÷ƒ’À;è TeX output 1997.03.30:1238‹ÿÿÿÿ s\È ý®£8 8G þo’‡}óDÓítG®G®cmr17¹The–7tó߆µTG® cmtt12ºamsopn“¹pacŒqk‘ÿäageŽŸoŒ’¥ðóX«Q cmr12»Mic•¬rhael‘ê¨Do“wnesŽŽŽŽŽŸoŒ’¥;«28–ê¨OctobSŽer“1996Ž¤ ’°"îV‘ÿVersion‘ê¨1.02ŽŸ&¾-‘#óò"V cmbx10Ä1Ž‘4?úIn®9troQÇductionŽŸŸ'MŽ‘ ‹S²-T‘þU>Ÿ'EŽ‘ãxX“construction.‘C|W‘ÿ*ªeŽ© ‘#w•¸ãan“t–UUto“ nd“out“what“the“next“tokš¸ãen“is“going“to“bGe,“so“w˜e“useŽŸ¾,‘5æXÆ\futurelet\@let@token\next@Ž¡ŸN¡‘#²The–h{Å\@let@token“²is“assigned“the“v‘ÿqÇalue“of“the“next“tokš¸ãen“and“then“w˜e“m˜ustŽ¦‘#de ne–uÅ\next@“²to“loGok“at“Å\@let@token“²and“decide“what“to“do.‘ÑW‘ÿ*ªe“could“nameŽ¦‘#Å\next@–Ò“²to“bGe“Å\nolimits@@“²or“something,‘ìºbut“bš¸ãy“alw˜a˜ys“using“Å\next@“²in“similarŽ¦‘#constructions–bÿwš¸ãe“cut“do˜wn“on“the“n˜um˜bGer“of“con˜trol“sequence“names“that“w˜e“use.Ž¦‘#But–î8this“means“that“Å\nolimits@“²m¸ãust“incorpGorate“the“appropriate“de nition“ofŽ¦‘#Å\next@².‘mƒNotice–H‰that“Å\next@“²turns“around“and“rede nes“itself“again;‘LÍonce“moreŽ¦‘#this–UUis“to“sa•¸ãv“e–UUa“con¸ãtrol“sequence“name.ŽŸ o‹‘2What–;Å\nolimits@“²doGes“is“kš¸ãeep“a“Å\limits“²t˜ypGed“b˜y“the“user“from“ha˜vingŽ¦‘#anš¸ãy–C‹e ect.‘.letter;‘EæT‘þU>Ÿ'EŽ‘ãxX“will“seize“it“and“cen¸ãter“it“on“the“math“axis“if“there“is“nothingŽ¡‘Yelse–UUinside“the“Å\mathop“²atom.Ž¦‘cª®Æ\DeclareRobustCommand{\qopname}[3]{%Ž¤ ‘mÚ\mathop{#1\kern\z@\operator@font#3}%Ž¡‘mÚ\csname‘¹–n#2limits@\endcsname}ŽŸßÆ‘ðƲ\DeclareMathOperatorŽŽŽ‘Y²The–{¿command“Å\DeclareMathOperator“²de nes“the“ rst“argumen¸ãt“to“bGe“an“op-Ž¤ ‘Yerator–Rpname“whose“text“is“the“second“argumen¸ãt.‘pÐThe“star“form“means“that“theŽ¡‘YopGerator–UUname“should“takš¸ãe“limits“(lik˜e“Å\max“²or“Å\lim²).Ž¦‘cª®Æ\newcommand{\DeclareMathOperator}{%ŽŸ ‘mÚ\@ifstar{\@declmathop\@empty}{\@declmathop‘¹–o}}ŽŸ³‘h²In–8ãthe“basic“set“of“opšGerator“names“(b˜eloš¸ãw)“w˜e“did“not“use“Å\DeclareRobustCommandŽ¡‘Y²bGecause–³of“the“hash“table“cost.‘ŠÛBut“wš¸ãe“use“it“here“to“minimize“the“c˜hances“ofŽ¡‘Ytrouble,–UUsince“w¸ãe“are“proGducing“a“user-de ned“command.Ž¦‘cª®Æ\long\def\@declmathop#1#2#3{%Ž¤ ‘mÚ\@ifdefinable{#2}{%Ž¡‘v‘\DeclareRobustCommand{#2}{\qopname\newmcodes@#1{#3}}}}Ž¡‘cª®%Ž¡‘cª®\@onlypreamble\DeclareMathOperatorŽ¡‘cª®\@onlypreamble\@declmathopŽŸ7‘cª®\def\arccos{\qopname\relax‘¹–o{arccos}}Ž¡‘cª®\def\arcsin{\qopname\relax‘¹–o{arcsin}}Ž¡‘cª®\def\arctan{\qopname\relax‘¹–o{arctan}}Ž¡‘cª®\def\arg{\qopname\relax‘¹–o{arg}}Ž¡‘cª®\def\cos{\qopname\relax‘¹–o{cos}}Ž¡‘cª®\def\cosh{\qopname\relax‘¹–o{cosh}}Ž¡‘cª®\def\cot{\qopname\relax‘¹–o{cot}}ŽŽŽŒ‹ ] s\È ý®£8‘#È1.‘ÇINTR¸ãODUCTION’òDz3ŽŽ 8G ýä‘-ª®Æ\def\coth{\qopname\relax‘¹–o{coth}}Ž¤ ‘-ª®\def\csc{\qopname\relax‘¹–o{csc}}Ž¡‘-ª®\def\deg{\qopname\relax‘¹–o{deg}}Ž¡‘-ª®\def\det{\qopname\relax\@empty{det}}Ž¡‘-ª®\def\dim{\qopname\relax‘¹–o{dim}}Ž¡‘-ª®\def\exp{\qopname\relax‘¹–o{exp}}Ž¡‘-ª®\def\gcd{\qopname\relax\@empty{gcd}}Ž¡‘-ª®\def\hom{\qopname\relax‘¹–o{hom}}Ž¡‘-ª®\def\inf{\qopname\relax\@empty{inf}}Ž¡‘-ª®\def\injlim{\qopname\relax\@empty{inj\,lim}}Ž¡‘-ª®\def\ker{\qopname\relax‘¹–o{ker}}Ž¡‘-ª®\def\lg{\qopname\relax‘¹–o{lg}}Ž¡‘-ª®\def\lim{\qopname\relax\@empty{lim}}Ž¡‘-ª®\def\liminf{\qopname\relax\@empty{lim\,inf}}Ž¡‘-ª®\def\limsup{\qopname\relax\@empty{lim\,sup}}Ž¡‘-ª®\def\ln{\qopname\relax‘¹–o{ln}}Ž¡‘-ª®\def\log{\qopname\relax‘¹–o{log}}Ž¡‘-ª®\def\max{\qopname\relax\@empty{max}}Ž¡‘-ª®\def\min{\qopname\relax\@empty{min}}Ž¡‘-ª®\def\Pr{\qopname\relax\@empty{Pr}}Ž¡‘-ª®\def\projlim{\qopname\relax\@empty{proj\,lim}}Ž¡‘-ª®\def\sec{\qopname\relax‘¹–o{sec}}Ž¡‘-ª®\def\sin{\qopname\relax‘¹–o{sin}}Ž¡‘-ª®\def\sinh{\qopname\relax‘¹–o{sinh}}Ž¡‘-ª®\def\sup{\qopname\relax\@empty{sup}}Ž¡‘-ª®\def\tan{\qopname\relax‘¹–o{tan}}Ž¡‘-ª®\def\tanh{\qopname\relax‘¹–o{tanh}}ŽŸ¤‘× 6\operator@fontŽŽŽ‘#²This–:command“is“proš¸ãvided“to“allo˜w“the“doGcumen˜t“st˜yles“to“decide“in“whic˜h“w˜a˜yŽ¤ ‘#math–.6opGerators“likš¸ãe“`max'“or“`log'“are“t˜ypGeset.‘üjThe“default“is“to“set“them“inŽ¡‘#¸hóý': cmti10ÉmathŽ‘?ñ¿gr‘ÿ}'oup‘¡˜¸iŽ‘_±*²zero–UUof“the“currenš¸ãt“math“v˜ersion.Ž©~‘-ª®Æ\def\operator@font{\mathgroup\symoperators}ŽŸæ‘2²F‘ÿ*ªor›»vbac•¸ãkw“ards˜compatibilit“y˜w“e˜k“eep˜this˜old˜command˜name˜for˜the˜timeŽ¡‘#bGeing:Ž¦‘-ª®Æ\def\operatornamewithlimits{\operatorname*}ŽŸ~‘2²These– Ûmacros“use“Å\mathpalette²s“so“that“they“will“c¸ãhange“size“in“script“andŽ¡‘#scriptscript–Rstš¸ãyles,‘!Sthough“it's“hard“to“imagine“they“will“ev˜er“bGe“used“there“(theŽ¡‘#arro¸ãws,–ÿ"particularly‘ÿ*ª,“loGok–Ý,bad“in“subscript“sizes).‘ MNotice“that“the“use“of“Å\ex@Ž¡‘#²means–á,that“the“vš¸ãertical“spacing“ma˜y“not“bGe“optimal“in“script“and“scriptscriptŽ¡‘#sizes.‘}Unfortunately–XvT‘þU>Ÿ'EŽ‘ãxX“proš¸ãvides“no“easy“w˜a˜y“to“do“math“moGde“v˜ertical“spacingŽ¡‘#that–UUv‘ÿqÇaries“with“currenš¸ãt“math“st˜yle“lik˜e“m˜u“units.Ž¦‘-ª®Æ\def\varlim@#1#2{\mathop{\vtop{\ialign{##\crcrŽ¤ ‘2dD\hfil$#1\m@th\operator@font‘¹–lim$\hfil\crcrŽ¡‘2dD\noalign{\nointerlineskip\kern\ex@}#2#1\crcrŽ¡‘2dD\noalign{\nointerlineskip\kern-\ex@}\crcr}}}}Ž¡‘-ª®\def\varinjlim{\mathpalette\varlim@\rightarrowfill@}Ž¡‘-ª®\def\varprojlim{\mathpalette\varlim@\leftarrowfill@}ŽŽŽŒ‹o s\È ý®£8‘Y²4’æ<|ÈTHE–UUÅAMSOPN“ÈP‘ÿ*ªA•¸ãCKA“GEŽŽ 8G ýä‘cª®Æ\def\varliminf{\mathpalette\varliminf@{}}Ž¤ ‘cª®\def\varliminf@#1{\mathop{\@@underline{\vrule\@depth.2\ex@\@width\z@Ž¡‘q×p\hbox{$#1\m@th\operator@font‘¹–lim$}}}}Ž¡‘cª®\def\varlimsup{\mathpalette\varlimsup@{}}Ž¡‘cª®\def\varlimsup@#1{\mathop{\@@overlineŽ¡‘mÚ{\hbox{$#1\m@th\operator@font‘¹–lim$}}}}ŽŸ‘cª®\DeclareOption{namelimits}{\let\nmlimits@\displaylimits}Ž¡‘cª®\DeclareOption{nonamelimits}{\let\nmlimits@\nolimits}Ž¡‘cª®\ProcessOptions\relaxŽŸ‘h²The–£usual“Å\endinput“²to“ensure“that“random“garbage“at“the“end“of“the“ leŽŸ ‘YdoGesn't–UUget“copied“b¸ãy“Ådocstrip².ŽŸ‘cª®Æ\endinputŽŽŽŒøƒ’À;ès\Ȳóý': cmti10óp®0J cmsl10óߤN cmtt9óßê