<!-- ###########################################################################
#
#   File name: latexent.ent
#   Project: Journals
#   Description: Latex control sequences as entities for inclusion in Journals DTDs
#
#
#   External documents:
#
#
#   Author: Peter Haworth/A J Cox
#   Date created: 15/03/00
#
#   sccs version: 1.00    last changed: 15/03/00
#
#   Copyright Institute of Physics Publishing 1999
#   Portions Copyright International Organization for Standardization 1986
############################################################################ -->

<!ENTITY percent  "&#37;">     <!-- percent sign -->
<!ENTITY ndash  "-">       <!-- en dash to hyphen -->
<!ENTITY mdash  " - ">     <!-- em dash to space hyphen space -->
<!ENTITY endash  "-">       <!-- en dash to hyphen -->
<!ENTITY emdash  " - ">     <!-- em dash to space hyphen space -->
<!ENTITY lquot "'">         <!-- left quote -->
<!ENTITY rquot "'">         <!-- right quote -->
<!ENTITY equal " = ">      <!-- equal sign -->
<!ENTITY minus "-">        <!-- minus sign -->
<!ENTITY underscore "_">        <!-- underscore -->
<!ENTITY plus "+">        <!-- minus sign -->
<!ENTITY lslash  "l">      <!-- l slash approximated to l  -->
<!ENTITY Lslash  "L">      <!-- L slash approximated to L (NB sometimes used in maths -->
                            <!-- where this approximation not appropriate!, graphic needed) -->
                            <!-- graphic not used normally as it screws up names -->
<!ENTITY pounds  "&#163;"> <!-- pound sign to CN 163 -->
<!ENTITY sim  "~">         <!-- tilde (\sim) to ~ (CN 126) -->
<!ENTITY registered "circled R">  <!-- registered trademark -->
<!ENTITY TM "<SUP>TM</SUP>">  <!-- trademark -->
<!ENTITY trademark "<SUP>TM</SUP>">  <!-- trademark -->


<!ENTITY dollar  "$">
<!ENTITY calA  "Script A">
<!ENTITY calB  "Script B">
<!ENTITY calC  "Script C">
<!ENTITY calD  "Script D">
<!ENTITY calE  "Script E">
<!ENTITY calF  "Script F">
<!ENTITY calG  "Script G">
<!ENTITY calH  "Script H">
<!ENTITY calI  "Script I">
<!ENTITY calJ  "Script J">
<!ENTITY calK  "Script K">
<!ENTITY calL  "Script L">
<!ENTITY calM  "Script M">
<!ENTITY calN  "Script N">
<!ENTITY calO  "Script O">
<!ENTITY calP  "Script P">
<!ENTITY calQ  "Script Q">
<!ENTITY calR  "Script R">
<!ENTITY calS  "Script S">
<!ENTITY calT  "Script T">
<!ENTITY calU  "Script U">
<!ENTITY calV  "Script V">
<!ENTITY calW  "Script W">
<!ENTITY calX  "Script X">
<!ENTITY calY  "Script Y">
<!ENTITY calZ  "Script Z">
<!ENTITY BbbA  "Bbb A">
<!ENTITY BbbB  "Bbb B">
<!ENTITY BbbC  "Bbb C">
<!ENTITY BbbD  "Bbb D">
<!ENTITY BbbE  "Bbb E">
<!ENTITY BbbF  "Bbb F">
<!ENTITY BbbG  "Bbb G">
<!ENTITY BbbH  "Bbb H">
<!ENTITY BbbI  "Bbb I">
<!ENTITY BbbJ  "Bbb J">
<!ENTITY BbbK  "Bbb K">
<!ENTITY BbbL  "Bbb L">
<!ENTITY BbbM  "Bbb M">
<!ENTITY BbbN  "Bbb N">
<!ENTITY BbbO  "Bbb O">
<!ENTITY BbbP  "Bbb P">
<!ENTITY BbbQ  "Bbb Q">
<!ENTITY BbbR  "Bbb R">
<!ENTITY BbbS  "Bbb S">
<!ENTITY BbbT  "Bbb T">
<!ENTITY BbbU  "Bbb U">
<!ENTITY BbbV  "Bbb V">
<!ENTITY BbbW  "Bbb W">
<!ENTITY BbbX  "Bbb X">
<!ENTITY BbbY  "Bbb Y">
<!ENTITY BbbZ  "Bbb Z">
<!ENTITY fraka  "fraktur a">
<!ENTITY frakb  "fraktur b">
<!ENTITY frakc  "fraktur c">
<!ENTITY frakd  "fraktur d">
<!ENTITY frake  "fraktur e">
<!ENTITY frakf  "fraktur f">
<!ENTITY frakg  "fraktur g">
<!ENTITY frakh  "fraktur h">
<!ENTITY fraki  "fraktur i">
<!ENTITY frakj  "fraktur j">
<!ENTITY frakk  "fraktur k">
<!ENTITY frakl  "fraktur l">
<!ENTITY frakm  "fraktur m">
<!ENTITY frakn  "fraktur n">
<!ENTITY frako  "fraktur o">
<!ENTITY frakp  "fraktur p">
<!ENTITY frakq  "fraktur q">
<!ENTITY frakr  "fraktur r">
<!ENTITY fraks  "fraktur s">
<!ENTITY frakt  "fraktur t">
<!ENTITY fraku  "fraktur u">
<!ENTITY frakv  "fraktur v">
<!ENTITY frakw  "fraktur w">
<!ENTITY frakx  "fraktur x">
<!ENTITY fraky  "fraktur y">
<!ENTITY frakz  "fraktur z">
<!ENTITY frakA  "fraktur A">
<!ENTITY frakB  "fraktur B">
<!ENTITY frakC  "fraktur C">
<!ENTITY frakD  "fraktur D">
<!ENTITY frakE  "fraktur E">
<!ENTITY frakF  "fraktur F">
<!ENTITY frakG  "fraktur G">
<!ENTITY frakH  "fraktur H">
<!ENTITY frakI  "fraktur I">
<!ENTITY frakJ  "fraktur J">
<!ENTITY frakK  "fraktur K">
<!ENTITY frakL  "fraktur L">
<!ENTITY frakM  "fraktur M">
<!ENTITY frakN  "fraktur N">
<!ENTITY frakO  "fraktur O">
<!ENTITY frakP  "fraktur P">
<!ENTITY frakQ  "fraktur Q">
<!ENTITY frakR  "fraktur R">
<!ENTITY frakS  "fraktur S">
<!ENTITY frakT  "fraktur T">
<!ENTITY frakU  "fraktur U">
<!ENTITY frakV  "fraktur V">
<!ENTITY frakW  "fraktur W">
<!ENTITY frakX  "fraktur X">
<!ENTITY frakY  "fraktur Y">
<!ENTITY frakZ  "fraktur Z">
<!ENTITY graveA  "<i>&#192;</i>">   <!-- A grave to CN 192 -->
<!ENTITY graveE  "<i>&#200;</i>">   <!-- E grave to CN 200 -->
<!ENTITY graveI  "<i>&#204;</i>">   <!-- I grave to CN 204 -->
<!ENTITY graveO  "<i>&#210;</i>">   <!-- O grave to CN 210 -->
<!ENTITY graveU  "<i>&#217;</i>">   <!-- U grave to CN 217 -->
<!ENTITY gravea  "<i>&#224;</i>">   <!-- a grave to CN 224 -->
<!ENTITY gravee  "<i>&#232;</i>">   <!-- e grave to CN 232 -->
<!ENTITY gravei  "<i>&#236;</i>">   <!-- i grave to CN 236 -->
<!ENTITY graveo  "<i>&#242;</i>">   <!-- o grave to CN 242 -->
<!ENTITY graveu  "<i>&#249;</i>">   <!-- u grave to CN 249 -->

<!ENTITY acuteA  "<i>&#193;</i>">   <!-- A acute to CN 193 -->
<!ENTITY acuteE  "<i>&#201;</i>">   <!-- E acute to CN 201 -->
<!ENTITY acuteI  "<i>&#205;</i>">   <!-- I acute to CN 205 -->
<!ENTITY acuteO  "<i>&#211;</i>">   <!-- O acute to CN 211 -->
<!ENTITY acuteU  "<i>&#218;</i>">   <!-- U acute to CN 218 -->
<!ENTITY acuteY  "<i>&#221;</i>">   <!-- Y acute to CN 221 -->
<!ENTITY acutea  "<i>&#225;</i>">   <!-- a acute to CN 225 -->
<!ENTITY acutee  "<i>&#233;</i>">   <!-- e acute to CN 233 -->
<!ENTITY acutei  "<i>&#237;</i>">   <!-- i acute to CN 237 -->
<!ENTITY acuteo  "<i>&#243;</i>">   <!-- o acute to CN 243 -->
<!ENTITY acuteu  "&#250;">   <!-- u acute to CN 250 -->
<!ENTITY acutey  "&#253;">   <!-- y acute to CN 253 -->

<!-- characters with accents not available in HTML -->
<!ENTITY cacute  "c acute">   
<!ENTITY nacute  "n acute">   
<!ENTITY sacute  "s acute">
<!ENTITY zacute  "z acute">
<!ENTITY Cacute  "C acute">   
<!ENTITY Nacute  "N acute">   
<!ENTITY Sacute  "S acute">
<!ENTITY Zacute  "Z acute">

<!ENTITY acedil  "a cedilla">
<!ENTITY bcedil  "b cedilla">
<!ENTITY dcedil  "d cedilla">
<!ENTITY ecedil  "e cedilla">
<!ENTITY fcedil  "f cedilla">
<!ENTITY gcedil  "g cedilla">
<!ENTITY hcedil  "h cedilla">
<!ENTITY icedil  "i cedilla">
<!ENTITY jcedil  "j cedilla">
<!ENTITY kcedil  "k cedilla">
<!ENTITY lcedil  "l cedilla">
<!ENTITY mcedil  "m cedilla">
<!ENTITY ncedil  "n cedilla">
<!ENTITY ocedil  "o cedilla">
<!ENTITY pcedil  "p cedilla">
<!ENTITY qcedil  "q cedilla">
<!ENTITY rcedil  "r cedilla">
<!ENTITY scedil  "s cedilla">
<!ENTITY tcedil  "t cedilla">
<!ENTITY ucedil  "u cedilla">
<!ENTITY vcedil  "v cedilla">
<!ENTITY wcedil  "w cedilla">
<!ENTITY xcedil  "x cedilla">
<!ENTITY ycedil  "y cedilla">
<!ENTITY zcedil  "z cedilla">

<!ENTITY Acedil  "A cedilla">
<!ENTITY Bcedil  "B cedilla">
<!ENTITY Dcedil  "D cedilla">
<!ENTITY Ecedil  "E cedilla">
<!ENTITY Fcedil  "F cedilla">
<!ENTITY Gcedil  "G cedilla">
<!ENTITY Hcedil  "H cedilla">
<!ENTITY Icedil  "I cedilla">
<!ENTITY Jcedil  "J cedilla">
<!ENTITY Kcedil  "K cedilla">
<!ENTITY Lcedil  "L cedilla">
<!ENTITY Mcedil  "M cedilla">
<!ENTITY Ncedil  "N cedilla">
<!ENTITY Ocedil  "O cedilla">
<!ENTITY Pcedil  "P cedilla">
<!ENTITY Qcedil  "Q cedilla">
<!ENTITY Rcedil  "R cedilla">
<!ENTITY Scedil  "S cedilla">
<!ENTITY Tcedil  "T cedilla">
<!ENTITY Ucedil  "U cedilla">
<!ENTITY Vcedil  "V cedilla">
<!ENTITY Wcedil  "W cedilla">
<!ENTITY Xcedil  "X cedilla">
<!ENTITY Ycedil  "Y cedilla">
<!ENTITY Zcedil  "Z cedilla">

<!ENTITY zdotacc "z dot">

<!ENTITY acheck  "check a">  <!-- hacek or check accent over character -->
<!ENTITY bcheck  "check b">
<!ENTITY ccheck  "check c">
<!ENTITY dcheck  "check d">
<!ENTITY echeck  "check e">
<!ENTITY fcheck  "check f">
<!ENTITY gcheck  "check g">
<!ENTITY hcheck  "check h">
<!ENTITY icheck  "check i">
<!ENTITY jcheck  "check j">
<!ENTITY kcheck  "check k">
<!ENTITY lcheck  "check l">
<!ENTITY mcheck  "check m">
<!ENTITY ncheck  "check n">
<!ENTITY ocheck  "check o">
<!ENTITY pcheck  "check p">
<!ENTITY qcheck  "check q">
<!ENTITY rcheck  "check r">
<!ENTITY scheck  "check s">
<!ENTITY tcheck  "check t">
<!ENTITY ucheck  "check u">
<!ENTITY vcheck  "check v">
<!ENTITY wcheck  "check w">
<!ENTITY xcheck  "check x">
<!ENTITY ycheck  "check y">
<!ENTITY zcheck  "check z">

<!ENTITY Acheck  "check A">  <!-- hacek or check accent over character -->
<!ENTITY Bcheck  "check B">
<!ENTITY Ccheck  "check C">
<!ENTITY Dcheck  "check D">
<!ENTITY Echeck  "check E">
<!ENTITY Fcheck  "check F">
<!ENTITY Gcheck  "check G">
<!ENTITY Hcheck  "check H">
<!ENTITY Icheck  "check I">
<!ENTITY Jcheck  "check J">
<!ENTITY Kcheck  "check K">
<!ENTITY Lcheck  "check L">
<!ENTITY Mcheck  "check M">
<!ENTITY Ncheck  "check N">
<!ENTITY Ocheck  "check O">
<!ENTITY Pcheck  "check P">
<!ENTITY Qcheck  "check Q">
<!ENTITY Rcheck  "check R">
<!ENTITY Scheck  "check S">
<!ENTITY Tcheck  "check T">
<!ENTITY Ucheck  "check U">
<!ENTITY Vcheck  "check V">
<!ENTITY Wcheck  "check W">
<!ENTITY Xcheck  "check X">
<!ENTITY Ycheck  "check Y">
<!ENTITY Zcheck  "check Z">

<!ENTITY abreve  "breve a">  <!-- breve accent over character -->
<!ENTITY bbreve  "breve b">
<!ENTITY cbreve  "breve c">
<!ENTITY dbreve  "breve d">
<!ENTITY ebreve  "breve e">
<!ENTITY fbreve  "breve f">
<!ENTITY gbreve  "breve g">
<!ENTITY hbreve  "breve h">
<!ENTITY ibreve  "breve i">
<!ENTITY jbreve  "breve j">
<!ENTITY kbreve  "breve k">
<!ENTITY lbreve  "breve l">
<!ENTITY mbreve  "breve m">
<!ENTITY nbreve  "breve n">
<!ENTITY obreve  "breve o">
<!ENTITY pbreve  "breve p">
<!ENTITY qbreve  "breve q">
<!ENTITY rbreve  "breve r">
<!ENTITY sbreve  "breve s">
<!ENTITY tbreve  "breve t">
<!ENTITY ubreve  "breve u">
<!ENTITY vbreve  "breve v">
<!ENTITY wbreve  "breve w">
<!ENTITY xbreve  "breve x">
<!ENTITY ybreve  "breve y">
<!ENTITY zbreve  "breve z">


<!ENTITY Abreve  "breve A">  <!-- breve accent over character -->
<!ENTITY Bbreve  "breve B">
<!ENTITY Cbreve  "breve C">
<!ENTITY Dbreve  "breve D">
<!ENTITY Ebreve  "breve E">
<!ENTITY Fbreve  "breve F">
<!ENTITY Gbreve  "breve G">
<!ENTITY Hbreve  "breve H">
<!ENTITY Ibreve  "breve I">
<!ENTITY Jbreve  "breve J">
<!ENTITY Kbreve  "breve K">
<!ENTITY Lbreve  "breve L">
<!ENTITY Mbreve  "breve M">
<!ENTITY Nbreve  "breve N">
<!ENTITY Obreve  "breve O">
<!ENTITY Pbreve  "breve P">
<!ENTITY Qbreve  "breve Q">
<!ENTITY Rbreve  "breve R">
<!ENTITY Sbreve  "breve S">
<!ENTITY Tbreve  "breve T">
<!ENTITY Ubreve  "breve U">
<!ENTITY Vbreve  "breve V">
<!ENTITY Wbreve  "breve W">
<!ENTITY Xbreve  "breve X">
<!ENTITY Ybreve  "breve Y">
<!ENTITY Zbreve  "breve Z">

<!-- barred characters (in maths) -->

<!ENTITY bara "bar a">
<!ENTITY barb "bar b">
<!ENTITY barc "bar c">
<!ENTITY bard "bar d">
<!ENTITY bare "bar e">
<!ENTITY barf "bar f">
<!ENTITY barg "bar g">
<!ENTITY barh "bar h">
<!ENTITY bari "bar i">
<!ENTITY barj "bar j">
<!ENTITY bark "bar k">
<!ENTITY barl "bar l">
<!ENTITY barm "bar m">
<!ENTITY barn "bar n">
<!ENTITY baro "bar o">
<!ENTITY barp "bar p">
<!ENTITY barq "bar q">
<!ENTITY barr "bar r">
<!ENTITY bars "bar s">
<!ENTITY bart "bar t">
<!ENTITY baru "bar u">
<!ENTITY barv "bar v">
<!ENTITY barw "bar w">
<!ENTITY barx "bar x">
<!ENTITY bary "bar y">
<!ENTITY barz "bar z">
<!ENTITY barpartial "bar partial">

<!ENTITY sqrt2 "sqrt2">
<!ENTITY sqrt3 "sqrt3">


<!ENTITY barA "bar A">
<!ENTITY barB "bar B">
<!ENTITY barC "bar C">
<!ENTITY barD "bar D">
<!ENTITY barE "bar E">
<!ENTITY barF "bar F">
<!ENTITY barG "bar G">
<!ENTITY barH "bar H">
<!ENTITY barI "bar I">
<!ENTITY barJ "bar J">
<!ENTITY barK "bar K">
<!ENTITY barL "bar L">
<!ENTITY barM "bar M">
<!ENTITY barN "bar N">
<!ENTITY barO "bar O">
<!ENTITY barP "bar P">
<!ENTITY barQ "bar Q">
<!ENTITY barR "bar R">
<!ENTITY barS "bar S">
<!ENTITY barT "bar T">
<!ENTITY barU "bar U">
<!ENTITY barV "bar V">
<!ENTITY barW "bar W">
<!ENTITY barX "bar X">
<!ENTITY barY "bar Y">
<!ENTITY barZ "bar Z">

<!ENTITY bar0 "bar 0">
<!ENTITY bar1 "bar 1">
<!ENTITY bar2 "bar 2">
<!ENTITY bar3 "bar 3">
<!ENTITY bar4 "bar 4">
<!ENTITY bar5 "bar 5">
<!ENTITY bar6 "bar 6">
<!ENTITY bar7 "bar 7">
<!ENTITY bar8 "bar 8">
<!ENTITY bar9 "bar 9">

<!ENTITY baralpha "bar alpha">
<!ENTITY barbeta "bar beta">
<!ENTITY bargamma "bar gamma">
<!ENTITY bardelta "bar delta">
<!ENTITY barepsilon "bar epsilon">
<!ENTITY barzeta "bar zeta">
<!ENTITY bareta "bar eta">
<!ENTITY bartheta "bar theta">
<!ENTITY bariota "bar iota">
<!ENTITY barkappa "bar kappa">
<!ENTITY barlambda "bar lambda">
<!ENTITY barmu "bar mu">
<!ENTITY barnu "bar nu">
<!ENTITY barxi "bar xi">
<!ENTITY barpi "bar pi">
<!ENTITY barrho "bar rho">
<!ENTITY barsigma "bar sigma">
<!ENTITY bartau "bar tau">
<!ENTITY barupsilon "bar upsilon">
<!ENTITY barphi "bar phi">
<!ENTITY barchi "bar chi">
<!ENTITY barpsi "bar psi">
<!ENTITY baromega "bar omega">
<!ENTITY barvarepsilon "bar varepsilon">
<!ENTITY barvartheta "bar vartheta">
<!ENTITY barvarpi "bar varpi">
<!ENTITY barvarrho "bar varrho">
<!ENTITY barvarsigma "bar varsigma">
<!ENTITY barvarphi "bar varphi">


<!-- dotted characters (in maths) -->

<!ENTITY dota "dot a">
<!ENTITY dotb "dot b">
<!ENTITY dotc "dot c">
<!ENTITY dotd "dot d">
<!ENTITY dote "dot e">
<!ENTITY dotf "dot f">
<!ENTITY dotg "dot g">
<!ENTITY doth "dot h">
<!ENTITY doti "dot i">
<!ENTITY dotj "dot j">
<!ENTITY dotk "dot k">
<!ENTITY dotl "dot l">
<!ENTITY dotm "dot m">
<!ENTITY dotn "dot n">
<!ENTITY doto "dot o">
<!ENTITY dotp "dot p">
<!ENTITY dotq "dot q">
<!ENTITY dotr "dot r">
<!ENTITY dots "dot s">
<!ENTITY dott "dot t">
<!ENTITY dotu "dot u">
<!ENTITY dotv "dot v">
<!ENTITY dotw "dot w">
<!ENTITY dotx "dot x">
<!ENTITY doty "dot y">
<!ENTITY dotz "dot z">

<!ENTITY dotA "dot A">
<!ENTITY dotB "dot B">
<!ENTITY dotC "dot C">
<!ENTITY dotD "dot D">
<!ENTITY dotE "dot E">
<!ENTITY dotF "dot F">
<!ENTITY dotG "dot G">
<!ENTITY dotH "dot H">
<!ENTITY dotI "dot I">
<!ENTITY dotJ "dot J">
<!ENTITY dotK "dot K">
<!ENTITY dotL "dot L">
<!ENTITY dotM "dot M">
<!ENTITY dotN "dot N">
<!ENTITY dotO "dot O">
<!ENTITY dotP "dot P">
<!ENTITY dotQ "dot Q">
<!ENTITY dotR "dot R">
<!ENTITY dotS "dot S">
<!ENTITY dotT "dot T">
<!ENTITY dotU "dot U">
<!ENTITY dotV "dot V">
<!ENTITY dotW "dot W">
<!ENTITY dotX "dot X">
<!ENTITY dotY "dot Y">
<!ENTITY dotZ "dot Z">
<!ENTITY dotalpha "dot alpha">
<!ENTITY dotbeta "dot beta">
<!ENTITY dotgamma "dot gamma">
<!ENTITY dotdelta "dot delta">
<!ENTITY dotepsilon "dot epsilon">
<!ENTITY dotzeta "dot zeta">
<!ENTITY doteta "dot eta">
<!ENTITY dottheta "dot theta">
<!ENTITY dotiota "dot iota">
<!ENTITY dotkappa "dot kappa">
<!ENTITY dotlambda "dot lambda">
<!ENTITY dotmu "dot mu">
<!ENTITY dotnu "dot nu">
<!ENTITY dotxi "dot xi">
<!ENTITY dotpi "dot pi">
<!ENTITY dotrho "dot rho">
<!ENTITY dotsigma "dot sigma">
<!ENTITY dottau "dot tau">
<!ENTITY dotupsilon "dot upsilon">
<!ENTITY dotphi "dot phi">
<!ENTITY dotchi "dot chi">
<!ENTITY dotpsi "dot psi">
<!ENTITY dotomega "dot omega">
<!ENTITY dotvarepsilon "dot varepsilon">
<!ENTITY dotvartheta "dot vartheta">
<!ENTITY dotvarpi "dot varpi">
<!ENTITY dotvarrho "dot varrho">
<!ENTITY dotvarsigma "dot varsigma">
<!ENTITY dotvarphi "dot varphi">
<!ENTITY dotpartial "dot partial">
<!ENTITY dotell "dot ell">
<!ENTITY dotnabla "dot nabla">

<!-- tilde characters (in maths) added 4/10 by Jo -->

<!ENTITY tildea "tilde a">
<!ENTITY tildeb "tilde b">
<!ENTITY tildec "tilde c">
<!ENTITY tilded "tilde d">
<!ENTITY tildee "tilde e">
<!ENTITY tildef "tilde f">
<!ENTITY tildeg "tilde g">
<!ENTITY tildeh "tilde h">
<!ENTITY tildei "tilde i">
<!ENTITY tildej "tilde j">
<!ENTITY tildek "tilde k">
<!ENTITY tildel "tilde l">
<!ENTITY tildem "tilde m">
<!ENTITY tilden "tilde n">
<!ENTITY tildeo "tilde o">
<!ENTITY tildep "tilde p">
<!ENTITY tildeq "tilde q">
<!ENTITY tilder "tilde r">
<!ENTITY tildes "tilde s">
<!ENTITY tildet "tilde t">
<!ENTITY tildeu "tilde u">
<!ENTITY tildev "tilde v">
<!ENTITY tildew "tilde w">
<!ENTITY tildex "tilde x">
<!ENTITY tildey "tilde y">
<!ENTITY tildez "tilde z">

<!ENTITY tildeA "tilde A">
<!ENTITY tildeB "tilde B">
<!ENTITY tildeC "tilde C">
<!ENTITY tildeD "tilde D">
<!ENTITY tildeE "tilde E">
<!ENTITY tildeF "tilde F">
<!ENTITY tildeG "tilde G">
<!ENTITY tildeH "tilde H">
<!ENTITY tildeI "tilde I">
<!ENTITY tildeJ "tilde J">
<!ENTITY tildeK "tilde K">
<!ENTITY tildeL "tilde L">
<!ENTITY tildeM "tilde M">
<!ENTITY tildeN "tilde N">
<!ENTITY tildeO "tilde O">
<!ENTITY tildeP "tilde P">
<!ENTITY tildeQ "tilde Q">
<!ENTITY tildeR "tilde R">
<!ENTITY tildeS "tilde S">
<!ENTITY tildeT "tilde T">
<!ENTITY tildeU "tilde U">
<!ENTITY tildeV "tilde V">
<!ENTITY tildeW "tilde W">
<!ENTITY tildeX "tilde X">
<!ENTITY tildeY "tilde Y">
<!ENTITY tildeZ "tilde Z">

<!-- tilde-greek characters (in maths) added by Jo 23/10-->
<!ENTITY tildealpha "tilde alpha">
<!ENTITY tildebeta "tilde beta">
<!ENTITY tildegamma "tilde gamma">
<!ENTITY tildedelta "tilde delta">
<!ENTITY tildeepsilon "tilde epsilon">
<!ENTITY tildezeta "tilde zeta">
<!ENTITY tildeeta "tilde eta">
<!ENTITY tildetheta "tilde theta">
<!ENTITY tildeiota "tilde iota">
<!ENTITY tildekappa "tilde kappa">
<!ENTITY tildelambda "tilde lambda">
<!ENTITY tildemu "tilde mu">
<!ENTITY tildenu "tilde nu">
<!ENTITY tildexi "tilde xi">
<!ENTITY tildepi "tilde pi">
<!ENTITY tilderho "tilde rho">
<!ENTITY tildesigma "tilde sigma">
<!ENTITY tildetau "tilde tau">
<!ENTITY tildeupsilon "tilde upsilon">
<!ENTITY tildephi "tilde phi">
<!ENTITY tildechi "tilde chi">
<!ENTITY tildepsi "tilde psi">
<!ENTITY tildeomega "tilde omega">
<!ENTITY tildevarepsilon "tilde varepsilon">
<!ENTITY tildevartheta "tilde vartheta">
<!ENTITY tildevarpi "tilde varpi">
<!ENTITY tildevarrho "tilde varrho">
<!ENTITY tildevarsigma "tilde varsigma">
<!ENTITY tildevarphi "tilde varphi">

<!ENTITY tildeGamma "tilde Gamma">
<!ENTITY tildeDelta "tilde Delta">
<!ENTITY tildeTheta "tilde Theta">
<!ENTITY tildeLambda "tilde Lambda">
<!ENTITY tildeXi "tilde Xi">
<!ENTITY tildePi "tilde Pi">
<!ENTITY tildeSigma "tilde Sigma">
<!ENTITY tildeUpsilon "tilde Upsilon">
<!ENTITY tildePhi "tilde Phi">
<!ENTITY tildePsi "tilde Psi">
<!ENTITY tildeOmega "tilde Omega">


<!-- hatted characters (in maths) -->

<!ENTITY hata "hat a">
<!ENTITY hatb "hat b">
<!ENTITY hatc "hat c">
<!ENTITY hatd "hat d">
<!ENTITY hate "hat e">
<!ENTITY hatf "hat f">
<!ENTITY hatg "hat g">
<!ENTITY hath "hat h">
<!ENTITY hati "hat i">
<!ENTITY hatj "hat j">
<!ENTITY hatk "hat k">
<!ENTITY hatl "hat l">
<!ENTITY hatm "hat m">
<!ENTITY hatn "hat n">
<!ENTITY hato "hat o">
<!ENTITY hatp "hat p">
<!ENTITY hatq "hat q">
<!ENTITY hatr "hat r">
<!ENTITY hats "hat s">
<!ENTITY hatt "hat t">
<!ENTITY hatu "hat u">
<!ENTITY hatv "hat v">
<!ENTITY hatw "hat w">
<!ENTITY hatx "hat x">
<!ENTITY haty "hat y">
<!ENTITY hatz "hat z">

<!ENTITY hatA "hat A">
<!ENTITY hatB "hat B">
<!ENTITY hatC "hat C">
<!ENTITY hatD "hat D">
<!ENTITY hatE "hat E">
<!ENTITY hatF "hat F">
<!ENTITY hatG "hat G">
<!ENTITY hatH "hat H">
<!ENTITY hatI "hat I">
<!ENTITY hatJ "hat J">
<!ENTITY hatK "hat K">
<!ENTITY hatL "hat L">
<!ENTITY hatM "hat M">
<!ENTITY hatN "hat N">
<!ENTITY hatO "hat O">
<!ENTITY hatP "hat P">
<!ENTITY hatQ "hat Q">
<!ENTITY hatR "hat R">
<!ENTITY hatS "hat S">
<!ENTITY hatT "hat T">
<!ENTITY hatU "hat U">
<!ENTITY hatV "hat V">
<!ENTITY hatW "hat W">
<!ENTITY hatX "hat X">
<!ENTITY hatY "hat Y">
<!ENTITY hatZ "hat Z">

<!ENTITY bhata "bold hat a">
<!ENTITY bhatb "bold hat b">
<!ENTITY bhatc "bold hat c">
<!ENTITY bhatd "bold hat d">
<!ENTITY bhate "bold hat e">
<!ENTITY bhatf "bold hat f">
<!ENTITY bhatg "bold hat g">
<!ENTITY bhath "bold hat h">
<!ENTITY bhati "bold hat i">
<!ENTITY bhatj "bold hat j">
<!ENTITY bhatk "bold hat k">
<!ENTITY bhatl "bold hat l">
<!ENTITY bhatm "bold hat m">
<!ENTITY bhatn "bold hat n">
<!ENTITY bhato "bold hat o">
<!ENTITY bhatp "bold hat p">
<!ENTITY bhatq "bold hat q">
<!ENTITY bhatr "bold hat r">
<!ENTITY bhats "bold hat s">
<!ENTITY bhatt "bold hat t">
<!ENTITY bhatu "bold hat u">
<!ENTITY bhatv "bold hat v">
<!ENTITY bhatw "bold hat w">
<!ENTITY bhatx "bold hat x">
<!ENTITY bhaty "bold hat y">
<!ENTITY bhatz "bold hat z">

<!ENTITY bhatA "bold hat A">
<!ENTITY bhatB "bold hat B">
<!ENTITY bhatC "bold hat C">
<!ENTITY bhatD "bold hat D">
<!ENTITY bhatE "bold hat E">
<!ENTITY bhatF "bold hat F">
<!ENTITY bhatG "bold hat G">
<!ENTITY bhatH "bold hat H">
<!ENTITY bhatI "bold hat I">
<!ENTITY bhatJ "bold hat J">
<!ENTITY bhatK "bold hat K">
<!ENTITY bhatL "bold hat L">
<!ENTITY bhatM "bold hat M">
<!ENTITY bhatN "bold hat N">
<!ENTITY bhatO "bold hat O">
<!ENTITY bhatP "bold hat P">
<!ENTITY bhatQ "bold hat Q">
<!ENTITY bhatR "bold hat R">
<!ENTITY bhatS "bold hat S">
<!ENTITY bhatT "bold hat T">
<!ENTITY bhatU "bold hat U">
<!ENTITY bhatV "bold hat V">
<!ENTITY bhatW "bold hat W">
<!ENTITY bhatX "bold hat X">
<!ENTITY bhatY "bold hat Y">
<!ENTITY bhatZ "bold hat Z">

<!ENTITY hatalpha "hat alpha">
<!ENTITY hatbeta "hat beta">
<!ENTITY hatgamma "hat gamma">
<!ENTITY hatdelta "hat delta">
<!ENTITY hatepsilon "hat epsilon">
<!ENTITY hatzeta "hat zeta">
<!ENTITY hateta "hat eta">
<!ENTITY hattheta "hat theta">
<!ENTITY hatiota "hat iota">
<!ENTITY hatkappa "hat kappa">
<!ENTITY hatlambda "hat lambda">
<!ENTITY hatmu "hat mu">
<!ENTITY hatnu "hat nu">
<!ENTITY hatxi "hat xi">
<!ENTITY hatpi "hat pi">
<!ENTITY hatrho "hat rho">
<!ENTITY hatsigma "hat sigma">
<!ENTITY hattau "hat tau">
<!ENTITY hatupsilon "hat upsilon">
<!ENTITY hatphi "hat phi">
<!ENTITY hatchi "hat chi">
<!ENTITY hatpsi "hat psi">
<!ENTITY hatomega "hat omega">
<!ENTITY hatvarepsilon "hat varepsilon">
<!ENTITY hatvartheta "hat vartheta">
<!ENTITY hatvarpi "hat varpi">
<!ENTITY hatvarrho "hat varrho">
<!ENTITY hatvarsigma "hat varsigma">
<!ENTITY hatvarphi "hat varphi">

<!ENTITY hat0 "hat 0">
<!ENTITY hat1 "hat 1">
<!ENTITY hat2 "hat 2">
<!ENTITY hat3 "hat 3">
<!ENTITY hat4 "hat 4">
<!ENTITY hat5 "hat 5">
<!ENTITY hat6 "hat 6">
<!ENTITY hat7 "hat 7">
<!ENTITY hat8 "hat 8">
<!ENTITY hat9 "hat 9">

<!ENTITY hatGamma "hat Gamma">
<!ENTITY hatDelta "hat Delta">
<!ENTITY hatTheta "hat Theta">
<!ENTITY hatXi "hat Xi">
<!ENTITY hatPi "hat Pi">
<!ENTITY hatSigma "hat Sigma">
<!ENTITY hatUpsilon "hat Upsilon">
<!ENTITY hatPhi "hat Phi">
<!ENTITY hatPsi "hat Psi">
<!ENTITY hatOmega "hat Omega">

<!ENTITY overline0 "overline 0">
<!ENTITY overline1 "overline 1">
<!ENTITY overline2 "overline 2">
<!ENTITY overline3 "overline 3">
<!ENTITY overline4 "overline 4">
<!ENTITY overline5 "overline 5">
<!ENTITY overline6 "overline 6">
<!ENTITY overline7 "overline 7">
<!ENTITY overline8 "overline 8">
<!ENTITY overline9 "overline 9">

<!-- Vectors; characters with over arrow -->

<!ENTITY veca "vec a">
<!ENTITY vecb "vec b">
<!ENTITY vecc "vec c">
<!ENTITY vecd "vec d">
<!ENTITY vece "vec e">
<!ENTITY vecf "vec f">
<!ENTITY vecg "vec g">
<!ENTITY vech "vec h">
<!ENTITY veci "vec i">
<!ENTITY vecj "vec j">
<!ENTITY veck "vec k">
<!ENTITY vecl "vec l">
<!ENTITY vecm "vec m">
<!ENTITY vecn "vec n">
<!ENTITY veco "vec o">
<!ENTITY vecp "vec p">
<!ENTITY vecq "vec q">
<!ENTITY vecr "vec r">
<!ENTITY vecs "vec s">
<!ENTITY vect "vec t">
<!ENTITY vecu "vec u">
<!ENTITY vecv "vec v">
<!ENTITY vecw "vec w">
<!ENTITY vecx "vec x">
<!ENTITY vecy "vec y">
<!ENTITY vecz "vec z">

<!ENTITY vecA "vec A">
<!ENTITY vecB "vec B">
<!ENTITY vecC "vec C">
<!ENTITY vecD "vec D">
<!ENTITY vecE "vec E">
<!ENTITY vecF "vec F">
<!ENTITY vecG "vec G">
<!ENTITY vecH "vec H">
<!ENTITY vecI "vec I">
<!ENTITY vecJ "vec J">
<!ENTITY vecK "vec K">
<!ENTITY vecL "vec L">
<!ENTITY vecM "vec M">
<!ENTITY vecN "vec N">
<!ENTITY vecO "vec O">
<!ENTITY vecP "vec P">
<!ENTITY vecQ "vec Q">
<!ENTITY vecR "vec R">
<!ENTITY vecS "vec S">
<!ENTITY vecT "vec T">
<!ENTITY vecU "vec U">
<!ENTITY vecV "vec V">
<!ENTITY vecW "vec W">
<!ENTITY vecX "vec X">
<!ENTITY vecY "vec Y">
<!ENTITY vecZ "vec Z">

<!ENTITY vec0 "vec 0">
<!ENTITY vec1 "vec 1">
<!ENTITY vec2 "vec 2">
<!ENTITY vec3 "vec 3">
<!ENTITY vec4 "vec 4">
<!ENTITY vec5 "vec 5">
<!ENTITY vec6 "vec 6">
<!ENTITY vec7 "vec 7">
<!ENTITY vec8 "vec 8">
<!ENTITY vec9 "vec 9">

<!ENTITY vecalpha "vec alpha">
<!ENTITY vecbeta "vec beta">
<!ENTITY vecgamma "vec gamma">
<!ENTITY vecdelta "vec delta">
<!ENTITY vecepsilon "vec epsilon">
<!ENTITY veczeta "vec zeta">
<!ENTITY veceta "vec eta">
<!ENTITY vectheta "vec theta">
<!ENTITY veciota "vec iota">
<!ENTITY veckappa "vec kappa">
<!ENTITY veclambda "vec lambda">
<!ENTITY vecmu "vec mu">
<!ENTITY vecnu "vec nu">
<!ENTITY vecxi "vec xi">
<!ENTITY vecpi "vec pi">
<!ENTITY vecrho "vec rho">
<!ENTITY vecsigma "vec sigma">
<!ENTITY vectau "vec tau">
<!ENTITY vecupsilon "vec upsilon">
<!ENTITY vecphi "vec phi">
<!ENTITY vecchi "vec chi">
<!ENTITY vecpsi "vec psi">
<!ENTITY vecomega "vec omega">
<!ENTITY vecvarepsilon "vec varepsilon">
<!ENTITY vecvartheta "vec vartheta">
<!ENTITY vecvarpi "vec varpi">
<!ENTITY vecvarrho "vec varrho">
<!ENTITY vecvarsigma "vec varsigma">
<!ENTITY vecvarphi "vec varphi">
<!ENTITY vecpartial "vec partial">
<!ENTITY vecell "vec ell">
<!ENTITY vecimath "vec imath">
<!ENTITY vecjmath "vec jmath">
<!ENTITY vecnabla "vec nabla">

<!ENTITY lbrace  "{">     <!-- left curly brace -->
<!ENTITY rbrace  "}">     <!-- right curly brace -->
<!ENTITY S  "&#167;">   <!-- section sign to CN 167 -->
<!ENTITY P  "&#182;">   <!-- paragraph sign to CN 182 -->
<!ENTITY hash  "#">        <!-- hash -->
<!ENTITY muchlt  "&lt;&lt;">  <!-- much less than to two less thans -->
<!ENTITY muchgt  "&gt;&gt;">  <!-- much greater than to two greater thans -->
<!ENTITY Angstrom  "&#197;">  <!-- Angstrom sign to CN 197 -->
<!ENTITY half  "&#189;">      <!-- 1/2 to CN 189 -->
<!ENTITY quarter  "&#188;">   <!-- 1/4 to CN 188 -->
<!ENTITY threequarter  "&#190;">  <!-- 3/4 to CN 190 -->
<!ENTITY threehalves  "3/2">  <!-- 3/2 -->
<!ENTITY fivehalves  "5/2">  <!-- 5/2 -->
<!ENTITY sevenhalves  "7/2">  <!-- 7/2 -->
<!ENTITY ninehalves  "9/2">  <!-- 9/2 -->
<!ENTITY degree  "&#176;">    <!-- degree sign to CN 176 -->
<!ENTITY lowast  "*">         <!-- lowast to on line * -->
<!ENTITY prime  "'">       <!-- prime to single quote (CN 39) -->
<!ENTITY ldots  "...">  <!-- ldots to ...       -->
<!ENTITY cdots  "&#183;&#183;&#183;">  <!-- cdots to 3 CN183's -->

<!-- IOP defined LaTeX entities -->
<!ENTITY ddiff  "d">    <!-- differential d -->
<!ENTITY eexp  "e">     <!-- exponential e -->
<!ENTITY iimg  "i">     <!-- imaginary i -->
<!ENTITY order  "O">    <!-- order of -->
<!ENTITY Tr   "Tr">     <!-- Trace -->
<!ENTITY tr   "tr">     <!-- trace -->
<!ENTITY re   "Re">     <!-- Real -->
<!ENTITY im   "Im">     <!-- Imaginary -->

<!-- Greek letters -->
<!ENTITY alpha  "$\alpha$">
<!ENTITY beta  "$\beta$">
<!ENTITY gamma  "$\gamma$">
<!ENTITY delta  "$\delta$">
<!ENTITY epsilon  "$\epsilon$">
<!ENTITY varepsilon  "$\varepsilon$">
<!ENTITY zeta  "$\zeta$">
<!ENTITY eta  "$\eta$">
<!ENTITY theta  "$\theta$">
<!ENTITY vartheta  "$\vartheta$">
<!ENTITY iota  "$\iota$">
<!ENTITY kappa  "$\kappa$">
<!ENTITY lambda  "$\lambda$">
<!ENTITY mu  "$\mu$">
<!ENTITY nu  "$\nu$">
<!ENTITY xi  "$\xi$">
<!ENTITY pi  "$\pi$">
<!ENTITY varpi  "$\varpi$">
<!ENTITY rho  "$\rho$">
<!ENTITY varrho  "$\varrho$">
<!ENTITY sigma  "$\sigma$">
<!ENTITY varsigma  "$\varsigma$">
<!ENTITY tau  "$\tau$">
<!ENTITY upsilon  "$\upsilon$">
<!ENTITY phi  "$\phi$">
<!ENTITY varphi  "$\varphi$">
<!ENTITY chi  "$\chi$">
<!ENTITY psi  "$\psi$">
<!ENTITY omega  "$\omega$">
<!ENTITY Gamma  "$\Gamma$">
<!ENTITY Delta  "$\Delta$">
<!ENTITY Theta  "$\Theta$">
<!ENTITY Lambda  "$\Lambda$">
<!ENTITY Xi  "$\Xi$">
<!ENTITY Pi  "$\Pi$">
<!ENTITY Sigma  "$\Sigma$">
<!ENTITY Upsilon  "$\Upsilon$">
<!ENTITY Phi  "$\Phi$">
<!ENTITY Psi  "$\Psi$">
<!ENTITY Omega  "$\Omega$">

<!-- Bold Greek letters -->
<!ENTITY balpha  "bold alpha">
<!ENTITY bbeta  "bold beta">
<!ENTITY bgamma  "bold gamma">
<!ENTITY bdelta  "bold delta">
<!ENTITY bepsilon  "bold epsilon">
<!ENTITY bvarepsilon  "bold varepsilon">
<!ENTITY bzeta  "bold zeta">
<!ENTITY bfeta  "bold eta">
<!ENTITY btheta  "bold theta">
<!ENTITY bvartheta  "bold vartheta">
<!ENTITY biota  "bold iota">
<!ENTITY bkappa  "bold kappa">
<!ENTITY blambda  "bold lambda">
<!ENTITY bmu  "bold mu">
<!ENTITY bnu  "bold nu">
<!ENTITY bxi  "bold xi">
<!ENTITY bpi  "bold pi">
<!ENTITY bvarpi  "bold varpi">
<!ENTITY brho  "bold rho">
<!ENTITY bvarrho  "bold varrho">
<!ENTITY bsigma  "bold sigma">
<!ENTITY bvarsigma  "bold varsigma">
<!ENTITY btau  "bold tau">
<!ENTITY bupsilon  "bold upsilon">
<!ENTITY bphi  "bold phi">
<!ENTITY bvarphi  "bold varphi">
<!ENTITY bchi  "bold chi">
<!ENTITY bpsi  "bold psi">
<!ENTITY bomega  "bold omega">
<!ENTITY bGamma  "bold Gamma">
<!ENTITY bDelta  "bold Delta">
<!ENTITY bTheta  "bold Theta">
<!ENTITY bLambda  "bold Lambda">
<!ENTITY bXi  "bold Xi">
<!ENTITY bPi  "bold Pi">
<!ENTITY bSigma  "bold Sigma">
<!ENTITY bUpsilon  "bold Upsilon">
<!ENTITY bPhi  "bold Phi">
<!ENTITY bPsi  "bold Psi">
<!ENTITY bOmega  "bold Omega">

<!ENTITY bnabla  "bold nabla">
<!-- Miscellaneous maths characters -->
<!ENTITY aleph  "$\aleph$">
<!ENTITY hbar  "$\hbar$">
<!ENTITY imath  "$\imath$">
<!ENTITY jmath  "$\jmath$">
<!ENTITY ell  "$\ell$">
<!ENTITY wp  "$\wp$">
<!ENTITY Re  "$\Re$">
<!ENTITY Im  "$\Im$">
<!ENTITY partial  "$\partial$">
<!ENTITY infty  "$\infty$">
<!ENTITY emptyset  "$\emptyset$">
<!ENTITY nabla  "$\nabla$">
<!ENTITY surd  "$\surd$">
<!ENTITY top  "$\top$">
<!ENTITY bot  "$\bot$">
<!ENTITY Vert  "||">
<!ENTITY vert  "|">
<!ENTITY angle  "$\angle$">
<!ENTITY triangle  "$\triangle$">
<!ENTITY backslash  "\">
<!ENTITY forall  "$\forall$">
<!ENTITY exists  "$\exists$">
<!ENTITY neg  "$\neg$">
<!ENTITY lnot  "$\neg$">
<!ENTITY flat  "$\flat$">
<!ENTITY natural  "$\natural$">
<!ENTITY sharp  "$\sharp$">
<!ENTITY clubsuit  "$\clubsuit$">
<!ENTITY diamondsuit  "$\diamondsuit$">
<!ENTITY heartsuit  "$\heartsuit$">
<!ENTITY spadesuit  "$\spadesuit$">
<!ENTITY sum  "$\sum$">
<!ENTITY prod  "$\prod$">
<!ENTITY coprod  "$\coprod$">
<!ENTITY int  "$\int$">
<!ENTITY oint  "$\oint$">
<!ENTITY bigcap  "$\bigcap$">
<!ENTITY bigcup  "$\bigcup$">
<!ENTITY bigsqcup  "$\bigsqcup$">
<!ENTITY bigvee  "$\bigvee$">
<!ENTITY bigwedge  "$\bigwedge$">
<!ENTITY bigodot  "$\bigodot$">

<!-- Binary operations -->
<!ENTITY mp  "$\mp$">
<!ENTITY pm  "&#177;">
<!ENTITY setminus  "$\setminus$">
<!ENTITY cdot  "&#183;">
<!ENTITY ast  "$\ast$">
<!ENTITY star  "$\star$">
<!ENTITY diamond  "$\diamond$">
<!ENTITY circ  "o">
<!ENTITY bullet  "$\bullet$">
<!ENTITY div  "$\div$">
<!ENTITY cap  "$\cap$">
<!ENTITY cup  "$\cup$">
<!ENTITY uplus  "$\uplus$">
<!ENTITY sqcap  "$\sqcap$">
<!ENTITY sqcup  "$\sqcup$">
<!ENTITY triangleleft  "$\triangleleft$">
<!ENTITY triangleright  "$\triangleright$">
<!ENTITY wr  "$\wr$">
<!ENTITY bigcirc  "$\bigcirc$">
<!ENTITY bigtriangleup  "$\bigtriangleup$">
<!ENTITY bigtriangledown  "$\bigtriangledown$">
<!ENTITY vee  "$\vee$">
<!ENTITY lor  "$\vee$">
<!ENTITY wedge  "$\wedge$">
<!ENTITY land  "$\wedge$">
<!ENTITY oplus  "$\oplus$">
<!ENTITY ominus  "$\ominus$">
<!ENTITY otimes  "$\otimes$">
<!ENTITY oslashed  "$\oslash$">
<!ENTITY odot  "$\odot$">
<!ENTITY dagger  "$\dagger$">
<!ENTITY dag  "$\dagger$">
<!ENTITY ddagger  "$\ddagger$">
<!ENTITY ddag  "$\ddagger$">
<!ENTITY amalg  "$\amalg$">

<!-- Relations -->

<!ENTITY leq  "$\leq$">
<!ENTITY le  "$\leq$">
<!ENTITY prec  "$\prec$">
<!ENTITY preceq  "$\preceq$">
<!ENTITY ll  "$\ll$">
<!ENTITY subset  "$\subset$">
<!ENTITY subseteq  "$\subseteq$">
<!ENTITY sqsubseteq  "$\sqsubseteq$">
<!ENTITY in  "$\in$">
<!ENTITY vdash  "$\vdash$">
<!ENTITY smile  "$\smile$">
<!ENTITY frown  "$\frown$">
<!ENTITY geq  "$\geq$">
<!ENTITY ge  "$\geq$">
<!ENTITY succ  "$\succ$">
<!ENTITY succeq  "$\succeq$">
<!ENTITY gg  "$\gg$">
<!ENTITY supset  "$\supset$">
<!ENTITY supseteq  "$\supseteq$">
<!ENTITY sqsupseteq  "$\sqsupseteq$">
<!ENTITY ni  "$\ni$">
<!ENTITY owns  "$\ni$">
<!ENTITY dashv  "$\dashv$">
<!ENTITY mid  "$\mid$">
<!ENTITY parallel  "$\parallel$">
<!ENTITY equiv  "$\equiv$">
<!ENTITY simeq  "$\simeq$">
<!ENTITY asymp  "$\asymp$">
<!ENTITY approx  "$\approx$">
<!ENTITY cong  "$\cong$">
<!ENTITY bowtie  "$\bowtie$">
<!ENTITY propto  "$\propto$">
<!ENTITY models  "$\models$">
<!ENTITY doteq  "$\doteq$">
<!ENTITY perp  "$\perp$">

<!-- Negated relations -->

<!ENTITY notlt  "$\not\lt$">
<!ENTITY notleq  "$\not\leq$">
<!ENTITY notprec  "$\not\prec$">
<!ENTITY notpreceq  "$\not\preceq$">
<!ENTITY notsubset  "$\not\subset$">
<!ENTITY notsubseteq  "$\not\subseteq$">
<!ENTITY notsqsubseteq  "$\not\sqsubseteq$">
<!ENTITY notgt  "$\not\gt$">
<!ENTITY notgeq  "$\not\geq$">
<!ENTITY notsucc  "$\not\succ$">
<!ENTITY notsucceq  "$\not\succeq$">
<!ENTITY notsupset  "$\not\supset$">
<!ENTITY notsupseteq  "$\not\supseteq$">
<!ENTITY notsqsupseteq  "$\not\sqsupseteq$">
<!ENTITY noteq  "$\not=$">
<!ENTITY neq  "$\not=$">
<!ENTITY ne  "$\not=$">
<!ENTITY notequiv  "$\not\equiv$">
<!ENTITY notsim  "$\not\sim$">
<!ENTITY notsimeq  "$\not\simeq$">
<!ENTITY notapprox  "$\not\approx$">
<!ENTITY notcong  "$\not\cong$">
<!ENTITY notasymp  "$\not\asymp$">

<!-- Arrows -->

<!ENTITY leftarrow  "$\leftarrow$">
<!ENTITY gets  "$\leftarrow$">
<!ENTITY Leftarrow  "$\Leftarrow$">
<!ENTITY rightarrow  "$\rightarrow$">
<!ENTITY to  "$\rightarrow$">
<!ENTITY Rightarrow  "$\Rightarrow$">
<!ENTITY leftrightarrow  "$\leftrightarrow$">
<!ENTITY Leftrightarrow  "$\Leftrightarrow$">
<!ENTITY mapsto  "$\mapsto$">
<!ENTITY hookleftarrow  "$\hookleftarrow$">
<!ENTITY leftharpoonup  "$\leftharpoonup$">
<!ENTITY leftharpoondown  "$\leftharpoondown$">
<!ENTITY rightleftharpoons  "$\rightleftharpoons$">
<!ENTITY longleftarrow  "$\longleftarrow$">
<!ENTITY Longleftarrow  "$\Longleftarrow$">
<!ENTITY longrightarrow  "$\longrightarrow$">
<!ENTITY Longrightarrow  "$\Longrightarrow$">
<!ENTITY longleftrightarrow  "$\longleftrightarrow$">
<!ENTITY Longleftrightarrow  "$\Longleftrightarrow$">
<!ENTITY iff  "&nbsp;$\Longleftrightarrow$&nbsp;">
<!ENTITY longmapsto  "$\longmapsto$">
<!ENTITY hookrightarrow  "$\hookrightarrow$">
<!ENTITY rightharpoonup  "$\rightharpoonup$">
<!ENTITY rightharpoondown  "$\rightharpoondown$">
<!ENTITY uparrow  "$\uparrow$">
<!ENTITY Uparrow  "$\Uparrow$">
<!ENTITY downarrow  "$\downarrow$">
<!ENTITY Downarrow  "$\Downarrow$">
<!ENTITY updownarrow  "$\updownarrow$">
<!ENTITY Updownarrow  "$\Updownarrow$">
<!ENTITY nearrow  "$\nearrow$">
<!ENTITY searrow  "$\searrow$">
<!ENTITY swarrow  "$\swarrow$">
<!ENTITY nwarrow  "$\nwarrow$">

<!-- Openings and closings -->

<!ENTITY lbrack  "[">
<!ENTITY lfloor  "$\lfloor$">
<!ENTITY langle  "$\langle$">
<!ENTITY lceil  "$\lceil$">
<!ENTITY rbrack  "]">
<!ENTITY rfloor  "$\rfloor$">
<!ENTITY rangle  "$\rangle$">
<!ENTITY rceil  "$\rceil$">

<!ENTITY arccos  "$\arccos$"> 
<!ENTITY arcsin  "$\arcsin$"> 
<!ENTITY arctan  "$\arctan$"> 
<!ENTITY arg  "$\arg$"> 
<!ENTITY cos  "$\cos$"> 
<!ENTITY cosh  "$\cosh$"> 
<!ENTITY cot  "$\cot$"> 
<!ENTITY coth  "$\coth$"> 
<!ENTITY csc  "$\csc$"> 
<!ENTITY det  "$\det$"> 
<!ENTITY dim  "$\dim$"> 
<!ENTITY exp  "$\exp$"> 
<!ENTITY gcd  "$\gcd$"> 
<!ENTITY hom  "$\hom$"> 
<!ENTITY inf  "$\inf$"> 
<!ENTITY ker  "$\ker$"> 
<!ENTITY lg  "$\lg$"> 
<!ENTITY lim  "$\lim$"> 
<!ENTITY liminf  "$\liminf$"> 
<!ENTITY limsup  "$\limsup$"> 
<!ENTITY ln  "$\ln$"> 
<!ENTITY log  "$\log$"> 
<!ENTITY max  "$\max$"> 
<!ENTITY min  "$\min$"> 
<!ENTITY Pr  "$\Pr$"> 
<!ENTITY sec  "$\sec$"> 
<!ENTITY sin  "$\sin$"> 
<!ENTITY sinh  "$\sinh$"> 
<!ENTITY sup  "$\sup$"> 
<!ENTITY tan  "$\tan$"> 
<!ENTITY tanh  "$\tanh$"> 

<!ENTITY digamma "$\digamma$">
<!ENTITY varkappa "$\varkappa$">
<!ENTITY beth "$\beth$">
<!ENTITY daleth "$\daleth$">
<!ENTITY gimel "$\gimel$">
<!ENTITY hslash "$\hslash$">
<!ENTITY vartriangle "$\vartriangle$">
<!ENTITY triangledown "$\triangledown$">
<!ENTITY square "$\square$">
<!ENTITY lozenge "$\lozenge$">
<!ENTITY circledS "$\circledS$">
<!ENTITY measuredangle "$\measuredangle$">
<!ENTITY nexists "$\nexists$">
<!ENTITY mho "$\mho$"> 
<!ENTITY Finv "$\Finv$">
<!ENTITY Game "$\Game$">
<!ENTITY Bbbk "$\Bbbk$">
<!ENTITY backprime "$\backprime$">
<!ENTITY varnothing "$\varnothing$">
<!ENTITY blacktriangle "$\blacktriangle$">
<!ENTITY blacktriangledown "$\blacktriangledown$">
<!ENTITY blacksquare "$\blacksquare$">
<!ENTITY blacklozenge "$\blacklozenge$">
<!ENTITY bigstar "$\bigstar$">
<!ENTITY sphericalangle "$\sphericalangle$">
<!ENTITY complement "$\complement$">
<!-- ENTITY eth "&#240;" previously defined -->
<!ENTITY diagup "$\diagup$">
<!ENTITY diagdown "$\diagdown$">
<!ENTITY dotplus "$\dotplus$">
<!ENTITY smallsetminus "$\smallsetminus$">
<!ENTITY Cap "$\Cap$">
<!ENTITY doublecap "$\doublecap$">
<!ENTITY Cup "$\Cup$">
<!ENTITY doublecup "$\doublecup$">
<!ENTITY barwedge "$\barwedge$">
<!ENTITY veebar "$\veebar$">
<!ENTITY doublebarwedge "$\doublebarwedge$">
<!ENTITY boxminus "$\boxminus$">
<!ENTITY boxtimes "$\boxtimes$">
<!ENTITY boxdot "$\boxdot$">
<!ENTITY boxplus "$\boxplus$">
<!ENTITY divideontimes "$\divideontimes$">
<!ENTITY ltimes "$\ltimes$">
<!ENTITY rtimes "$\rtimes$">
<!ENTITY leftthreetimes "$\leftthreetimes$">
<!ENTITY rightthreetimes "$\rightthreetimes$">
<!ENTITY curlywedge "$\curlywedge$">
<!ENTITY curlyvee "$\curlyvee$">
<!ENTITY circleddash "$\circleddash$">
<!ENTITY circledast "$\circledast$">
<!ENTITY circledcirc "$\circledcirc$">
<!ENTITY centerdot "$\centerdot$">
<!ENTITY intercal "$\intercal$">
<!ENTITY leqq "$\leqq$">
<!ENTITY leqslant "$\leqslant$">
<!ENTITY eqslantless "$\eqslantless$">
<!ENTITY lesssim "$\lesssim$">
<!ENTITY lessapprox "$\lessapprox$">
<!ENTITY approxeq "$\approxeq$">
<!ENTITY lessdot "$\lessdot$">
<!ENTITY lll "$\lll$">
<!ENTITY llless "$\llless$">
<!ENTITY lessgtr "$\lessgtr$">
<!ENTITY lesseqgtr "$\lesseqgtr$">
<!ENTITY lesseqqgtr "$\lesseqqgtr$">
<!ENTITY doteqdot "$\doteqdot$">
<!ENTITY Doteq "$\Doteq$">
<!ENTITY risingdotseq "$\risingdotseq$">
<!ENTITY fallingdotseq "$\fallingdotseq$">
<!ENTITY backsim "$\backsim$">
<!ENTITY backsimeq "$\backsimeq$">
<!ENTITY subseteqq "$\subseteqq$">
<!ENTITY Subset "$\Subset$">
<!ENTITY sqsubset "$\sqsubset$">
<!ENTITY preccurlyeq "$\preccurlyeq$">
<!ENTITY curlyeqprec "$\curlyeqprec$">
<!ENTITY precsim "$\precsim$">
<!ENTITY precapprox "$\precapprox$">
<!ENTITY vartriangleleft "$\vartriangleleft$">
<!ENTITY trianglelefteq "$\trianglelefteq$">
<!ENTITY vDash "$\vDash$">
<!ENTITY Vvdash "$\Vvdash$">
<!ENTITY smallsmile "$\smallsmile$">
<!ENTITY smallfrown "$\smallfrown$">
<!ENTITY bumpeq "$\bumpeq$">
<!ENTITY Bumpeq "$\Bumpeq$">
<!ENTITY geqq "$\geqq$">
<!ENTITY geqslant "$\geqslant$">
<!ENTITY eqslantgtr "$\eqslantgtr$">
<!ENTITY gtrsim "$\gtrsim$">
<!ENTITY gtrapprox "$\gtrapprox$">
<!ENTITY gtrdot "$\gtrdot$">
<!ENTITY ggg "$\ggg$">
<!ENTITY gggtr "$\gggtr$">
<!ENTITY gtrless "$\gtrless$">
<!ENTITY gtreqless "$\gtreqless$">
<!ENTITY gtreqqless "$\gtreqqless$">
<!ENTITY eqcirc "$\eqcirc$">
<!ENTITY circeq "$\circeq$">
<!ENTITY triangleq "$\triangleq$">
<!ENTITY thicksim "$\thicksim$">
<!ENTITY thickapprox "$\thickapprox$">
<!ENTITY supseteqq "$\supseteqq$">
<!ENTITY Supset "$\Supset$">
<!ENTITY sqsupset "$\sqsupset$">
<!ENTITY succcurlyeq "$\succcurlyeq$">
<!ENTITY curlyeqsucc "$\curlyeqsucc$">
<!ENTITY succsim "$\succsim$">
<!ENTITY succapprox "$\succapprox$">
<!ENTITY vartriangleright "$\vartriangleright$">
<!ENTITY trianglerighteq "$\trianglerighteq$">
<!ENTITY Vdash "$\Vdash$">
<!ENTITY shortmid "$\shortmid$">
<!ENTITY shortparallel "$\shortparallel$">
<!ENTITY between "$\between$">
<!ENTITY pitchfork "$\pitchfork$">
<!ENTITY varpropto "$\varpropto$">
<!ENTITY blacktriangleleft "$\blacktriangleleft$">
<!ENTITY therefore "$\therefore$">
<!ENTITY backepsilon "$\backepsilon$">
<!ENTITY blacktriangleright "$\blacktriangleright$">
<!ENTITY because "$\because$">
<!ENTITY nless "$\nless$">
<!ENTITY ngtr "$\ngtr$">
<!ENTITY nleq "$\nleq$">
<!ENTITY ngeq "$\ngeq$">
<!ENTITY nleqslant "$\nleqslant$">
<!ENTITY ngeqslant "$\ngeqslant$">
<!ENTITY nleqq "$\nleqq$">
<!ENTITY ngeqq "$\ngeqq$">
<!ENTITY lneq "$\lneq$">
<!ENTITY gneq "$\gneq$">
<!ENTITY lneqq "$\lneqq$">
<!ENTITY gneqq "$\gneqq$">
<!ENTITY lvertneqq "$\lvertneqq$">
<!ENTITY gvertneqq "$\gvertneqq$">
<!ENTITY lnsim "$\lnsim$">
<!ENTITY gnsim "$\gnsim$">
<!ENTITY lnapprox "$\lnapprox$">
<!ENTITY gnapprox "$\gnapprox$">
<!ENTITY nprec "$\nprec$">
<!ENTITY nsucc "$\nsucc$">
<!ENTITY npreceq "$\npreceq$">
<!ENTITY nsucceq "$\nsucceq$">
<!ENTITY precneqq "$\precneqq$">
<!ENTITY succneqq "$\succneqq$">
<!ENTITY precnsim "$\precnsim$">
<!ENTITY succnsim "$\succnsim$">
<!ENTITY precnapprox "$\precnapprox$">
<!ENTITY succnapprox "$\succnapprox$">
<!ENTITY nsim "$\nsim$">
<!ENTITY ncong "$\ncong$">
<!ENTITY nshortmid "$\nshortmid$">
<!ENTITY nshortparallel "$\nshortparallel$">
<!ENTITY nmid "$\nmid$">
<!ENTITY nparallel "$\nparallel$">
<!ENTITY nvdash "$\nvdash$">
<!ENTITY nvDash "$\nvDash$">
<!ENTITY nVdash "$\nVdash$">
<!ENTITY nVDash "$\nVDash$">
<!ENTITY ntriangleleft "$\ntriangleleft$">
<!ENTITY ntriangleright "$\ntriangleright$">
<!ENTITY ntrianglelefteq "$\ntrianglelefteq$">
<!ENTITY ntrianglerighteq "$\ntrianglerighteq$">
<!ENTITY nsubseteq "$\nsubseteq$">
<!ENTITY nsupseteq "$\nsupseteq$">
<!ENTITY nsubseteqq "$\nsubseteqq$">
<!ENTITY nsupseteqq "$\nsupseteqq$">
<!ENTITY subsetneq "$\subsetneq$">
<!ENTITY supsetneq "$\supsetneq$">
<!ENTITY varsubsetneq "$\varsubsetneq$">
<!ENTITY varsupsetneq "$\varsupsetneq$">
<!ENTITY subsetneqq "$\subsetneqq$">
<!ENTITY supsetneqq "$\supsetneqq$">
<!ENTITY varsubsetneqq "$\varsubsetneqq$">
<!ENTITY varsupsetneqq "$\varsupsetneqq$">
<!ENTITY leftleftarrows "$\leftleftarrows$">
<!ENTITY rightrightarrows "$\rightrightarrows$">
<!ENTITY leftrightarrows "$\leftrightarrows$">
<!ENTITY rightleftarrows "$\rightleftarrows$">
<!ENTITY Lleftarrow "$\Lleftarrow$">
<!ENTITY Rrightarrow "$\Rrightarrow$">
<!ENTITY twoheadleftarrow "$\twoheadleftarrow$">
<!ENTITY twoheadrightarrow "$\twoheadrightarrow$">
<!ENTITY leftarrowtail "$\leftarrowtail$">
<!ENTITY rightarrowtail "$\rightarrowtail$">
<!ENTITY looparrowleft "$\looparrowleft$">
<!ENTITY looparrowright "$\looparrowright$">
<!ENTITY leftrightharpoons "$\leftrightharpoons$">
<!ENTITY curvearrowleft "$\curvearrowleft$">
<!ENTITY curvearrowright "$\curvearrowright$">
<!ENTITY circlearrowleft "$\circlearrowleft$">
<!ENTITY circlearrowright "$\circlearrowright$">
<!ENTITY Lsh "$\Lsh$">
<!ENTITY Rsh "$\Rsh$">
<!ENTITY upuparrows "$\upuparrows$">
<!ENTITY downdownarrows "$\downdownarrows$">
<!ENTITY upharpoonleft "$\upharpoonleft$">
<!ENTITY upharpoonright "$\upharpoonright$">
<!ENTITY restriction "$\restriction$">
<!ENTITY downharpoonleft "$\downharpoonleft$">
<!ENTITY downharpoonright "$\downharpoonright$">
<!ENTITY multimap "$\multimap$">
<!ENTITY rightsquigarrow "$\rightsquigarrow$">
<!ENTITY leftrightsquigarrow "$\leftrightsquigarrow$">
<!ENTITY nleftarrow "$\nleftarrow$">
<!ENTITY nrightarrow "$\nrightarrow$">
<!ENTITY nLeftarrow "$\nLeftarrow$">
<!ENTITY nRightarrow "$\nRightarrow$">
<!ENTITY nleftrightarrow "$\nleftrightarrow$">
<!ENTITY nLeftrightarrow "$\nLeftrightarrow$">
<!ENTITY notin "$\notin$">

<!-- miscellaneous characters from PostScript Times Roman font -->
<!ENTITY ldchevron  "ldchevron">
<!ENTITY rdchevron  "rdchevron">
<!ENTITY lchevron  "lchevron">
<!ENTITY rchevron  "rchevron">

<!-- Received -->                                          
<!ENTITY received  "Received ">                  
<!ENTITY finalform  ", in final form ">          
<!ENTITY accepted  ", accepted for publication ">
<!ENTITY online  ", online ">