  2799.  
  2800. LaTeX Warning: Reference `Kgammabound' on page 120 undefined on input line 1355.
  2801.  
  2802.  
  2803.  
  2804. LaTeX Warning: Reference `eq:thetaj' on page 120 undefined on input line 1355.
  2805.  
  2806.  
  2807. LaTeX Warning: Reference `eq:thetaj'' on page 120 undefined on input line 1355.
  2808.  
  2809.  
  2810. LaTeX Warning: Reference `Gammaappendix' on page 120 undefined on input line 135
  2811. 5.
  2812.  
  2813.  
  2814. LaTeX Warning: Reference `eq:thetaj' on page 120 undefined on input line 1363.
  2815.  
  2816.  
  2817. LaTeX Warning: Reference `eq:thetaj'' on page 120 undefined on input line 1363.
  2818.  
  2819.  
  2820. LaTeX Warning: Reference `rethetajupper' on page 120 undefined on input line 136
  2821. 9.
  2822.  
  2823.  
  2824. LaTeX Warning: Reference `rethetajlower' on page 120 undefined on input line 136
  2825. 9.
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  2827.  
  2828. LaTeX Warning: Reference `startofsignlist' on page 120 undefined on input line 1
  2829. 369.
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  2831.  
  2832. LaTeX Warning: Reference `endofsignlist' on page 120 undefined on input line 136
  2833. 9.
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  2835. [120]
  2836.  
  2837. LaTeX Warning: Reference `Varcbound' on page 121 undefined on input line 1395.
  2838.  
  2839.  
  2840. LaTeX Warning: Reference `Karcbound' on page 121 undefined on input line 1395.
  2841.  
  2842.  
  2843. LaTeX Warning: Reference `Kgammabound' on page 121 undefined on input line 1395.
  2844.  
  2845.  
  2846.  
  2847. LaTeX Warning: Reference `Karcbound' on page 121 undefined on input line 1395.
  2848.  
  2849.  
  2850. LaTeX Warning: Reference `eq:inttildeJ' on page 121 undefined on input line 1406
  2851. .
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  2853. [121] [122]
  2854.  
  2855. LaTeX Warning: Reference `rekappalowbound' on page 123 undefined on input line 1
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  2859. LaTeX Warning: Reference `eq:nu20' on page 123 undefined on input line 1444.
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  2862. LaTeX Warning: Reference `eq:nu22' on page 123 undefined on input line 1444.
  2863.  
  2864.  
  2865. LaTeX Warning: Reference `MKml' on page 123 undefined on input line 1444.
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  2868. LaTeX Warning: Reference `firstineq' on page 123 undefined on input line 1444.
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  2871. LaTeX Warning: Reference `lastineq' on page 123 undefined on input line 1444.
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  2873. [123]
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  2875. LaTeX Warning: Reference `MKml' on page 124 undefined on input line 1465.
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  2877.  
  2878. LaTeX Warning: Reference `drres' on page 124 undefined on input line 1465.
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  2881. LaTeX Warning: Reference `dtres' on page 124 undefined on input line 1465.
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  2883. [124]
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  2885. LaTeX Warning: Reference `Reskmexpr' on page 125 undefined on input line 1487.
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  2887. [125]
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  2889. LaTeX Warning: Reference `dtres' on page 126 undefined on input line 1507.
  2890.  
  2891.  
  2892. LaTeX Warning: Reference `K1'' on page 126 undefined on input line 1507.
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  2894.  
  2895. LaTeX Warning: Reference `K2'' on page 126 undefined on input line 1507.
  2896.  
  2897.  
  2898. LaTeX Warning: Reference `Resk1' on page 126 undefined on input line 1507.
  2899.  
  2900.  
  2901. LaTeX Warning: Reference `Resk2' on page 126 undefined on input line 1507.
  2902.  
  2903. [126]
  2904.  
  2905. LaTeX Warning: Reference `rayleighsubsection' on page 127 undefined on input lin
  2906. e 1524.
  2907.  
  2908.  
  2909. LaTeX Warning: Reference `kappanotroot' on page 127 undefined on input line 1534
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  2912.  
  2913. LaTeX Warning: Reference `kappaisroot' on page 127 undefined on input line 1534.
  2914.  
  2915.  
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  2917. LaTeX Warning: Reference `Pappendix' on page 127 undefined on input line 1534.
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  2920. LaTeX Warning: Reference `eq:thetaj' on page 127 undefined on input line 1534.
  2921.  
  2922.  
  2923. LaTeX Warning: Reference `rekappalowbound' on page 127 undefined on input line 1
  2924. 538.
  2925.  
  2926.  
  2927. LaTeX Warning: Reference `rekappaupbound' on page 127 undefined on input line 15
  2928. 38.
  2929.  
  2930.  
  2931. LaTeX Warning: Reference `Pappendix' on page 127 undefined on input line 1538.
  2932.  
  2933.  
  2934. LaTeX Warning: Reference `eq:thetaj' on page 127 undefined on input line 1540.
  2935.  
  2936.  
  2937. LaTeX Warning: Reference `eq:thetaj' on page 127 undefined on input line 1540.
  2938.  
  2939.  
  2940. LaTeX Warning: Reference `eq:nudef' on page 127 undefined on input line 1542.
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  2944. LaTeX Warning: Reference `eq:thetaj' on page 128 undefined on input line 1550.
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  2946.  
  2947. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
  2948. (hyperref) removing `subscript' on input line 1567.
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  2950.  
  2951. LaTeX Warning: Reference `Pappendix' on page 128 undefined on input line 1569.
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  2954. Overfull \hbox (7.1852pt too wide) in paragraph at lines 1581--1581
  2955. [][]
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  2959. LaTeX Warning: Reference `Pappendix' on page 129 undefined on input line 1585.
  2960.  
  2961.  
  2962. LaTeX Warning: Reference `kappanotroot' on page 129 undefined on input line 1585
  2963. .
  2964.  
  2965.  
  2966. LaTeX Warning: Reference `kappaisroot' on page 129 undefined on input line 1585.
  2967.  
  2968.  
  2969. [129] [130]
  2970.  
  2971. LaTeX Warning: Reference `beforekappabar' on page 131 undefined on input line 16
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  2974. [131]
  2975.  
  2976. ./app.tex:1671: LaTeX Error: Counter too large.
  2977.  
  2978. See the LaTeX manual or LaTeX Companion for explanation.
  2979. Type H <return> for immediate help.
  2980. ...
  2981.  
  2982. l.1671 ...}\bar{\kappa}|>0.84k_s>2\delta$ \footnote{
  2983. see \eqref{rekappalowbound...
  2984. ? X
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  2998. LuaTeX warning (dest): name{Hfootnote.55} has been referenced but does not exist
  2999. , replaced by a fixed one
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  3001. LuaTeX warning (dest): name{Hfootnote.54} has been referenced but does not exist
  3002. , replaced by a fixed one
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  3005. ced by a fixed one
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  3007. LuaTeX warning (dest): name{glo:hatthetaj} has been referenced but does not exis
  3008. t, replaced by a fixed one
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  3010. LuaTeX warning (dest): name{AMS.32} has been referenced but does not exist, repl
  3011. aced by a fixed one
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  3017. ced by a fixed one
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  3020. replaced by a fixed one
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  3022. LuaTeX warning (dest): name{glo:frake} has been referenced but does not exist, r
  3023. eplaced by a fixed one
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  3025. LuaTeX warning (dest): name{glo:gammathetaj} has been referenced but does not ex
  3026. ist, replaced by a fixed one
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  3028. LuaTeX warning (dest): name{glo:Gamma} has been referenced but does not exist, r
  3029. eplaced by a fixed one
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  3031. LuaTeX warning (dest): name{glo:varepsilon} has been referenced but does not exi
  3032. st, replaced by a fixed one
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  3035. replaced by a fixed one
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  3038. replaced by a fixed one
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  3040. LuaTeX warning (dest): name{glo:tildet1} has been referenced but does not exist,
  3041. replaced by a fixed one
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  3043. LuaTeX warning (dest): name{glo:tildeR1} has been referenced but does not exist,
  3044. replaced by a fixed one
  3045.  
  3046. LuaTeX warning (dest): name{glo:ttildez} has been referenced but does not exist,
  3047. replaced by a fixed one
  3048.  
  3049. LuaTeX warning (dest): name{glo:Rtildez} has been referenced but does not exist,
  3050. replaced by a fixed one
  3051.  
  3052. LuaTeX warning (dest): name{glo:hljj} has been referenced but does not exist, re
  3053. placed by a fixed one
  3054.  
  3055. LuaTeX warning (dest): name{glo:besselfn1} has been referenced but does not exis
  3056. t, replaced by a fixed one
  3057.  
  3058. LuaTeX warning (dest): name{glo:hatHm} has been referenced but does not exist, r
  3059. eplaced by a fixed one
  3060.  
  3061. LuaTeX warning (dest): name{glo:j'} has been referenced but does not exist, repl
  3062. aced by a fixed one
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  3064. LuaTeX warning (dest): name{glo:wJpm} has been referenced but does not exist, re
  3065. placed by a fixed one
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  3067. LuaTeX warning (dest): name{glo:J} has been referenced but does not exist, repla
  3068. ced by a fixed one
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  3070. LuaTeX warning (dest): name{glo:thetaj} has been referenced but does not exist,
  3071. replaced by a fixed one
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  3073. LuaTeX warning (dest): name{glo:IFT} has been referenced but does not exist, rep
  3074. laced by a fixed one
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  3076. LuaTeX warning (dest): name{glo:FT} has been referenced but does not exist, repl
  3077. aced by a fixed one
  3078.  
  3079. LuaTeX warning (dest): name{glo:boldk} has been referenced but does not exist, r
  3080. eplaced by a fixed one
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  3082. LuaTeX warning (dest): name{glo:deltafn} has been referenced but does not exist,
  3083. replaced by a fixed one
  3084.  
  3085. LuaTeX warning (dest): name{glo:omega} has been referenced but does not exist, r
  3086. eplaced by a fixed one
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  3088. LuaTeX warning (dest): name{glo:gi} has been referenced but does not exist, repl
  3089. aced by a fixed one
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  3091. LuaTeX warning (dest): name{glo:j} has been referenced but does not exist, repla
  3092. ced by a fixed one
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  3094. LuaTeX warning (dest): name{glo:kj} has been referenced but does not exist, repl
  3095. aced by a fixed one
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  3097. LuaTeX warning (dest): name{glo:symbolset} has been referenced but does not exis
  3098. t, replaced by a fixed one
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  3100. LuaTeX warning (dest): name{glo:ks} has been referenced but does not exist, repl
  3101. aced by a fixed one
  3102.  
  3103. LuaTeX warning (dest): name{glo:kp} has been referenced but does not exist, repl
  3104. aced by a fixed one
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  3106. LuaTeX warning (dest): name{glo:kronecker} has been referenced but does not exis
  3107. t, replaced by a fixed one
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  3109. LuaTeX warning (dest): name{glo:lambda} has been referenced but does not exist,
  3110. replaced by a fixed one
  3111.  
  3112. LuaTeX warning (dest): name{glo:mu} has been referenced but does not exist, repl
  3113. aced by a fixed one
  3114.  
  3115. LuaTeX warning (dest): name{glo:boldx} has been referenced but does not exist, r
  3116. eplaced by a fixed one
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  3119. eplaced by a fixed one
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  3121. LuaTeX warning (dest): name{glo:f0} has been referenced but does not exist, repl
  3122. aced by a fixed one
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  3124. LuaTeX warning (dest): name{glo:g0} has been referenced but does not exist, repl
  3125. aced by a fixed one
  3126.  
  3127. </usr/share/texmf/fonts/opentype/public/lm/lmroman12-regular.otf></usr/share/tex
  3128. mf/fonts/opentype/public/lm/lmroman10-bolditalic.otf></usr/share/texmf/fonts/ope
  3129. ntype/public/lm/lmroman6-regular.otf></usr/share/texmf/fonts/opentype/public/lm/
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  3131. f></usr/share/texmf/fonts/opentype/public/lm/lmroman10-italic.otf></usr/share/te
  3132. xmf/fonts/opentype/public/lm/lmroman8-regular.otf></usr/share/texmf/fonts/openty
  3133. pe/public/lm/lmroman10-regular.otf></usr/share/texmf/fonts/opentype/public/lm/lm
  3134. roman8-regular.otf></usr/share/texmf/fonts/opentype/public/lm/lmroman6-regular.o
  3135. tf></usr/share/texmf/fonts/opentype/public/lm/lmroman7-regular.otf></usr/share/t
  3136. exmf/fonts/opentype/public/lm/lmroman10-bold.otf></home/jonathan/texmf/xits-math
  3137. .otf></home/jonathan/texmf/xits-math.otf></home/jonathan/texmf/xits-math.otf></u
  3138. sr/share/texmf/fonts/opentype/public/lm/lmroman10-regular.otf></usr/share/texmf/
  3139. fonts/opentype/public/lm/lmroman12-bold.otf>
  3140. Output written on thes.pdf (131 pages, 2779663 bytes).
  3141.  
  3142. PDF statistics: 1583 PDF objects out of 1728 (max. 8388607)
  3143. 1336 compressed objects within 14 object streams
  3144. 432 named destinations out of 1000 (max. 131072)
  3145. 137 words of extra memory for PDF output out of 10000 (max. 10000000)
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