International Journal of Computational Geometry and Applications (World Scientific)

@book{ColBenh:93,
  editor    =   "Fr\'ed\'eric Benhamou and Alain Colmerauer" ,
  title     =   "Constraint {L}ogic {P}rogramming, {S}elected {R}esearch",
  publisher =   "MIT Press",
  year      =   "1993"}

@book{ArmsRace1,
  author    =   "L. F. Richardson",
  title     =   "Arms and {I}nsecurity",
  publisher =   "Boxwood",
  address   =   "Pittsburg",
  pages     =   "200--253",
  year      =   "1960"}

@book{ComplexVariables,
  author    =   "R. V. Churchill and J. W. Brown",
  title     =   "Complex {V}ariables and {A}pplications",
  publisher =   "McGraw-Hill",
  pages     =   "215--253",
  year      =   "1990",
  edition   =   "5th"}

@inproceedings{conftypical,
  author    =   "R. K. Gupta and S. D. Senturia",
  title     =   "Pull-in Time Dynamics as a Measure of Absolute Pressure",
  booktitle =   "Proc. {IEEE} International Workshop on
                Microelectromechanical Systems ({MEMS}'97)",
  address   =   "Nagoya, Japan",
  month     =   jan,
  year      =   "1997",
  pages     =   "290-294",
  note = "\url{https://doi.org/10.1109/MEMSYS.1997.581830}"}

@inproceedings{Moss94,
  author    =   "F. Moss",
  title     =   "Stochastic resonance: From the ice ages to the monkey's ear",
  pages     =   "205--253",
  year      =   "1994",
  crossref  =   "Weiss94",
note = "\url{https://doi.org/10.1137/1.9781611971552.ch5}"}

@proceedings{Weiss94,
  title     =   "Contemporary {P}roblems in {S}tatistical {P}hysics",
  booktitle =   "Contemporary {P}roblems in {S}tatistical {P}hysics",
  editor    =   "G. H. Weiss",
  publisher =   "SIAM, Philadelphia",
  year      =   "1994"}

@article{best,
    author  =   "Westbury, Bruce W.",
     title  =   "{$R$}-matrices and the magic square",
   journal  =   "J. Phys. A.",
  fjournal  =   "Journal of Physics. A. Mathematical and General",
    volume  =   "36",
      year  =   "2003",
    number  =   "7",
     pages  =   "1947--1959",
      issn  =   "0305-4470",
     coden  =   "JPHAC5",
   mrclass  =   "17B10",
  mrnumber  =   "1 960 703",
  note = "\url{https://doi.org/10.1088/0305-4470/36/11/501}"}

@article{pier,
    author  =   "Deligne, Pierre X. and Gross, Benedict H.",
     title  =   "On the exceptional series, and its descendants",
   journal  =   "C. R. Math. Acad. Sci. Paris",
  fjournal  =   "Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris",
    volume  =   "335",
      year  =   "2002",
    number  =   "11",
     pages  =   "877--881",
      issn  =   "1631-073X",
   mrclass  =   "20Gxx",
  mrnumber  =   "1 952 563",
note = "\url{https://doi.org/10.1016/S1631-073X(02)02590-6}"}

@article{jame,
    author  =   "Landsberg, James. M. and Manivel, L.",
     title  =   "Triality, exceptional {L}ie algebras and {D}eligne dimension formulas",
   journal  =   "Adv. Math.",
  fjournal  =   "Advances in Mathematics",
    volume  =   "171",
      year  =   "2002",
    number  =   "1",
     pages  =   "59--85",
      issn  =   "0001-8708",
     coden  =   "ADMTA4",
   mrclass  =   "17B20 (17B25)",
  mrnumber  =   "1 933 384",
mrreviewer  =   "Dmitri I. Panyushev",
note  =   "\url{https://doi.org/10.1006/aima.2002.2071}"}

@techreport{hobby1992,
     author =   "John D. Hobby",
      title =   "{A User's Manual for MetaPost}",
       year =   "1992",
      month =   "apr",
   language =   "english",
institution =   "AT\&T Bell Laboratories",
    address =   "Murray Hill, New Jersey",
       date =   "April 1992",
     number =   "162",
     npages =   "ii+88~pages"}

@techreport{CSTR116,
     author =   "Kernighan, Brian W.",
      title =   "{PIC}---{A} Graphics Language for Typesetting",
       type =   "Computing Science Technical Report",
     number =   "116",
institution =   "AT\&T Bell Laboratories",
    address =   "Murray Hill, New Jersey",
       year =   "1984"}

@unpublished{VoQS,
  author    =   "Ball, Martin J. and Esling, John and Dickson, Craig",
  title     =   "{VoQS: Voice Quality Symbols}",
  note      =   "Revised to 1994",
  year      =   "1994"}

@phdthesis{Brown:1988:IEL,
  author    =   "Marcus E. Brown",
  title     =   "An Interactive Environment for Literate Programming",
  school    =   "Texas A\&M University",
  address   =   "TX, USA",
  pages     =   "ix + 102",
  month     =   "aug",
  year      =   "1988"}

@inbook{inbook,
  author    =   "D. W. Baker and N. L. Carter",
  year      =   "1972",
  title     =   "Seismic {V}elocity {A}nisotropy {C}alculated for {U}ltramafic {M}inerals
                and {A}ggregates",
  booktitle =   "Flow and {F}racture of {R}ocks",
  publisher =   "Am. Geophys. Union",
  series    =   "Geophys. Mono.",
  volume    =   "16",
  pages     =   "157--166",
note  =   "\url{https://doi.org/10.1029/GM016p0157}"}


@mastersthesis{segms,
  author    =   "G[unter] S[ergei] Lodha",
  title     =   "Quantitative interpretation of ariborne
                electromagnetic response for a spherical model",
  school    =   "University of Toronto",
  year      =   "1974"}

@incollection{Jones:Phoneme,
  author    =   "Jones, Daniel",
  title     =   "{The term `phoneme'}",
  editor    =   "Jones, W. E. and Laver, J.",
  booktitle =   "Phonetics in Linguistics: A Book of Reading",
  publisher =   "Longman",
  address   =   "London",
  pages     =   "187--204",
  year      =   "1973"}

@booklet{URW:kerning,
  author       = "Bill Murrey",
  title        = "Kerning on the Fly",
  howpublished = "URW Non-Plus-Ultra Typography series",
  address      = "Pittsburg",
  year         = "1991"}

%% WSPC ijcga BibTeX Style File -- version 1.0
%% BibTeX version 0.99c, intended for LaTeX2e
%%
%% 2009/12/14 Rajesh <[email protected]>
%% World Scientific Publishing Co. Pte. Ltd.
%%
%% This is file `ws-ijcga.bst',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% merlin.mbs  (with options: `seq-no,nm-init,ed-au,tit-qq,qx,thtit-a,vol-bf,vnum-x,volp-blk,jdt-p,pp-last,num-xser,jnm-x,pub-date,pre-pub,edby,edbyx,blk-com,pp,ed,xedn,jabr,and-xcom,nfss')
%% ----------------------------------------
%% *** Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems ***
%% *** prepared by Przemyslaw Wesolek ***
%% 
%% Copyright 1994-2002 Patrick W Daly
 % ===============================================================
 % IMPORTANT NOTICE:
 % This bibliographic style (bst) file has been generated from one or
 % more master bibliographic style (mbs) files, listed above.
 %
 % This generated file can be redistributed and/or modified under the terms
 % of the LaTeX Project Public License Distributed from CTAN
 % archives in directory macros/latex/base/lppl.txt; either
 % version 1 of the License, or any later version.
 % ===============================================================
 % Name and version information of the main mbs file:
 % \ProvidesFile{merlin.mbs}[2002/10/21 4.05 (PWD, AO, DPC)]
 %   For use with BibTeX version 0.99a or later
 %-------------------------------------------------------------------
 % This bibliography style file is intended for texts in ENGLISH
 % This is a numerical citation style, and as such is standard LaTeX.
 % It requires no extra package to interface to the main text.
 % The form of the \bibitem entries is
 %   \bibitem{key}...
 % Usage of \cite is as follows:
 %   \cite{key} ==>>          [#]
 %   \cite[chap. 2]{key} ==>> [#, chap. 2]
 % where # is a number determined by the ordering in the reference list.
 % The order in the reference list is that by which the works were originally
 %   cited in the text, or that in the database.
 %---------------------------------------------------------------------

ENTRY
  { address
    author
    booktitle
    chapter
    edition
    editor
    howpublished
    institution
    journal
    key
    month
    note
    number
    organization
    pages
    publisher
    school
    series
    title
    type
    volume
    year
    url
  }
  {}
  { label }
INTEGERS {output.state before.all mid.sentence after.sentence after.block }
FUNCTION {init.state.consts}
{ #0 'before.all :=
  #1 'mid.sentence :=
  #2 'after.sentence :=
  #3 'after.block :=
}
STRINGS {s t}
FUNCTION {output.nonnull}
{ 's :=
  output.state mid.sentence =
    { ", " * write$ }
    { output.state after.block =
        { add.period$ write$
          newline$
          "\newblock " write$
        }
        { output.state before.all =
            'write$
            { add.period$ " " * write$ }
          if$
        }
      if$
      mid.sentence 'output.state :=
    }
  if$
  s
}
FUNCTION {output}
{ duplicate$ empty$
    'pop$
    'output.nonnull
  if$
}
FUNCTION {output.check}
{ 't :=
  duplicate$ empty$
    { pop$ "empty " t * " in " * cite$ * warning$ }
    'output.nonnull
  if$
}
FUNCTION {fin.entry}
{ add.period$
  write$
  newline$
}
FUNCTION {new.block}
{ output.state before.all =
    'skip$
    { after.block 'output.state := }
  if$
}
FUNCTION {new.sentence}
{ output.state after.block =
    'skip$
    { output.state before.all =
        'skip$
        { after.sentence 'output.state := }
      if$
    }
  if$
}
FUNCTION {add.blank}
{  " " * before.all 'output.state :=
}
FUNCTION {date.block}
{
  skip$
}
FUNCTION {not}
{   { #0 }
    { #1 }
  if$
}
FUNCTION {and}
{   'skip$
    { pop$ #0 }
  if$
}
FUNCTION {or}
{   { pop$ #1 }
    'skip$
  if$
}
FUNCTION {non.stop}
{ duplicate$
   "}" * add.period$
   #-1 #1 substring$ "." =
}
FUNCTION {new.block.checka}
{ empty$
    'skip$
    'new.block
  if$
}
FUNCTION {new.block.checkb}
{ empty$
  swap$ empty$
  and
    'skip$
    'new.block
  if$
}
FUNCTION {new.sentence.checka}
{ empty$
    'skip$
    'new.sentence
  if$
}
FUNCTION {new.sentence.checkb}
{ empty$
  swap$ empty$
  and
    'skip$
    'new.sentence
  if$
}
FUNCTION {field.or.null}
{ duplicate$ empty$
    { pop$ "" }
    'skip$
  if$
}
FUNCTION {emphasize}
{ duplicate$ empty$
    { pop$ "" }
    { "\emph{" swap$ * "}" * }
  if$
}
FUNCTION {bolden}
{ duplicate$ empty$
    { pop$ "" }
    { "\textbf{" swap$ * "}" * }
  if$
}
FUNCTION {tie.or.space.prefix}
{ duplicate$ text.length$ #3 <
    { "~" }
    { " " }
  if$
  swap$
}
FUNCTION {capitalize}
{ "u" change.case$ "t" change.case$ }

FUNCTION {space.word}
{ " " swap$ * " " * }
 % Here are the language-specific definitions for explicit words.
 % Each function has a name bbl.xxx where xxx is the English word.
 % The language selected here is ENGLISH
FUNCTION {bbl.and}
{ "and"}

FUNCTION {bbl.etal}
{ "et~al." }

FUNCTION {bbl.editors}
{ "eds." }

FUNCTION {bbl.editor}
{ "ed." }

FUNCTION {bbl.edby}
{ "edited by" }

FUNCTION {bbl.edition}
{ "edition" }

FUNCTION {bbl.volume}
{ "volume" }

FUNCTION {bbl.of}
{ "of" }

FUNCTION {bbl.number}
{ "number" }

FUNCTION {bbl.nr}
{ "no." }

FUNCTION {bbl.in}
{ "in" }

FUNCTION {bbl.pages}
{ "pp." }

FUNCTION {bbl.page}
{ "p." }

FUNCTION {bbl.chapter}
{ "chapter" }

FUNCTION {bbl.techrep}
{ "Technical Report" }

FUNCTION {bbl.mthesis}
{ "Master's thesis" }

FUNCTION {bbl.phdthesis}
{ "Ph.D. thesis" }

MACRO {jan} {"January"}

MACRO {feb} {"February"}

MACRO {mar} {"March"}

MACRO {apr} {"April"}

MACRO {may} {"May"}

MACRO {jun} {"June"}

MACRO {jul} {"July"}

MACRO {aug} {"August"}

MACRO {sep} {"September"}

MACRO {oct} {"October"}

MACRO {nov} {"November"}

MACRO {dec} {"December"}

MACRO {acmcs} {"ACM Comput. Surv."}

MACRO {acta} {"Acta Inf."}

MACRO {cacm} {"Commun. ACM"}

MACRO {ibmjrd} {"IBM J. Res. Dev."}

MACRO {ibmsj} {"IBM Syst.~J."}

MACRO {ieeese} {"IEEE Trans. Software Eng."}

MACRO {ieeetc} {"IEEE Trans. Comput."}

MACRO {ieeetcad}
 {"IEEE Trans. Comput. Aid. Des."}

MACRO {ipl} {"Inf. Process. Lett."}

MACRO {jacm} {"J.~ACM"}

MACRO {jcss} {"J.~Comput. Syst. Sci."}

MACRO {scp} {"Sci. Comput. Program."}

MACRO {sicomp} {"SIAM J. Comput."}

MACRO {tocs} {"ACM Trans. Comput. Syst."}

MACRO {tods} {"ACM Trans. Database Syst."}

MACRO {tog} {"ACM Trans. Graphic."}

MACRO {toms} {"ACM Trans. Math. Software"}

MACRO {toois} {"ACM Trans. Office Inf. Syst."}

MACRO {toplas} {"ACM Trans. Progr. Lang. Syst."}

MACRO {tcs} {"Theor. Comput. Sci."}

FUNCTION {bibinfo.check}
{ swap$
  duplicate$ missing$
    {
      pop$ pop$
      ""
    }
    { duplicate$ empty$
        {
          swap$ pop$
        }
        { swap$
          pop$
        }
      if$
    }
  if$
}
FUNCTION {bibinfo.warn}
{ swap$
  duplicate$ missing$
    {
      swap$ "missing " swap$ * " in " * cite$ * warning$ pop$
      ""
    }
    { duplicate$ empty$
        {
          swap$ "empty " swap$ * " in " * cite$ * warning$
        }
        { swap$
          pop$
        }
      if$
    }
  if$
}
STRINGS  { bibinfo}
INTEGERS { nameptr namesleft numnames }

FUNCTION {format.names}
{ 'bibinfo :=
  duplicate$ empty$ 'skip$ {
  's :=
  "" 't :=
  #1 'nameptr :=
  s num.names$ 'numnames :=
  numnames 'namesleft :=
    { namesleft #0 > }
    { s nameptr
      "{f.~}{vv~}{ll}{, jj}"
      format.name$
      bibinfo bibinfo.check
      't :=
      nameptr #1 >
        {
          namesleft #1 >
            { ", " * t * }
            {
              s nameptr "{ll}" format.name$ duplicate$ "others" =
                { 't := }
                { pop$ }
              if$
              t "others" =
                {
                  " " * bbl.etal *
                }
                {
                  bbl.and
                  space.word * t *
                }
              if$
            }
          if$
        }
        't
      if$
      nameptr #1 + 'nameptr :=
      namesleft #1 - 'namesleft :=
    }
  while$
  } if$
}
FUNCTION {format.names.ed}
{
  format.names
}
FUNCTION {format.authors}
{ author "author" format.names
}
FUNCTION {get.bbl.editor}
{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ }

FUNCTION {format.editors}
{ editor "editor" format.names duplicate$ empty$ 'skip$
    {
      "," *
      " " *
      get.bbl.editor
      *
    }
  if$
}
FUNCTION {format.note}
{
 note empty$
    { "" }
    { note #1 #1 substring$
      duplicate$ "{" =
        'skip$
        { output.state mid.sentence =
          { "l" }
          { "u" }
        if$
        change.case$
        }
      if$
      note #2 global.max$ substring$ * "note" bibinfo.check
    }
  if$
}

FUNCTION {format.title}
{ title
  duplicate$ empty$ 'skip$
    { "t" change.case$ }
  if$
  "title" bibinfo.check
  duplicate$ empty$ 'skip$
    {
      "\enquote{" swap$ *
      "}, " *
    }
  if$
}
FUNCTION {end.quote.title}
{ title empty$
    'skip$
    { before.all 'output.state := }
  if$
}
FUNCTION {output.bibitem}
{ newline$
  "\bibitem{" write$
  cite$ write$
  "}" write$
  newline$
  ""
  before.all 'output.state :=
}

FUNCTION {n.dashify}
{
  't :=
  ""
    { t empty$ not }
    { t #1 #1 substring$ "-" =
        { t #1 #2 substring$ "--" = not
            { "--" *
              t #2 global.max$ substring$ 't :=
            }
            {   { t #1 #1 substring$ "-" = }
                { "-" *
                  t #2 global.max$ substring$ 't :=
                }
              while$
            }
          if$
        }
        { t #1 #1 substring$ *
          t #2 global.max$ substring$ 't :=
        }
      if$
    }
  while$
}

FUNCTION {word.in}
{ bbl.in
  " " * }

FUNCTION {format.url}
    { title emphasize }

FUNCTION {format.date}
{
  month "month" bibinfo.check
  duplicate$ empty$
  year  "year"  bibinfo.check duplicate$ empty$
    { swap$ 'skip$
        { "there's a month but no year in " cite$ * warning$ }
      if$
      *
    }
    { swap$ 'skip$
        {
          swap$
          " " * swap$
        }
      if$
      *
    }
  if$
}
FUNCTION{format.year}
{ year "year" bibinfo.check duplicate$ empty$
    {  "empty year in " cite$ *
       warning$
    }
    {
  "(" swap$ * ")" *
    }
  if$
}
FUNCTION {format.btitle}
{ title "title" bibinfo.check
  duplicate$ empty$ 'skip$
    {
      emphasize
    }
  if$
}
FUNCTION {either.or.check}
{ empty$
    'pop$
    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
  if$
}
FUNCTION {format.bvolume}
{ volume empty$
    { "" }
    { bbl.volume volume tie.or.space.prefix
      "volume" bibinfo.check * *
      series "series" bibinfo.check
      duplicate$ empty$ 'pop$
        { swap$ bbl.of space.word * swap$
          emphasize * }
      if$
      "volume and number" number either.or.check
    }
  if$
}
FUNCTION {format.number.series}
{ volume empty$
    { number empty$
        { series field.or.null }
        { series empty$
            { number "number" bibinfo.check }
        { output.state mid.sentence =
            { bbl.number }
            { bbl.number capitalize }
          if$
          number tie.or.space.prefix "number" bibinfo.check * *
          bbl.in space.word *
          series "series" bibinfo.check *
        }
      if$
    }
      if$
    }
    { "" }
  if$
}

FUNCTION {format.edition}
{ edition duplicate$ empty$ 'skip$
    {
      output.state mid.sentence =
        { "l" }
        { "t" }
      if$ change.case$
      "edition" bibinfo.check
      " " * bbl.edition *
    }
  if$
}
INTEGERS { multiresult }
FUNCTION {multi.page.check}
{ 't :=
  #0 'multiresult :=
    { multiresult not
      t empty$ not
      and
    }
    { t #1 #1 substring$
      duplicate$ "-" =
      swap$ duplicate$ "," =
      swap$ "+" =
      or or
        { #1 'multiresult := }
        { t #2 global.max$ substring$ 't := }
      if$
    }
  while$
  multiresult
}
FUNCTION {format.pages}
{ pages duplicate$ empty$ 'skip$
    { duplicate$ multi.page.check
        {
          bbl.pages swap$
          n.dashify
        }
        {
          bbl.page swap$
        }
      if$
      tie.or.space.prefix
      "pages" bibinfo.check
      * *
    }
  if$
}
FUNCTION {first.page}
{ 't :=
  ""
    {  t empty$ not t #1 #1 substring$ "-" = not and }
    { t #1 #1 substring$ *
      t #2 global.max$ substring$ 't :=
    }
  while$
}

FUNCTION {format.journal.pages}
{ pages duplicate$ empty$ 'pop$
    { swap$ duplicate$ empty$
        { pop$ pop$ format.pages }
        {
          " " *
          format.year * " " *
          swap$
          first.page
          "pages" bibinfo.check
          *
        }
      if$
    }
  if$
}
FUNCTION {format.vol.num.pages}
{ volume field.or.null
  duplicate$ empty$ 'skip$
    {
      "volume" bibinfo.check
    }
  if$
  bolden
}

FUNCTION {format.chapter.pages}
{ chapter empty$
    'format.pages
    { type empty$
    { "ch.~" chapter * }
    { type "l" change.case$ chapter tie.or.space.prefix }
      if$
      pages empty$
    'skip$
    { ", " * format.pages * }
      if$
    }
  if$
}

FUNCTION {format.booktitle}
{
  booktitle "booktitle" bibinfo.check
  emphasize
}
FUNCTION {format.in.ed.booktitle}
{ format.booktitle duplicate$ empty$ 'skip$
    {
      editor "editor" format.names.ed duplicate$ empty$ 'pop$
        {
          get.bbl.editor
          " " * swap$ *
          swap$
          "," *
          " " * swap$
          * }
      if$
      word.in swap$ *
    }
  if$
}
FUNCTION {empty.misc.check}
{ author empty$ title empty$ howpublished empty$
  month empty$ year empty$ note empty$
  and and and and and
    { "all relevant fields are empty in " cite$ * warning$ }
    'skip$
  if$
}
FUNCTION {format.thesis.type}
{ type duplicate$ empty$
    'pop$
    { swap$ pop$
      "t" change.case$ "type" bibinfo.check
    }
  if$
}
FUNCTION {format.tr.number}
{ number "number" bibinfo.check
  type duplicate$ empty$
    { pop$ bbl.techrep }
    'skip$
  if$
  "type" bibinfo.check
  swap$ duplicate$ empty$
    { pop$ "t" change.case$ }
    { tie.or.space.prefix * * }
  if$
}
FUNCTION {format.article.crossref}
{
  key duplicate$ empty$
    { pop$
      journal duplicate$ empty$
        { "need key or journal for " cite$ * " to crossref " * crossref * warning$ }
        { "journal" bibinfo.check emphasize word.in swap$ * }
      if$
    }
    { word.in swap$ * " " *}
  if$
  "\cite{" * crossref * "}" *
}
FUNCTION {format.crossref.editor}
{ editor #1 "{vv~}{ll}" format.name$
  "editor" bibinfo.check
  editor num.names$ duplicate$
  #2 >
    { pop$
      "editor" bibinfo.check
      " " * bbl.etal
      *
    }
    { #2 <
        'skip$
        { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
            {
              "editor" bibinfo.check
              " " * bbl.etal
              *
            }
            {
             bbl.and space.word
              * editor #2 "{vv~}{ll}" format.name$
              "editor" bibinfo.check
              *
            }
          if$
        }
      if$
    }
  if$
}
FUNCTION {format.book.crossref}
{ volume duplicate$ empty$
    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
      pop$ word.in
    }
    { bbl.volume
      swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of space.word *
    }
  if$
  editor empty$
  editor field.or.null author field.or.null =
  or
    { key empty$
        { series empty$
            { "need editor, key, or series for " cite$ * " to crossref " *
              crossref * warning$
              "" *
            }
            { series emphasize * }
          if$
        }
        { key * }
      if$
    }
    { format.crossref.editor * }
  if$
  " \cite{" * crossref * "}" *
}
FUNCTION {format.incoll.inproc.crossref}
{
  editor empty$
  editor field.or.null author field.or.null =
  or
    { key empty$
        { format.booktitle duplicate$ empty$
            { "need editor, key, or booktitle for " cite$ * " to crossref " *
              crossref * warning$
            }
            { word.in swap$ * }
          if$
        }
        { word.in key * " " *}
      if$
    }
    { word.in format.crossref.editor * " " *}
  if$
  " \cite{" * crossref * "}" *
}
FUNCTION {format.org.or.pub}
{ 't :=
  ""
  year empty$
    { "empty year in " cite$ * warning$ }
    'skip$
  if$
  address empty$ t empty$ and
  year empty$ and
    'skip$
    {
      add.blank "(" *
      t empty$
        { address "address" bibinfo.check *
        }
        { t *
          address empty$
            'skip$
            { ", " * address "address" bibinfo.check * }
          if$
        }
      if$
      year empty$
        'skip$
        { t empty$ address empty$ and
            'skip$
            { ", " * }
          if$
          year "year" bibinfo.check
          *
        }
      if$
      ")" *
    }
  if$
}
FUNCTION {format.publisher.address}
{ publisher "publisher" bibinfo.warn format.org.or.pub
}

FUNCTION {format.organization.address}
{ organization "organization" bibinfo.check format.org.or.pub
}

FUNCTION {article}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  end.quote.title
  crossref missing$
    {
      journal
      "journal" bibinfo.check
      emphasize
      "journal" output.check
      add.blank
      format.vol.num.pages output
    }
    { format.article.crossref output.nonnull
    }
  if$
  format.journal.pages
  format.note output
  fin.entry
}
FUNCTION {book}
{ output.bibitem
  author empty$
    { format.editors "author and editor" output.check
    }
    { format.authors output.nonnull
      crossref missing$
        { "author and editor" editor either.or.check }
        'skip$
      if$
    }
  if$
  format.btitle "title" output.check
  crossref missing$
    { format.bvolume output
      format.number.series output
      format.publisher.address output
    }
    {
      format.book.crossref output.nonnull
      format.date "year" output.check
    }
  if$
  format.edition output
  format.note output
  fin.entry
}
FUNCTION {booklet}
{ output.bibitem
  format.authors output
  format.title "title" output.check
  end.quote.title
  howpublished "howpublished" bibinfo.check output
  address "address" bibinfo.check output
  format.date output
  format.note output
  fin.entry
}

FUNCTION {inbook}
{ output.bibitem
  author empty$
    { format.editors "author and editor" output.check
    }
    { format.authors output.nonnull
      crossref missing$
        { "author and editor" editor either.or.check }
        'skip$
      if$
    }
  if$
  format.btitle "title" output.check
  crossref missing$
    {
      format.publisher.address output
      format.bvolume output
      format.chapter.pages "chapter and pages" output.check
      format.number.series output
    }
    {
      format.chapter.pages "chapter and pages" output.check
      format.book.crossref output.nonnull
      format.date "year" output.check
    }
  if$
  format.edition output
  format.note output
  fin.entry
}

FUNCTION {incollection}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  end.quote.title
  crossref missing$
    { format.in.ed.booktitle "booktitle" output.check
      format.publisher.address output
      format.bvolume output
      format.number.series output
      format.chapter.pages output
      format.edition output
    }
    { format.incoll.inproc.crossref output.nonnull
      format.chapter.pages output
    }
  if$
  format.note output
  fin.entry
}
FUNCTION {inproceedings}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  end.quote.title
  crossref missing$
    { format.in.ed.booktitle "booktitle" output.check
      publisher empty$
        { format.organization.address output }
        { organization "organization" bibinfo.check output
          format.publisher.address output
        }
      if$
      format.bvolume output
      format.number.series output
    }
    { format.incoll.inproc.crossref output.nonnull
    }
  if$
  format.pages output
  format.note output
  fin.entry
}
FUNCTION {conference} { inproceedings }
FUNCTION {manual}
{ output.bibitem
  author empty$
    { organization "organization" bibinfo.check
      duplicate$ empty$ 'pop$
        { output
          address "address" bibinfo.check output
        }
      if$
    }
    { format.authors output.nonnull }
  if$
  format.btitle "title" output.check
  author empty$
    { organization empty$
        {
          address "address" bibinfo.check output
        }
        'skip$
      if$
    }
    {
      organization "organization" bibinfo.check output
      address "address" bibinfo.check output
    }
  if$
  format.edition output
  format.date output
  format.note output
  fin.entry
}

FUNCTION {mastersthesis}
{ output.bibitem
  format.authors "author" output.check
  format.title
  "title" output.check
  end.quote.title
  bbl.mthesis format.thesis.type output.nonnull
  school "school" bibinfo.warn output
  address "address" bibinfo.check output
  format.date "year" output.check
  format.note output
  fin.entry
}

FUNCTION {misc}
{ output.bibitem
  format.authors output
  format.title output
  end.quote.title
  howpublished "howpublished" bibinfo.check output
  format.date output
  format.note output
  fin.entry
  empty.misc.check
}
FUNCTION {phdthesis}
{ output.bibitem
  format.authors "author" output.check
  format.title
  "title" output.check
  end.quote.title
  bbl.phdthesis format.thesis.type output.nonnull
  school "school" bibinfo.warn output
  address "address" bibinfo.check output
  format.date "year" output.check
  format.note output
  fin.entry
}

FUNCTION {proceedings}
{ output.bibitem
  editor empty$
    { organization "organization" bibinfo.check output
    }
    { format.editors output.nonnull }
  if$
  format.btitle "title" output.check
  format.bvolume output
  format.number.series output
  editor empty$
    { publisher empty$
        'skip$
        {
          format.publisher.address output
        }
      if$
    }
    { publisher empty$
        {
          format.organization.address output }
        {
          organization "organization" bibinfo.check output
          format.publisher.address output
        }
      if$
     }
  if$
  format.note output
  fin.entry
}

FUNCTION {techreport}
{ output.bibitem
  format.authors "author" output.check
  format.title
  "title" output.check
  end.quote.title
  format.tr.number output.nonnull
  institution "institution" bibinfo.warn output
  address "address" bibinfo.check output
  format.date "year" output.check
  format.note output
  fin.entry
}

FUNCTION {unpublished}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  end.quote.title
  format.date output
  format.note "note" output.check
  fin.entry
}

FUNCTION {default.type} { misc }
READ
STRINGS { longest.label }
INTEGERS { number.label longest.label.width }
FUNCTION {initialize.longest.label}
{ "" 'longest.label :=
  #1 'number.label :=
  #0 'longest.label.width :=
}
FUNCTION {longest.label.pass}
{ number.label int.to.str$ 'label :=
  number.label #1 + 'number.label :=
  label width$ longest.label.width >
    { label 'longest.label :=
      label width$ 'longest.label.width :=
    }
    'skip$
  if$
}
EXECUTE {initialize.longest.label}
ITERATE {longest.label.pass}
FUNCTION {begin.bib}
{ preamble$ empty$
    'skip$
    { preamble$ write$ newline$ }
  if$
  "\begin{thebibliography}{"  longest.label  * "}" *
  write$ newline$
%  "\newcommand{\enquote}[1]{``#1''}"
   "\newcommand{\enquote}[1]{#1}"
  write$ newline$
}
EXECUTE {begin.bib}
EXECUTE {init.state.consts}
ITERATE {call.type$}
FUNCTION {end.bib}
{ newline$
  "\end{thebibliography}" write$ newline$
}
EXECUTE {end.bib}
FUNCTION {disp.msg.screen} { #1 }
FUNCTION {type.msg}
{ disp.msg.screen
     { "<ws-ijcga.bst>"
       top$
       "BibTeX style file for ijcga"
       top$
       "version 1 (2010/03/03), numbered, superscript citation"
       top$
       "for support: Rajesh, [email protected]"
       top$
     }
     { skip$ }
   if$
}
EXECUTE {type.msg}
%% End of customized bst file
%%
%% End of file `ws-ijcga.bst'.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Text Area: 8in (include Runningheads) x 5in
%% ws-ijcga.cls   :   18-11-2024
%% Class file to use with ws-ijcga.tex written in LaTeX2E. 
%% The content, structure, format and layout of this style file is the 
%% property of World Scientific Publishing Co. Pte. Ltd. 
%% Copyright 2024 by World Scientific Publishing Co. 
%% All rights are reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\NeedsTeXFormat{LaTeX2e}[1995/06/01]
\ProvidesClass{ws-ijcga}[2024/11/18 v1.5g Standardized LaTeX document class]
\@twosidetrue\@mparswitchtrue\@twocolumnfalse
\newif\if@openright
\@openrighttrue
\newif\if@restonecol
%
%
\newdimen\trimheight \trimheight9.75truein
\newdimen\trimwidth \trimwidth6.50truein
\newdimen\typeheight \typeheight48.1pc
\newdimen\typewidth \typewidth30pc
\newdimen\wsdraftrule \wsdraftrule=0pt
\newdimen\tempdimen
\newdimen\tablewidth
\newdimen\normaltextheight
\newbox\tempbox
\newdimen\tablewd
%
%
\DeclareOption{wsdraft}{\setlength\overfullrule{5pt}\wsdraftrule0.1pt}
\DeclareOption{final}{\setlength\overfullrule{0pt}}

\ExecuteOptions{a4paper,10pt,twoside,onecolumn,final}
\ProcessOptions
%
%\hoffset=-1.5cm
%\voffset=-0.5cm
%
\newcommand\appendixname{Appendix}
\newcommand\abstractname{Abstract}
\newcommand\bibname{References}%
\newcommand\contentsname{Contents}
\newcommand\indexname{Index}
\newcommand\figurename{Fig.}
\newcommand\tablename{Table}
\newcommand\partname{Part}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Font Defs. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\foliofont{\fontsize{8}{10}\selectfont}
\def\bibfont{\fontsize{9}{11}\selectfont}
\def\rhfont{\footnotesize\itshape{}}
\def\catchlinefont{\footnotesize}
\def\titlefont{\fontsize{10}{13}\bfseries\boldmath\selectfont\centering{}}
%\def\authorfont{\centering\footnotesize}
\def\authorfont{\footnotesize}
\def\affiliationfont{\centering\footnotesize\it}
\def\abstractfont{\footnotesize}
%\let\affiliationfont\rhfont
\def\datefont{\footnotesize}
\def\sectionfont{\bfseries\boldmath\rightskip2pc plus1fill{}}
\def\subsectionfont{\bfseries\boldmath\itshape\rightskip2pc plus1fill{}}
\def\subsubsectionfont{\itshape\rightskip2pc plus1fill{}}
\def\paragraphfont{\bfseries\boldmath}
\def\subparagraphfont{\itshape}
\def\figurecaptionfont{\footnotesize}
\def\tablefont{\footnotesize}
\def\tablecaptionfont{\footnotesize}
\def\tabnotefont{\footnotesize}
\def\TCHfont{\bf}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Font Defs. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
\DeclareOldFontCommand{\rm}{\rmfamily}{\mathrm}
\DeclareOldFontCommand{\sf}{\sffamily}{\mathsf}
\DeclareOldFontCommand{\tt}{\ttfamily}{\mathtt}
\DeclareOldFontCommand{\bf}{\bfseries}{\mathbf}
\DeclareOldFontCommand{\it}{\itshape}{\mathit}
\DeclareOldFontCommand{\sl}{\slshape}{\@nomath\sl}
\DeclareOldFontCommand{\sc}{\scshape}{\@nomath\sc}
\DeclareRobustCommand\cal{\@fontswitch\relax\mathcal}
\DeclareRobustCommand\mit{\@fontswitch\relax\mathnormal}
\DeclareOldFontCommand{\bi}{\bfseries\itshape}{\@nomath\bi}
\renewcommand{\rmdefault}{cmr}%
%
\renewcommand\normalsize{%
   \@setfontsize\normalsize\@xpt{13}%\@xiiipt
   \abovedisplayskip 6\p@\@plus4\p@\@minus2\p@
   \abovedisplayshortskip\abovedisplayskip
   \belowdisplayshortskip\abovedisplayshortskip
   \belowdisplayskip\abovedisplayskip
   \let\@listi\@listI}
\normalsize
%
\newcommand\small{%
   \@setfontsize\small\@ixpt{11}%
   \abovedisplayskip 8\p@ \@plus3\p@ \@minus4\p@
   \abovedisplayshortskip \z@ \@plus2\p@
   \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@
   \def\@listi{\leftmargin\leftmargini
               \topsep 4\p@ \@plus2\p@ \@minus2\p@
               \parsep 2\p@ \@plus\p@ \@minus\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip}
%
\newcommand\footnotesize{%
   \@setfontsize\footnotesize\@viiipt{10}%
   \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@
   \abovedisplayshortskip \z@ \@plus\p@
   \belowdisplayshortskip 3\p@ \@plus\p@ \@minus2\p@
   \def\@listi{\leftmargin\leftmargini
               \topsep 3\p@ \@plus\p@ \@minus\p@
               \parsep 2\p@ \@plus\p@ \@minus\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip}
%
\newcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt}
\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}
\newcommand\large{\@setfontsize\large\@xiipt{14}}%
\newcommand\Large{\@setfontsize\Large\@xivpt{16}}%%
\newcommand\LARGE{\@setfontsize\LARGE\@xviipt{22}}
\newcommand\huge{\@setfontsize\huge\@xxpt{25}}
\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%

\setlength\parindent{1.5em}
%
\setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@}
\setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@}
%
\setlength\headheight{5\p@}
\setlength\headsep   {19pt}
\setlength\topskip   {7\p@}
\setlength\footskip{24pt}%18pt
\setlength\maxdepth{4\p@}
%
\setlength\textwidth{\typewidth}
\@settopoint\textwidth
\setlength\textheight\typeheight
\advance\textheight-\headheight
\advance\textheight-\headsep
\setlength\normaltextheight{\textheight}
%
\setlength\oddsidemargin{21mm}%.625in%
\setlength\evensidemargin{\trimwidth}
\addtolength\evensidemargin{-\textwidth}
\addtolength\evensidemargin{-\oddsidemargin}
\setlength\topmargin{.85926in}%
%
\setlength\marginparwidth{.75in}
\setlength\marginparsep{7\p@}
\setlength\marginparpush{5\p@}
%
\setlength\footnotesep{6\p@}
\setlength{\skip\footins}{18\p@ \@plus 5\p@ \@minus 2\p@}
%
\setlength\floatsep    {18\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\textfloatsep{18\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\intextsep   {18\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\dblfloatsep    {18\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\dbltextfloatsep{18\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\@fptop{0\p@}
\setlength\@fpsep{8\p@ \@plus 2fil}
\setlength\@fpbot{0\p@ \@plus 1fil}
\setlength\@dblfptop{0\p@ \@plus 1fil}
\setlength\@dblfpsep{8\p@ \@plus 2fil}
\setlength\@dblfpbot{0\p@ \@plus 1fil}
%
\setlength\partopsep{0\p@}
\setlength\lineskip{1\p@}
\setlength\normallineskip{1\p@}%
\renewcommand\baselinestretch{}%{}
\setlength\parskip{0\p@}
%
\@lowpenalty   51
\@medpenalty  151
\@highpenalty 301
%
\setcounter{topnumber}{3}
\renewcommand\topfraction{.98}
\setcounter{bottomnumber}{3}
\renewcommand\bottomfraction{.98}
\setcounter{totalnumber}{6}
\renewcommand\textfraction{.01}
\renewcommand\floatpagefraction{.98100}
\setcounter{dbltopnumber}{2}
\renewcommand\dbltopfraction{.981}
\renewcommand\dblfloatpagefraction{.99}
%
\setlength\arraycolsep{1.5\p@}
\setlength\tabcolsep{6\p@}
\setlength\arrayrulewidth{.4\p@}
\setlength\doublerulesep{2\p@}
\setlength\tabbingsep{\labelsep}
%\skip\@mpfootins = \skip\footins
%
\setlength\fboxsep{3\p@}
\setlength\fboxrule{.4\p@}
%
\setlength\columnsep{10\p@}
\setlength\columnseprule{0\p@}
%
%
\DeclareMathSizes{28}{28}{25}{20}
\DeclareMathSizes{24}{24}{21}{18}
\DeclareMathSizes{22}{22}{19}{17}
\DeclareMathSizes{20}{20}{17}{15}
\DeclareMathSizes{18}{18}{15}{10}
\DeclareMathSizes{12}{11}{8}{5}
\DeclareMathSizes{11}{11}{8}{5}
\DeclareMathSizes{10}{10}{7}{5}
\DeclareMathSizes{9.5}{9}{7}{5}
\DeclareMathSizes{9}{9}{7}{5}
\DeclareMathSizes{8}{8}{6}{5}
\DeclareMathSizes{7}{7}{5}{5}
\DeclareMathSizes{6}{6}{5}{5}
\DeclareMathSizes{5}{5}{5}{5}
\def\bm#1{\mathchoice
        {\mbox{\boldmath$#1$}}%
          {\mbox{\boldmath$#1$}}%
          {\mbox{\boldmath$\scriptstyle#1$}}%
          {\mbox{\boldmath$\scriptscriptstyle#1$}}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%% Article FM %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\title#1{\gdef\@title{{{#1}}}}
\newcommand\maketitle{\par
  \begingroup
   \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
    \def\@makefnmark{\rlap{\@textsuperscript{\normalfont\@thefnmark}}}%
    \long\def\@makefntext##1{\noindent
        \@textsuperscript{\normalfont\@thefnmark}{##1}}%
      \newpage
      \global\@topnum\z@
      \@maketitle
    \thispagestyle{plain}\@thanks
  \endgroup
  \setcounter{footnote}{0}%
  \global\let\thanks\relax
  \global\let\maketitle\relax
  \global\let\@maketitle\relax
  \global\let\@thanks\@empty
  \global\let\@author\@empty
  \global\let\@title\@empty
  \global\let\title\relax
  \global\let\author\relax
}
\def\@maketitle{%
  \newpage
  \null
  \vspace*{-10pt}
   \vspace*{-25pt}% to have the bylines on the beginning of the page
  \@clinebuf
  \vspace*{52pt}
  \begin{center}%
  \let\footnote \thanks
  {\titlefont\@title \par}%
  \vspace*{28pt}
  \@aabuffer\par
  \end{center}%
}
%
\def\thebepage{\thepage}
\def\theeepage{\pageref{eof}}
%
\newenvironment{history}{%
	\addvspace{-2pt plus-2pt minus-2pt}
   \authorfont\begin{center}\vskip-\lastskip
}{%
   \end{center}
	\addvspace{15pt plus2pt minus2pt}
}
%
\def\email#1{\it #1\par}
\def\http#1{\it http://#1\par}
\def\url#1{\it #1\par}
\def\received#1{Received~#1\par}
\def\revised#1{Revised~#1\par}
\def\accepted#1{Accepted~#1\par}
\def\published#1{Published~#1\par}
\def\comby#1{Communicated\ by~#1\par}
%
\def\@clinebuf{}
\def\catchline{\expandafter\def\expandafter\@clinebuf\expandafter
        {\@clinebuf\catchlinefont
        \noindent International Journal of Computational Geometry\par 
        \noindent \& Applications\par
        \noindent \copyright\ World Scientific Publishing Company\par
        }\relax\par
        }%
\def\No{No.}
%
\def\@aabuffer{}
\def\author#1{\expandafter\def\expandafter\@aabuffer\expandafter
        {\@aabuffer{\authorfont{{{#1}}}}\relax\par
        \vspace*{3pt}}}
%
\def\address#1{\expandafter\def\expandafter\@aabuffer\expandafter
        {\@aabuffer{\affiliationfont{#1}}\relax\par
        \vspace*{13pt}}}
%
\def\keywords#1{\par
	\vspace*{8pt}
	{\authorfont{\leftskip18pt\rightskip\leftskip
	\noindent{\it Keywords}\/:\ #1\par}}\par}
%
\def\category#1#2{\par
        \vspace*{8pt}
        {\authorfont{\leftskip18pt\rightskip\leftskip
        \noindent{\it Categories}\/:\ #1:\ #2\par}}\par}
%
\newenvironment{abstract}{\par%
	\abstractfont
  	\noindent\leftskip18pt\rightskip18pt
}{%
  \par}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sectioning %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\setcounter{secnumdepth}{3}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]
\renewcommand\thesection      {\arabic{section}}
\renewcommand\thesubsection   {\thesection.\arabic{subsection}}
\renewcommand\thesubsubsection{\thesubsection .\arabic{subsubsection}}
\renewcommand\theparagraph    {\thesubsubsection.\arabic{paragraph}}
\renewcommand\thesubparagraph {\theparagraph.\arabic{subparagraph}}
%
\newcommand\section{\@startsection{section}{1}{\z@}{-18pt \@plus-3pt minus-6pt}{5pt}{\sectionfont}}
\newcommand\subsection{\@startsection{subsection}{2}{\z@}{-18pt \@plus-3pt minus-6pt}{5pt}{\subsectionfont}}
\newcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}{-18pt \@plus-3pt minus-3pt}{5pt}{\subsubsectionfont}}
\newcommand\paragraph{\@startsection{paragraph}{4}{\z@}{12pt \@plus -3pt}{-.5em}{\paragraphfont}}
\newcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}{3.25ex \@plus1ex}{-1em}{\subparagraphfont}}
%
\def\@seccntformat#1{{\upshape{\csname the#1\endcsname.}}\hskip .5em}
%
%\gdef\@author{}
%
%%%%%%%%%%%%%%%%%%%%%%%% Table of Contents %%%%%%%%%%%%%%%%%%%%%%%
%
\newcommand\@pnumwidth{1.55em}
\newcommand\@tocrmarg{2.55em}
\newcommand\@dotsep{4.5}
\setcounter{tocdepth}{3}
\newcommand\tableofcontents{%
    \section*{\contentsname
        \@mkboth{%
           \contentsname}{\contentsname}}%
    \@starttoc{toc}%
    }
\newcommand\l@section[2]{%
  \ifnum \c@tocdepth >\z@
    \addpenalty\@secpenalty
    \addvspace{1.0em \@plus\p@}%
    \setlength\@tempdima{1.5em}%
    \begingroup
      \parindent \z@ \rightskip \@pnumwidth
      \parfillskip -\@pnumwidth
      \leavevmode \bfseries
      \advance\leftskip\@tempdima
      \hskip -\leftskip
      #1\nobreak\hfil \nobreak\hbox to \@pnumwidth{\hss #2}\par
    \endgroup
  \fi}
\newcommand\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\newcommand\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\newcommand\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\newcommand\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\newcommand\listoffigures{%
    \section*{\listfigurename
      \@mkboth{\listfigurename}%
              {\listfigurename}}%
    \@starttoc{lof}%
    }
\newcommand\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\newcommand\listoftables{%
    \section*{\listtablename
      \@mkboth{%
          \listtablename}{\listtablename}}%
    \@starttoc{lot}%
    }
\let\l@table\l@figure
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Lists %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\setlength\leftmargini{3pc}
\setlength\leftmarginii{2.2em}
\setlength\leftmarginiii{1.87em}
\setlength\leftmarginiv{1.7em}
\setlength\leftmarginv{1em}
\setlength\leftmarginvi{1em}
\setlength\leftmargin{\leftmargini}
\setlength\listparindent{\parindent}
\setlength\labelsep{.5em}
\setlength\labelwidth{\leftmargini}
\addtolength\labelwidth{-\labelsep}
\@beginparpenalty -\@lowpenalty
\@endparpenalty   -\@lowpenalty
\@itempenalty     -\@lowpenalty
\renewcommand\theenumi{\arabic{enumi}}
\renewcommand\theenumii{\alph{enumii}}
\renewcommand\theenumiii{\roman{enumiii}}
\renewcommand\theenumiv{\Alph{enumiv}}
\newcommand\labelenumi{(\theenumi)}
\newcommand\labelenumii{(\theenumii)}
\newcommand\labelenumiii{\theenumiii.}
\newcommand\labelenumiv{\theenumiv.}
\renewcommand\p@enumii{\theenumi}
\renewcommand\p@enumiii{\theenumi(\theenumii)}
\renewcommand\p@enumiv{\p@enumiii\theenumiii}
\newcommand\labelitemi{$\m@th\bullet$}
\newcommand\labelitemii{\normalfont\bfseries --}
\newcommand\labelitemiii{$\m@th\ast$}
\newcommand\labelitemiv{$\m@th\cdot$}
%
%
\def\@listI{\leftmargin\leftmargini
            \listparindent\parindent
            \parsep \z@\labelsep.5em
            \topsep 6.5\p@ \@plus3\p@% \@minus2\p@
            \itemsep0\p@}
%
\let\@listi\@listI
\@listi
%
\def\@listii {\leftmargin\leftmarginii
              \labelwidth\leftmarginii
              \advance\labelwidth-\labelsep
              \topsep    3.5\p@ \@plus2\p@ \@minus\p@
              \parsep    \z@
              \itemsep\z@}
\def\@listiii{\leftmargin\leftmarginiii
              \labelwidth\leftmarginiii
              \advance\labelwidth-\labelsep
              \topsep 3.5\p@ \@plus\p@\@minus\p@
              \parsep \z@
             % \partopsep \p@ \@plus\z@ \@minus\p@
              \itemsep0\p@}%
\def\@listiv {\leftmargin\leftmarginiv
              \labelwidth\leftmarginiv
              \advance\labelwidth-\labelsep}
\def\@listv  {\leftmargin\leftmarginv
              \labelwidth\leftmarginv
              \advance\labelwidth-\labelsep}
\def\@listvi {\leftmargin\leftmarginvi
              \labelwidth\leftmarginvi
              \advance\labelwidth-\labelsep}
%
\def\enummax#1{\setbox\tempbox=\hbox{#1\hskip\labelsep}%
  \expandafter\global\csname leftmargin\romannumeral\the\@enumdepth\endcsname\wd\tempbox}
%
\def\enumerate{\@ifnextchar[{\@enumerate}{\@enumerate[\csname label\@enumctr\endcsname]}}
%
\def\@enumerate[#1]{\ifnum \@enumdepth >3 \@toodeep\else
      \advance\@enumdepth \@ne\edef\@enumctr{enum\romannumeral\the\@enumdepth}%
      \enummax{#1}\list
      {\csname label\@enumctr\endcsname}{\usecounter
        {\@enumctr}\def\makelabel##1{\hss\llap{##1}}}\fi}
%
\let\Item\item
\newenvironment{enumeroman}{%
  \def\theenumi{\roman{enumi}}\def\theenumii{\alph{enumii}}%
  \def\labelenumi{(\theenumi)}\def\labelenumii{(\theenumii)}%
                \let\item\Item
  \begin{enumerate}%
}{%
  \end{enumerate}}
%
\newenvironment{alphlist}{%
  \def\theenumi{\alph{enumi}}\def\theenumii{\roman{enumii}}%
  \def\labelenumi{(\theenumi)}\def\labelenumii{(\theenumii)}%
                \let\item\Item
  \begin{enumerate}%
}{%
  \end{enumerate}}
%
\newenvironment{arabiclist}{%
        \def\theenumi{\arabic{enumi}}\def\theenumii{\alph{enumii}}
        \def\labelenumi{(\theenumi)}\def\labelenumii{(\theenumii)}%
        \let\item\Item
        \begin{enumerate}
        }{%
        \end{enumerate}}
%
\newenvironment{romanlist}{%
        \def\theenumi{\roman{enumi}}\def\theenumii{\alph{enumii}}
        \def\labelenumi{(\theenumi)}\def\labelenumii{(\theenumii)}%
        \let\item\Item
        \begin{enumerate}
        }{%
        \end{enumerate}}
%
\newenvironment{itemlist}{%
        \def\labelenumi{\labelitemi}
        \let\item\Item
        \begin{enumerate}
        }{%
        \end{enumerate}}
%
\newenvironment{description}
               {\list{}{\labelwidth\z@ \itemindent-\leftmargin
                        \let\makelabel\descriptionlabel}}
               {\endlist}
\newcommand*\descriptionlabel[1]{\hspace\labelsep
                                \normalfont\bfseries #1}
%
\newenvironment{unnumlist}{%
        \let\item\Item
        \leftmargini2pc
        \ifnum \@enumdepth >3 \@toodeep\else
        \advance\@enumdepth \@ne
        \list{}{\itemindent-2pc\topsep6pt
              \def\makelabel##1{\hss\llap{##1}}}%
   \fi
}{%
  \endlist}
%
%%%%%%%%%%%%%%%%%%%%%%%%%% Poetry %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newenvironment{verse}
               {\let\\\@centercr
                \list{}{\itemsep      \z@
                        \itemindent   -1.5em%
                        \listparindent\itemindent
                        \rightmargin  \leftmargin
                        \advance\leftmargin 1.5em}%
                \item\relax}
               {\endlist}
\let\poetry\verse
\let\endpoetry\endverse
%
%%%%%%%%%%%%%%%%%%%%%%%% Extract %%%%%%%%%%%%%%%%%%%%%%%
%
\newenvironment{quotation}
               {\list{}{\listparindent 1.5em%
                        \itemindent    \listparindent
                        \rightmargin   \leftmargin
                        \parsep        \z@ \@plus\p@}%
                \item\relax}
               {\endlist}
\newenvironment{quote}
               {\list{}{\rightmargin\leftmargin}%
                \item\relax}
               {\endlist}
%
\let\extract\quotation
\let\endextract\endquotation
%
\def\source#1{\par\hspace*{\fill}{\it#1}\par}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Maths %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\renewcommand\theequation{\arabic{equation}}
%
\def\bstrut{\vrule width0pt depth5pt}
\def\tstrut{\vrule width0pt height10pt}
\jot=3pt
%

\renewenvironment{equation}{\@equation}{\end@equation}
%
\def\refstepeqcnt{\refstepcounter{equation}}
\def\eqnnum{\displaywidth\linewidth\hbox{\@eqnnum}}
%
\def\@equation{\let\topsep\abovedisplayskip\@beginparpenalty\predisplaypenalty\@endparpenalty\postdisplaypenalty
     \refstepeqcnt
     \trivlist \item[]\leavevmode
       \hbox to\linewidth\bgroup\hfill $\m@th% $
       \displaystyle}%
\def\end@equation{$\hfill\eqnnum\egroup\endtrivlist}
%
\renewenvironment{eqnarray}{%
   \stepcounter{equation}%
   \def\@currentlabel{\p@equation\theequation}%
   \global\@eqnswtrue
   \m@th
   \global\@eqcnt\z@
   \tabskip\@centering
   \let\\\@eqncr
   $$\everycr{}\halign to\displaywidth\bgroup
       \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
      &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil
      &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep
         $\displaystyle{##}$\hfil\tabskip\@centering
      &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup
         \tabskip\z@skip
      \cr}
        {%
      \@@eqncr
      \egroup
      \global\advance\c@equation\m@ne
   $$\global\@ignoretrue
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Floats %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\FigName{figure}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\figurename{Fig.}
\newcounter{figure}
\renewcommand\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename~\thefigure}
\newenvironment{figure}
               {\@float{figure}}
               {\end@float}
\newenvironment{figure*}
               {\@dblfloat{figure}}
               {\end@dblfloat}
%
%%%%%%%%%%%%%%%%%%%%%%%%%% Tables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcounter{table}
\def\tablename{Table}
\renewcommand\thetable{\@arabic\c@table}
\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename~\thetable}
\newenvironment{table}
               {\@float{table}}
               {\end@float}
\newenvironment{table*}
               {\@dblfloat{table}}
               {\end@dblfloat}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\tableformat#1{\centerline{#1}}
\newdimen\tabledim
\long\def\tbl#1#2{%
\global\setbox\tempbox\hbox{\tablefont #2}%
 \global\tabledim\wd\tempbox
 \tableformat{\vbox{\hsize\tabledim
                   \caption{#1}
                   \box\tempbox}}%
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\long\def\ttbl#1#2#3{%
%       \parindent\z@
%       \noindent
%       \tablecaptionfont
%       \caption{#2}%
%       \tablewd\hsize
%       \advance\tablewd-#1
%       \global\divide\tablewd\tw@
%       \ifdim \wd\wscaptionbox<#1
%       \centerline{\unhbox\wscaptionbox}
%       \else
%       {\leftskip\tablewd% plus1fill{}
%       \rightskip\tablewd% plus1fill{}
%       \unhbox\wscaptionbox\par}
%       \fi
%       \vskip-8pt
%       \centerline{#3}
%}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newenvironment{InTextTable}{%
        \par\addvspace{16pt plus6pt minus6pt}%
        \begin{center}
        \tablecaptionfont\noindent\ignorespaces
}{%
        \end{center}
        \par\addvspace{17pt plus6pt minus6pt}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\tabnotehead{Note}
\def\tabsourcehead{Source}
\newenvironment{tabnote}{%
   \par\addvspace{2pt}
   \setbox\tempbox\vbox\bgroup\hsize\tabledim\parindent12pt
   \tabnotefont
   \@ifnextchar[{\@tabnote}{\@tabnote[\tabnotehead]}%
}{%
                \par\egroup
   \tableformat{\box\tempbox}}
%
\def\@tabnote[#1]{\vskip6pt\noindent\def\@Tempa{#1}\ifx\@Tempa\@empty\hskip0pt\else{\it#1}:\hskip5pt\ignorespaces\fi}
%
\def\tabmark#1{\noindent\hbox{\normalsize$\m@th^{#1}$}\ignorespaces}
%
\newenvironment{tabsource}{%
   \let\tabnotehead\tabsourcehead
   \begin{tabnote}
}{%
   \end{tabnote}
}
%
\def\Hline{%
  \noalign{\ifnum0=`}\fi\hrule \@height 2\arrayrulewidth \futurelet
   \@tempa\@xhline}
%
\def\x{@{\extracolsep{\fill}}}
\def\toprule{\Hline\\[-6.5pt]}
\def\colrule{\\[-10pt]\hline\\[-6pt]}
\def\TMcolrule{\\[-9.5pt]\hline\\[-9.5pt]}
\def\botrule{\\[-9pt]\Hline}
\def\crule#1{\\[-10pt]#1\\[-6pt]}
%
%%%%%%%%%%%%%%%%%%%%%%%% Caption %%%%%%%%%%%%%%%%%%%%%%%
%
\newlength\abovecaptionskip
\newlength\belowcaptionskip
\setlength\abovecaptionskip{10\p@}
%\setlength\belowcaptionskip{0\p@}
\setlength\belowcaptionskip{4\p@}
\long\def\@makecaption#1#2{%
  \figurecaptionfont
  \vskip\abovecaptionskip
  \sbox\@tempboxa{#1. #2}%
  \ifdim \wd\@tempboxa >\hsize
    #1. #2\par
  \else
    \global \@minipagefalse
    \hbox to \hsize{\hfil\box\@tempboxa\hfil}%
  \fi
  \vskip\belowcaptionskip}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Footnote %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\renewcommand\footnoterule{%
  \kern-3\p@
  \hrule depth0pt height0pt \@width.2\columnwidth
  \kern2.6\p@}
\newcommand\@makefntext[1]{%
    \parindent 1em%
    \noindent
     \@makefnmark#1}
%
\def\@fnsymbol#1{\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or
        \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
        \or \ddagger\ddagger \else\@ctrerr\fi}}
%
\def\thefootnote{\alph{footnote}}
\def\@makefnmark{{$^{\rm \@thefnmark}$}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Page Style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\mark{{}{}}
%
\def\ps@plain{%
     \let\@mkboth\@gobbletwo
     \let\@oddhead\@empty
     \def\@oddfoot{\hfill\mbox{\lower12pt\hbox{\foliofont\thepage}}\hfill}%
%     \def\@oddfoot{\hfill\mbox{\hbox{\foliofont\thepage}}\hfill}%
     \let\@evenhead\@empty
     \let\@evenfoot\@oddfoot}
%
\def\RightMark{}
%
\def\ps@headings{%
    \let\@oddfoot\@empty
    \let\@evenfoot\@empty
    \def\@evenhead{\rhfont{\upshape{\thepage}}\hskip1em\leftmark\hfill}%
    \def\@oddhead{\hfill\rhfont\rightmark\hskip1em{\upshape{\thepage}}}%
    \let\@mkboth\markboth
    \def\authormark##1{\markboth{##1}{\RightMark}}%
    \def\chaptermark##1{\gdef\RightMark{##1}\markright{##1}}}%
    %\def\sectionmark##1{\gdef\RightMark{##1}\markright{##1}}}%
%
\def\ps@myheadings{%
    \let\@oddfoot\@empty\let\@evenfoot\@empty
    \def\@evenhead{\rlap{\foliofont \thepage}\hfill{\rhfont\leftmark}\hfill}%
    \def\@oddhead{\hfill{\rhfont\rightmark}\hfill{\foliofont\thepage}}%
    \let\@mkboth\@gobbletwo
    \let\chaptermark\@gobble
    \let\sectionmark\@gobble}
%
\def\ps@pblind{%
        \let\@mkboth\@gobbletwo
        \def\@evenhead{}%
        \def\@oddhead{}
        \def\@oddfoot{\hfill\mbox{\lower8pc\hbox{}}\hfill}
   \let\@evenfoot\@oddfoot}
%

%%%%%%%%%%%%%%%%%%%%%%%%%%%% THEOREM ENVIRONMENTS %%%%%%%%%%%%%%%%%%%%%%%%

\let\Definitionfont\upshape
\let\Questionfont\upshape
\let\Notationfont\upshape
\let\Remarkfont\upshape
\let\Examplefont\upshape
\let\Stepfont\upshape
\let\Propfont\upshape
%
\let\Theoremfont\itshape
\let\Corollaryfont\itshape
\let\Propositionfont\itshape
\let\Lemmafont\itshape
\let\Stepheadfont\itshape
\let\Claimfont\itshape
\let\Conjecturefont\itshape
\let\Theoremheadfont\bfseries
\let\Corollaryheadfont\bfseries
\let\Propositionheadfont\bfseries
\let\Lemmaheadfont\bfseries
\let\Definitionheadfont\bfseries
\let\Questionheadfont\bfseries
\let\Notationheadfont\bfseries
\def\Exampleheadfont{\bfseries}
\def\Remarkheadfont{\bfseries}
\def\Propheadfont{\bfseries}
\def\Claimheadfont{\bfseries}
\def\Conjectureheadfont{\bfseries}
%

\newtheorem{theorem}{Theorem}%[section]   
\newtheorem{corollary}{Corollary}%[section]
\newtheorem{lemma}{Lemma}%[section]
\newtheorem{proposition}{Proposition}%[section]
\newtheorem{definition}{Definition}%[section]
\newtheorem{example}{Example}%[section]
\newtheorem{remark}{Remark}%[section]
\newtheorem{notation}{Notation}[section]
\newtheorem{question}{Question}[section]
\newtheorem{prop}{Prop}[section]
\newtheorem{step}{Step}
\newtheorem{claim}{Claim}[section]
\newtheorem{conjecture}{Conjecture}[section]
%

\def\@xthm#1#2{\@begintheorem{#2}{\csname the#1\endcsname}{}\ignorespaces}
%

%%%%%%%%%%%%%%%%%%%%%% UPDATED BY SOORAN1 - 6-6-2001 %%%%%%%%%%%%%%%%%%%%%
%
\def\@ythm#1#2[#3]{\@opargbegintheorem{#2}{\csname
       the#1\endcsname}{#3}\ignorespaces}%
%

\def\@begintheorem#1#2#3{\par\addvspace{8pt plus3pt minus2pt}%
              \noindent{\csname#1headfont\endcsname#1\ \ignorespaces#3 #2.}%
              \csname#1font\endcsname\hskip.5em\ignorespaces}
\def\@endtheorem{\par\addvspace{8pt plus3pt minus2pt}\@endparenv}
%

%%%%%%%%%%%%%%%%%%%%%% UPDATED BY SOORAN2 - 6-6-2001 %%%%%%%%%%%%%%%%%%%%%
%
\def\@opargbegintheorem#1#2#3{\par\addvspace{6pt plus3pt minus2pt}%
	\def\@tempa{#3}%
	\noindent{\bf #1 #2 \ifx\@tempa\empty\unskip\else\unskip\ (#3).\fi\hskip.5em}\csname#1font\endcsname\ignorespaces
%	\noindent{\bf #2 \ifx\@tempa\empty\unskip\else\unskip: #3\fi\hskip1em}\it
\ignorespaces}

%
\def\@endtheorem{\par\addvspace{6pt plus3pt minus2pt}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% THEOREM ENVIRONMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%
%

\newif\iflogo
\def\prbox{\hbox to \hsize{\hfill\fboxsep0pt\fbox{\phantom{\vrule width5pt height5pt depth0pt}}}\global\logofalse}
%

\newenvironment{proof}{%
        \par\addvspace{12pt plus3pt minus3pt}
   \global\logotrue
   \@ifnextchar[{\@proof}{\@proof[Proof]}%
   }{%
        \par\iflogo\vskip-\lastskip
        \vskip-\baselineskip\prbox\par
        \addvspace{12pt plus3pt minus3pt}\fi}
%
\def\@proof[#1]{\noindent{\normalfont\bfseries#1.}\hskip.5em\ignorespaces}
%

%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Bibliography %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout
        {\string\citation{#2}}\fi       
\def\@citea{}\@cite{\@for\@citeb:=#2\do         
        {\@citea\def\@citea{,}\@ifundefined     
        {b@\@citeb}{{\bf ?}\@warning 
        {Citation `\@citeb' on page \thepage \space undefined}} 
        {\csname b@\@citeb\endcsname}}}{#1}} 
 \newif\if@cghi 
\def\cite{\@cghitrue\@ifnextchar [{\@tempswatrue 
        \@citex}{\@tempswafalse\@citex[]}} 
\def\citelow{\@cghifalse\@ifnextchar [{\@tempswatrue 
        \@citex}{\@tempswafalse\@citex[]}} 
\def\@cite#1#2{{$\null^{#1}$\if@tempswa\typeout 
        {WSPC warning: optional citation argument  
        ignored: `#2'} \fi}} 
\newcommand{\citeup}{\cite} 
% 
\def\@refcitex[#1]#2{\if@filesw\immediate\write\@auxout 
        {\string\citation{#2}}\fi 
\def\@citea{}\@refcite{\@for\@citeb:=#2\do 
        {\@citea\def\@citea{, }\@ifundefined 
        {b@\@citeb}{{\bf ?}\@warning 
        {Citation `\@citeb' on page \thepage \space undefined}} 
        \hbox{\csname b@\@citeb\endcsname}}}{#1}} 
 \def\@refcite#1#2{{#1\if@tempswa\typeout 
        {WSPC warning: optional citation argument 
        ignored: `#2'} \fi}} 
 \def\refcite{\@ifnextchar[{\@tempswatrue
        \@refcitex}{\@tempswafalse\@refcitex[]}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newdimen\bibindent
\bibindent=2em
\def\@biblabel#1{#1.}
\newenvironment{thebibliography}[1]
     {\section*{\bibname}\bibfont%
      \list{\@biblabel{\arabic{enumiv}}}%
           {\settowidth\labelwidth{\@biblabel{#1}}%
            \leftmargin\labelwidth
            \labelsep6pt%.33em
            \advance\leftmargin\labelsep
            \itemsep0pt\parsep0pt
            \usecounter{enumiv}%
            \renewcommand\theenumiv{\arabic{enumiv}}}%
      \sloppy\clubpenalty4000\widowpenalty4000%
      \sfcode`\.=\@m}
     {\def\@noitemerr
       {\@latex@warning{Empty `thebibliography' environment}}%
      \endlist}
\newcommand\newblock{}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Appendix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcounter{appendix}
\newcommand\appendix{\par
        \refstepcounter{appendix}
        \setcounter{section}{0}%
        \setcounter{lemma}{0}
        \setcounter{theorem}{0}
        \setcounter{definition}{0}
        \setcounter{corollary}{0}
        \setcounter{equation}{0}
        \@addtoreset{equation}{section}
\renewcommand\thesection{\appendixname\ \Alph{section}}
\renewcommand\thesubsection{\Alph{section}.\arabic{subsection}}%
\renewcommand\theequation{\Alph{section}.\arabic{equation}}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%For contents pages %%%%%%%%%%%%%%%%%%%%%%%%
%
\def\journalname{\uppercase{International Journal of Computational
Geometry & Applications}}
\def\No{No.}
\def\chead#1#2#3{\par
\thispagestyle{empty}
{\centering{%
{\titlefont\journalname}\par
{\sl Vol.~#1, \No~#2 (#3)}\par
\vspace*{34pt}
\noindent CONTENTS\par}}
\vspace*{14pt}}
\def\leaderfill{\leaders\hbox to 1em{\hss.\hss}\hfill}
\def\centry#1#2#3{\par
        {\foliofont
        \setbox\tempbox\hbox{#3}
        {\rightskip3.5pc plus1fil
        \noindent{\uppercase{#1}}\par}
        {\leftskip12pt{\rightskip1pc plus1fil
        \ignorespaces\noindent#2\leaderfill\hspace*{2pt}\hskip\wd\tempbox\par}\par}\par
        \vskip-\lastskip
        \vskip-\baselineskip
        \hbox to \hsize{\hfill#3}\par}
        \addvspace{8pt plus1pt minus1pt}\par}
%%
\def\cent#1#2#3{\par{\foliofont
        {\rightskip2pc plus1fil
        \noindent\par}
        {\noindent{\uppercase{#1}}\ignorespaces#2\leaderfill\hspace*{2pt}#3\par}}\par
        \addvspace{8pt plus1pt minus1pt}\par
        }
%
\def\ehead#1#2#3{\par
        \addvspace{12pt plus1pt minus1pt}
        {\foliofont\rightskip4pc plus1fil
        \noindent{\bf #1{#2}{#3}\par}
        \vspace*{4pt}}\par}
%
\def\eehead#1#2#3{\par
        \addvspace{12pt plus1pt minus1pt}
        {\foliofont\rightskip4pc plus1fil
        \noindent{\bf #1{#2}{#3}\par}
        \vspace*{4pt}}\par}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Trim Marks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcommand\today{\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
        \space\number\day, \number\year}
\newcount\minute
\newcount\hour
\def\currenttime{%
        \minute\time
        \hour\minute
        \divide\hour60
        \the\hour:\multiply\hour60\advance\minute-\hour\the\minute}
%
%
\def\wsdraftnote{\today\quad\currenttime\qquad\qquad\jobname}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\cropmarks{\nointerlineskip%
     \vbox to 0pt{\vskip-8.6pt
        \parindent0pt\hspace*{6pt}\wsdraftnote
     \par\advance\trimheight by 2pc
     \vbox to \trimheight{\offinterlineskip\parindent0pt\vskip-2pc
     \hbox to \trimwidth{\raise2.6pc\hbox{\vrule height0pc width0pt}\raisebox{2pc}
   {\hspace*{-2.6pc}\vrule width0pc height0pt}\hfill\raisebox{2pc}
   {\vrule width0pc height0pt}\hspace*{-2.6pc}\raise2.6pc\hbox{\vrule height0pc width0pt}}\vfill
     \hbox to \trimwidth{\lower1.2pc\hbox{\vrule height0pc width0pt}\raisebox{1.4pc}
        {\hspace*{-2.6pc}\vrule width0pc height0pt}\hfill 
    \lower1.2pc\hbox{\vrule height0pc width0pt}\rlap{\hspace*{0.6pc}\raisebox{1.4pc}{\vrule width0pc height0pt}}}}}
     \vbox to 0pt{\offinterlineskip\parindent0pt\vskip\topmargin%\vskip1.3pt
     \tempdimen\normaltextheight
     \advance\tempdimen24pt
     \moveright\@themargin
     \vbox to \tempdimen{\hrule height\wsdraftrule 
     \vbox to 0pt{\vskip\headheight\vskip\headsep%\vskip3pt
                \vrule height\wsdraftrule width\textwidth}%
      \hbox to \textwidth{\vrule width\wsdraftrule \hfill\vrule height\tempdimen width\wsdraftrule}%
           \hrule height\wsdraftrule}}}%%
\def\xcropmarks{\nointerlineskip%
     \vbox to 0pt{\vskip-8.6pt
        \parindent0pt\hspace*{6pt}\wsdraftnote
     \par\advance\trimheight by 2pc
     \vbox to \trimheight{\offinterlineskip\parindent0pt\vskip-2pc
     \hbox to \trimwidth{\raise2.6pc\hbox{\vrule height0pc width0pt}\raisebox{2pc}
   {\hspace*{-2.6pc}\vrule width0pc height0pt}\hfill\raisebox{2pc}
   {\vrule width0pc height0pt}\hspace*{-2.6pc}\raise2.6pc\hbox{\vrule height0pc width0pt}}\vfill
     \hbox to \trimwidth{\lower1.2pc\hbox{\vrule height0pc width0pt}\raisebox{1.4pc}
        {\hspace*{-2.6pc}\vrule width0pc height0pt}\hfill 
    \lower1.2pc\hbox{\vrule height0pc width0pt}\rlap{\hspace*{0.6pc}\raisebox{1.4pc}{\vrule width0pc height0pt}}}}}
     \vbox to 0pt{\offinterlineskip\parindent0pt\vskip\topmargin%\vskip1.3pt
     \tempdimen\normaltextheight
     \advance\tempdimen27pt
     \moveright\@themargin
     \vbox to \tempdimen{\hrule height\wsdraftrule 
     \vbox to 0pt{\vskip\headheight\vskip\headsep%\vskip3pt
                \vrule height\wsdraftrule width\textwidth}%
      \hbox to \textwidth{\vrule width\wsdraftrule \hfill\vrule height\tempdimen width\wsdraftrule}%
           \hrule height\wsdraftrule}}}%%
%
\let\trimmarks\cropmarks
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Output Routine %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\@outputpage{%
\begingroup           % the \endgroup is put in by \aftergroup
  \let \protect \noexpand
  \@resetactivechars
  \let\-\@dischyph
  \let\'\@acci\let\`\@accii\let\=\@acciii
  \let\\\@normalcr
  \let\par\@@par          %% 15 Sep 87
  \shipout \vbox{%
    \set@typeset@protect
    \aftergroup \endgroup
    \aftergroup \set@typeset@protect
                                % correct? or just restore by ending
                                % the group?
  \if@specialpage
    \global\@specialpagefalse\@nameuse{ps@\@specialstyle}%
  \fi
  \if@twoside
    \ifodd\count\z@ \let\@thehead\@oddhead \let\@thefoot\@oddfoot
         \let\@themargin\oddsidemargin
    \else \let\@thehead\@evenhead
       \let\@thefoot\@evenfoot \let\@themargin\evensidemargin
    \fi
  \fi
  \reset@font
  \normalsize
  \baselineskip\z@skip \lineskip\z@skip \lineskiplimit\z@
    \@begindvi\trimmarks
    \vskip \topmargin
    \moveright\@themargin \vbox {%
      \setbox\@tempboxa \vbox to\headheight{%
        \vfil
        \color@hbox
          \normalcolor
          \hb@xt@\textwidth {%
            \let \label \@gobble
            \let \index \@gobble
            \let \glossary \@gobble %% 21 Jun 91
            \@thehead
            }%
        \color@endbox
        }%                        %% 22 Feb 87
      \dp\@tempboxa \z@
      \box\@tempboxa
      \vskip \headsep
      \box\@outputbox
      \baselineskip \footskip
      \color@hbox
        \normalcolor
        \hb@xt@\textwidth{%
          \let \label \@gobble
          \let \index \@gobble      %% 22 Feb 87
          \let \glossary \@gobble   %% 21 Jun 91
          \@thefoot
          }%
      \color@endbox
      }%
    }%
\global \@colht \textheight
\stepcounter{page}%
\let\firstmark\botmark
}
%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Local Defs. %%%%%%%%%%%%%%%%%%%%%%
%
\def\mtb{\fboxsep=0pt\fbox{\phantom{e}}}
\def\breakhere{\par\vskip-\lastskip
                        \pagebreak}
\def\forcebreak{\vadjust{\pagebreak}}
%
\def\and{\hbox{\lowercase{and }}}
\def\aand{\\[10pt]{\upshape{and}}\\[-3pt]}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%% Process Options %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pagestyle{headings}
\pagenumbering{arabic} 
\onecolumn
\frenchspacing
\flushbottom
\def\sloppy{\tolerance=100000\hfuzz=\maxdimen \vfuzz=\maxdimen}
\sloppy
\vbadness=12000
\hbadness=12000
\RequirePackage{amsfonts}
\RequirePackage{amssymb}
\RequirePackage{amsmath}
\RequirePackage{graphicx}
\endinput
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of file %%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Text Area: 8in (include Runningheads) x 5in
%% ws-ijcga.tex   :   18-11-2024
%% Class file to use with ws-ijcga.cls written in LaTeX2E.
%% The content, structure, format and layout of this style file is the
%% property of World Scientific Publishing Co. Pte. Ltd.
%% Copyright 2024 by World Scientific Publishing Co.
%% All rights are reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\documentclass{ws-ijcga}
%\documentclass[wsdraft]{ws-ijcga}

\usepackage{xcolor}
\usepackage[verbose,hypertexnames=false]{hyperref}
\hypersetup{colorlinks=false,allbordercolors=blue,pdfborderstyle={/S/U/W 1}}
% \label, \ref and \cite commands are highly recommended

\begin{document}

\markboth{Authors' Names}
{Instructions for Typing Manuscripts (Paper's Title)}

%%%%%%%%%%%%%%%%%%%%% Publisher's Area please ignore %%%%%%%%%%%%%%%
%
\catchline{}{}{}{}{}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\title{Your paper}

\author{First Author\footnote{
Typeset names in 8 pt Roman, initial caps. Use the footnote to indicate the
present or permanent address of the author.}}

\address{University Department, University Name, Address\\
City, State ZIP/Zone,Country\,\footnote{State completely without
abbreviations, the affiliation and mailing address,
including country. Typeset in 8 pt italic.}\\
e-mail address}

\author{Second Author}

\address{Group, Laboratory, Address\\
City, State ZIP/Zone, Country\\
e-mail address}

\maketitle

\begin{history}
\received{(Day Month Year)}
\revised{(Day Month Year)}
\accepted{(Day Month Year)}
\published{(Day Month Year)}
\comby{(Handling Editor)}
\end{history}

\begin{abstract}
The abstract should summarize the context, content
and conclusions of the paper in less than 200 words. It should
not contain any references or displayed equations. Typeset the
abstract in 8 pt roman with baselineskip of 10 pt, making
an indentation of 1.5 pica on the left and right margins.
\end{abstract}

\keywords{Keyword1; keyword2; keyword3.}

\section{General Appearance}
Contributions to the {\it International Journal of Computational Geometry \& Applications} will mostly be processed by using the \hbox{authors'} source files. These should be submitted with the manuscripts, and resubmitted in the final form if a paper requires revision before being accepted for publication.

\section{The Main Text}
Contributions are to be in English. Authors are encouraged to
have their contribution checked for grammar. American spelling
should be used. Abbreviations are allowed but should be spelled
out in full when first used. Integers ten and below are to be
spelled out. Italicize foreign language phrases (e.g.~Latin, French).

The text is to be typeset in 10 pt roman, single spaced
with baselineskip of 13~pt. Text area (including copyright block)
is 8 inches high and 5 inches wide for the first page.
Text area (excluding running title) is 7.7 inches high and
5 inches wide for subsequent pages.  Final pagination and
insertion of running titles will be done by the publisher.

\section{Major Headings}
Major headings should be typeset in boldface with the first
letter of important words capitalized.

\subsection{Sub-headings}
Sub-headings should be typeset in boldface italic and capitalize
the first letter of the first word only. Section numbers to be in
boldface roman.

\subsubsection{Sub-subheadings}
Typeset sub-subheadings in medium face italic and capitalize the
first letter of the first word only. Section numbers to be in
roman.

\subsection{Numbering and spacing}
Sections, sub-sections and sub-subsections are numbered in
Arabic.  Use double spacing before all section headings, and
single spacing after section headings. Flush left all paragraphs
that follow after section headings.

\subsection{Lists of items}
Lists may be laid out with each item marked by a bullet:
\begin{itemlist}
 \item item one,
 \item item two.
\end{itemlist}
Items may also be numbered in lowercase roman numerals:
\begin{romanlist}
\item item one
\item item two
	\begin{romanlist}[(b)]
	\item Lists within lists can be numbered with lowercase
              roman letters,
	\item second item.
	\end{romanlist}
\end{romanlist}

\section{Equations}
Displayed equations should be numbered consecutively,
with the number set flush right and enclosed in parentheses
\begin{equation}
\mu(n, t) = {\sum^\infty_{i=1} 1(d_i < t, N(d_i)= n)}
{\int^t_{\sigma=0} 1(N(\sigma) = n)d\sigma}\,.
\label{eq:jaa}
\end{equation}

Equations should be referred to in abbreviated form,
e.g.~``Eq.~(\ref{eq:jaa})'' or ``(2)''. In multiple-line
equations, the number should be given on the last line.

For multiline equations, prefer using \verb|align| or \verb|align*| instead of \verb|eqnarray|.
\begin{align}
g(x) & = \sum_{k=1}^{N} y_k g(x_k) \nonumber\\
& = \sum_{k=1}^{N} y_k \sum_{l=1}^{M} b_{kl} w_l \nonumber\\
& = \sum_{k=1}^{N} \sum_{l=1}^{M} b_{kl} y_k w_l
\end{align}

Displayed equations are to be centered on the page width.
Standard English letters like x are to appear as $x$
(italicized) in the text if they are used as mathematical
symbols. Punctuation marks are used at the end of equations as
if they appeared directly in the text.

\section{Theorem Environments}

\begin{theorem} \label{theo1}
Theorems, lemmas, etc. are to be numbered consecutively in the
paper. Use double spacing before and after theorems, lemmas, etc.
\end{theorem}

\begin{lemma}[Optional Head]
\label{lem1}
Theorems, lemmas, etc. are to be numbered consecutively in the paper.
Use double spacing before and after theorems, lemmas, etc.
\end{lemma}

The labels cited in the theorem environments text can
cross link to the body text e.g. Theorem~\ref{theo1}
and Lemma~\ref{lem1}.

\begin{proof}
Proofs should end with a box.
\end{proof}

\section{Illustrations and Photographs}
Figures are to be inserted in the text nearest their first reference.
Figure~\ref{fig1} placements can be either top or bottom.
Soft copies of illustrations are to be in either EPS, PS or TIF format, preferably on a PC platform. Please prepare in 300 dpi for line drawings (black and white); 300 dpi for halftones (gray scale); 300 dpi for colour images. Must be in CMYK (Cyan, Magenta, Yellow and Black) for colour separation. If the author requires the publisher to reduce the figures, ensure that the figures (including letterings and numbers) are large enough to be clearly seen after reduction.
If photographs are to be used, only black and white ones are acceptable.

\begin{figure}[t]
\centerline{\includegraphics[width=5cm]{ijcgaf1}}
\vspace*{8pt}
\caption{A schematic illustration of dissociative recombination. The direct mechanism, 4m$^2_\pi$ is initiated when the molecular ion S$_{\rm L}$ captures an electron with kinetic energy.}
\label{fig1}
\end{figure}

Figures are to be sequentially numbered in Arabic numerals. The
caption must be placed below the figure. Typeset in 8 pt roman
with baselineskip of 10~pt. Use double spacing between a
caption and the text that follows immediately.

Previously published material must be accompanied by written
permission from the author and publisher.

\section{Tables}
Tables should be inserted in the text as close to the point of
reference as possible. Some space should be left above and below
the table.

Tables should be numbered sequentially in the text in Arabic
numerals. Captions are to be centralized above the tables.
Typeset tables and captions in 8 pt roman with baselineskip of 10 pt.

\begin{table}[ht]
\tbl{Comparison of acoustic for frequencies for piston-cylinder problem.\label{tab1}}
{\begin{tabular}{@{}cccc@{}}
\toprule
Piston mass & Analytical frequency & TRIA6-$S_1$ model &\% Error \\
& (Rad/s) & (Rad/s) \\
\colrule
1.0\hphantom{00} & \hphantom{0}281.0 & \hphantom{0}280.81 & 0.07 \\
0.1\hphantom{00} & \hphantom{0}876.0 & \hphantom{0}875.74 & 0.03 \\
0.01\hphantom{0} & 2441.0 & 2441.0\hphantom{0} & 0.0\hphantom{0} \\
0.001 & 4130.0 & 4129.3\hphantom{0} & 0.16\\
\botrule
\end{tabular}}
\begin{tabnote}
Table notes
\end{tabnote}
\end{table}

If tables need to extend over to a second page, the continuation of the table should be preceded by a caption, e.g.~``{\it Table 2.} $(${\it Continued}$)$''

\section{Running Heads}
Please provide a shortened runninghead (not more than eight words) for
the title of your paper. This will appear on the top right-hand side of your paper.

\section{Footnotes}
Footnotes should be numbered sequentially in superscript
lowercase roman letters.\footnote{Footnotes should be
typeset in 8 pt roman at the bottom of the page.}

\section*{Acknowledgements}
This section should come before the References.
Funding information may also be included here.

\section*{ORCID}
You are encouraged to include in your user information the ORCID (\url{https://orcid.org/}) or register for one if you don't have it. This ID will help to identify you in the researcher community and make it easier to keep track of all your publications.
Please provide a valid ORCID here, e.g.,

\noindent Josiah Carberry - \url{https://orcid.org/0000-0002-1825-0097}

\noindent Rajesh Babu - \url{https://orcid.org/0009-0006-0415-6880}

\appendix

\section{Appendices}
Appendices should be used only when absolutely necessary. They
should come after the References. If there is more than one
appendix, number them alphabetically. Number displayed equations
occurring in the Appendix in this way, e.g.~(\ref{appeqn}), (A.2),
etc.
\begin{equation}
\mu(n, t) = {\sum^\infty_{i=1} 1(d_i < t, N(d_i)= n)}
{\int^t_{\sigma=0} 1(N(\sigma) = n)d\sigma}\,.
\label{appeqn}
\end{equation}

\section*{References}
References are to be listed in the order cited in the text in Arabic numerals.
They can be typed in superscripts after punctuation marks,
e.g.~``$\ldots$ in the statement.\cite{dolve}'' or used directly,
e.g.~``see Ref.~5 for examples.'' Please list using the style shown in
the following examples.  For journal names, use the standard
abbreviations.  Typeset references in 9 pt roman.

\begin{thebibliography}{0}
\bibitem{lorentz}
R. Lorentz and D. B. Benson,
Deterministic and nondeterministic flow-chart interpretations,
{\it J. Comput. System Sci.} {\bf 27} (1983) 400--433, \url{https://doi.org/10.1016/0022-0000(83)90050-8}.

\bibitem{beeson}
M. J. Beeson, {\it Foundations of Constructive Mathematics}
(Springer, Berlin, 1985),
\url{https://doi.org/10.1007/978-3-642-68952-9}.

\bibitem{clark}
K. L. Clark, Negations as failure, in
{\it Logic and Data Bases}, eds. H. Gallaire and J.~Winker
(Plenum Press, New York, 1973) 293--306,
\url{https://doi.org/10.1007/978-1-4684-3384-5_11}.

\bibitem{joliat}
M. Joliat,
A simple technique for partial elimination of unit productions from LR({\it k}) parsers,
{\it IEEE Trans. Comput.} {\bf 27} (1976) 753--764,
\url{https://doi.org/10.1109/TC.1976.1674686}.

\bibitem{dolve}
D. Dolve, Unanimity in an unknown and unreliable environment, in
{\it Proc. 22nd Annual Symp. Foundations of Computer
Science}, Nashville, TN (Oct. 1981) pp.~159--168.

\bibitem{tamassia}
R. Tamassia, C. Batini and M. Talamo,
An algorithm for automatic layout of entity relationship diagrams, in
{\it Entity-Relationship Approach to Software Engineering, Proc. 3rd
Int.  Conf. Entity-Relationship Approach},
eds. C. G. Davis, S. Jajodia, P. A. Ng and R. T. Yeh
(North-Holland, Amsterdam, 1983) pp.~421--439.

\bibitem{gewirtz}
W. L. Gewirtz, Investigations in the theory of descriptive complexity,
Ph. D. Thesis, New York University (1974).
\end{thebibliography}

\end{document} 

\documentclass{ws-ijcga}
\usepackage{xcolor}
\usepackage[sort,compress]{cite}
\usepackage[verbose]{hyperref}
\hypersetup{colorlinks=false,allbordercolors=blue,pdfborderstyle={/S/U/W 1}}

\begin{document}

\title{Bib\TeX ing\\[.5ex] in \\[.5ex] WSPC Bib\/ Style}

\markboth{WSPC}{Using World Scientific's Bib\TeX\/ Style File}

\maketitle

\section{Usage}

\begin{verbatim}
\documentclass{ws-ijcga}
\usepackage{xcolor}
\usepackage[sort,compress]{cite}
\usepackage[verbose]{hyperref}
\begin{document}
\section{Output}
Sample output using ws-ijcga bibliography style file ...
text\cite{best,pier,jame} ...
\bibliographystyle{ws-ijcga}
\bibliography{sample}
\end{document}
\end{verbatim}

\section{Output}
Sample output using ws-ijcga bibliography style file

\begin{enumerate}[(13)]
\item article: see \cite{best,pier,jame}

\item proceedings: see \cite{Weiss94}

\item inproceedings: see \cite{conftypical,Moss94}

\item book: see\cite{ArmsRace1}

\item edition: see \cite{ComplexVariables}

\item editor: see \cite{ColBenh:93}

\item series: see \cite{inbook}

\item tech report: see \cite{hobby1992,CSTR116}

\item unpublished: see \cite{VoQS}

\item phd thesis: see \cite{Brown:1988:IEL}

\item masters thesis: see \cite{segms}

\item incollection: see \cite{Jones:Phoneme}

\item booklet: see Ref.~\citen{URW:kerning}
\end{enumerate}

\bibliographystyle{ws-ijcga}
\bibliography{sample}

\end{document}