International Journal of Algebra and Computation (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",
  editor    =   "H. C. Heard and I. Y. Borg and N. L. Carter and C. B. Raleigh",
  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 airborne
                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"}

@misc{netpbm,
  author    =   "Bill Davidsen",
  title     =   "NETPBM",
  year      =   "1993",
  note      =   "ftp://ftp.wustl.edu/graphics/graphics/packages/\break NetPBM."}

% in-house BiB pattern 2
% WSPC IJAC BibTeX Style File -- version 1.0
% BibTeX version 0.99c, intended for LaTeX2e
%
% This style was made from 'abbrv.bst' with lots of tweaking to make
% it look like IJAC.
%
% If you make bug fixes, improvements, etc. please send in yours
% comments and suggetions to Rajesh <[email protected]>
%
% Copyright (C) 2004, all rights reserved.
% Copying of this file is authorized only if either
% (1) you make absolutely no changes to your copy, including name, or
% (2) if you do make changes, you name it something other than
% btxbst.doc, plain.bst, unsrt.bst, alpha.bst, abbrv.bst and ws-ijac.bst.
% This restriction helps ensure that all standard styles are identical.
% The file btxbst.doc has the documentation for this style.

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.quote after.sentence
        after.quoted.block after.block }

FUNCTION {init.state.consts}
{ #0 'before.all :=
  #1 'mid.sentence :=
  #2 'after.quote :=
  #3 'after.sentence :=
  #4 'after.quoted.block :=
  #5 'after.block :=
}

FUNCTION {disp.msg.screen} { #1 }

FUNCTION {type.msg}
{ disp.msg.screen
     { "<ws-ijac.bst>"
       top$
       "World Scientific's Bibliography Style File for IJAC"
       top$
       "version 1.0 (26-3-2004)"
       top$
       "-- by Rajesh <[email protected]>"
       top$
       "<Sorted version, follows inhouse BiB pattern 2>"
       top$
     }
     { skip$ }
   if$
}

STRINGS { s t }

FUNCTION {output.nonnull}
{ 's :=
  output.state mid.sentence =
    { ", " * write$ }
    { output.state after.quote =
    { " " * write$ }
    { output.state after.block =
        { add.period$ write$
          newline$
          "\newblock " write$
        }
        { output.state before.all =
        'write$
        { output.state after.quoted.block =
            { write$
              newline$
              "\newblock " write$
            }
            { add.period$ " " * write$ }
          if$
        }
          if$
        }
      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 {output.bibitem}
{ newline$
  "\bibitem{" write$
  cite$ write$
  "}" write$
  newline$
  ""
  before.all 'output.state :=
}

FUNCTION {blank.sep}
{
 after.quote 'output.state :=
}

FUNCTION {fin.entry}
{ output.state after.quoted.block =
    'skip$
    'add.period$
  if$
  write$
  newline$
}

FUNCTION {new.block}
{ output.state before.all =
    'skip$
    { output.state after.quote =
    { after.quoted.block 'output.state := }
    { after.block 'output.state := }
      if$
    }
  if$
}

FUNCTION {new.sentence}
{ output.state after.block =
    'skip$
    { output.state before.all =
    'skip$
    { after.sentence 'output.state := }
      if$
    }
  if$
}

FUNCTION {not}
{   { #0 }
    { #1 }
  if$
}

FUNCTION {and}
{   'skip$
    { pop$ #0 }
  if$
}

FUNCTION {or}
{   { pop$ #1 }
    'skip$
  if$
}

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 {field.or.null}
{ duplicate$ empty$
    { pop$ "" }
    'skip$
  if$
}

FUNCTION {emphasize}
{ duplicate$ empty$
    { pop$ "" }
    { "{\em " swap$ * "}" * }
  if$
}

FUNCTION {bold}
{ duplicate$ empty$
    { pop$ "" }
    { "{\bf " swap$ * "}" * }
  if$
}

INTEGERS { nameptr namesleft numnames }

FUNCTION {format.names}
{ 's :=
  #1 'nameptr :=
  s num.names$ 'numnames :=
  numnames 'namesleft :=
    { namesleft #0 > }
    { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't :=
      nameptr #1 >
    { namesleft #1 >
        { ", " * t * }
        { numnames #2 >
        { "" * }
        'skip$
          if$
          t "others" =
        { " {\em et~al.}" * }
        { " and " * t * }
          if$
        }
      if$
    }
    't
      if$
      nameptr #1 + 'nameptr :=
      namesleft #1 - 'namesleft :=
    }
  while$
}

FUNCTION {format.authors}
{ author empty$
    { "" }
    { author format.names }
  if$
}

FUNCTION {format.editors}
{ editor empty$
    { "" }
    { editor format.names
      editor num.names$ #1 >
    { " (eds.)" * }
    { " (ed.)" * }
      if$
    }
  if$
}

FUNCTION {format.eeditors}
{ editor empty$
    { "" }
    { editor num.names$ #1 >
    { " eds." * }
    { " ed." * }
      if$
    editor format.names}
  if$
}

FUNCTION {format.title}
{ title empty$
    { "" }
    { "" title "t" change.case$ * "" * }
  if$
}

FUNCTION {format.title.p}
{ title empty$
    { "" }
    { "" title "t" change.case$ * "" * }
  if$
}

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 {format.mdate}
{ year empty$
    { month empty$
    { "" }
    { "there's a month but no year in " cite$ * warning$
      month
    }
      if$
    }
    { month empty$
    { " (" year * ")" *}
    { " (" * month * "" year * ")" *}
      if$
    }
  if$
}


FUNCTION {format.date}
{ year empty$
    { month empty$
    { "" }
    { "there's a month but no year in " cite$ * warning$
      month
    }
      if$
    }
    { month empty$
    { " (" year * ")" *}
    { " (" * month * "" year * ")" *}
      if$
    }
  if$
}

FUNCTION {format.btitle}
    { title emphasize }

FUNCTION {tie.or.space.connect}
{ duplicate$ text.length$ #3 <
    { "~" }
    { " " }
  if$
  swap$ * *
}

FUNCTION {empty.field.to.null.string}
{ duplicate$ empty$
    { pop$ "" }
    { skip$ }
  if$
}

FUNCTION {either.or.check}
{ empty$
    'pop$
    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
  if$
}

FUNCTION {format.bvolume}
{ volume empty$
    { "" }
    { "" volume bold tie.or.space.connect
      series empty$
	'skip$
	{ " of " * series emphasize * }
      if$
      "volume and number" number either.or.check
    }
  if$
}

FUNCTION {format.number.series}
{ volume empty$
    { number empty$
    { series field.or.null }
    { output.state mid.sentence =
        { "no.~" }
        { "No.~" }
      if$
      number *
      series empty$
        { "there's a number but no series in " cite$ * warning$ }
        { " in " * series * }
      if$
    }
      if$
    }
    { "" }
  if$
}

FUNCTION {format.edition}
{ edition empty$
    { "" }
    { output.state mid.sentence =
    { edition "l" change.case$ " edn." * }
    { edition "t" change.case$ " edn." * }
      if$
    }
  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 {first.page.number}
{ 't :=
  ""
    { t "" =
        { #0 }
        { t #1 #1 substring$ "-" = not }
      if$
    }
    { t #1 #1 substring$ *
      t #2 global.max$ substring$ 't :=
    }
  while$
}

FUNCTION {format.pages}
{ pages empty$
    { "" }
    { pages multi.page.check
        { "" pages n.dashify tie.or.space.connect }
        { "p." pages tie.or.space.connect }
      if$
    }
  if$
}

FUNCTION {format.ppages}
{ pages empty$
    { "" }
    { pages multi.page.check
        { "pp." pages n.dashify tie.or.space.connect }
        { "p." pages tie.or.space.connect }
      if$
    }
  if$
}

FUNCTION {format.number}
{ number empty$
    { "" }
    { "("  number * ")" *}
  if$
}

FUNCTION {format.journal.volume.number}
{ journal empty$
    { "empty " t * " in " * cite$ * warning$ ""}
    { journal emphasize }
  if$
  volume empty$      %% warning if no volume
    { "empty volume in " cite$ * warning$ " " *}
    { " " * volume bold *}      %% make volume bold
%%    { "vol.~" volume * }
  if$
  month empty$
    { format.number *}
    'skip$
  if$
}

FUNCTION {format.series.volume.number}
{ series empty$
%%    { "empty " t * " in " * cite$ * warning$ ""}
    { "" }                  
    { series emphasize }
  if$
  volume empty$ 
    { "" *}                 
    { " " * volume bold *}  
%%    { "vol.~" volume * }
  if$
  month empty$
    { format.number *}
    'skip$
  if$
}

% following not used
FUNCTION {format.volume}
{ volume empty$
    { "" }
    { volume bold }            
%%    { "vol.~" volume * }
  if$
}

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

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

FUNCTION {format.in.ed.booktitle}
{ booktitle empty$
    { "" }
    { editor empty$
	{ " in " booktitle emphasize * }
	{ " in " format.editors * ", " * booktitle emphasize * }
      if$
    }
  if$
}

FUNCTION {format.thesis.type}
{ type empty$
    'skip$
    { pop$
      output.state after.block =
    { type "t" change.case$ }
    { type "l" change.case$ }
      if$
    }
  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.tr.number}
{ type empty$
    { "Tech. Rep." }
    'type
  if$
  number empty$
    { "l" change.case$ }
    { number tie.or.space.connect }
  if$
}


FUNCTION {format.paddress}
{ address empty$
    { "" }
    { "(" address * ")" * }
  if$
}

FUNCTION {format.article.crossref}
{ key empty$
    { journal empty$
    { "need key or journal for " cite$ * " to crossref " * crossref *
      warning$
      ""
    }
    { " in {\em " journal * "\/}" * }
      if$
    }
    { " in " key * }
  if$
  "\cite{" * crossref * "}" *
}

FUNCTION {format.crossref.editor}
{ editor #1 "{vv~}{ll}" format.name$
  editor num.names$ duplicate$
  #2 >
    { pop$ " {\em et~al.}" * }
    { #2 <
    'skip$
    { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
        { " {\em et~al.}" * }
        { " and " * editor #2 "{vv~}{ll}" format.name$ * }
      if$
    }
      if$
    }
  if$
}

FUNCTION {format.book.crossref}
{ volume empty$
    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
      "In "
    }
    { "Vol.~" volume *
      " of " *
    }
  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$
          "" *
        }
        { "{\em " * series * "\/}" * }
      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$
    { booktitle empty$
        { "need editor, key, or booktitle for " cite$ * " to crossref " *
          crossref * warning$
          ""
        }
        { " in {\em " booktitle * "\/}" * }   
      if$
    }
    { " in " key * }
      if$
    }
    { " in " format.crossref.editor * }   
  if$
  "\cite{" * crossref * "}" *
}

FUNCTION {push.url}
{}

FUNCTION {push.date}
% format: month year
{ year empty$
    { month empty$
        { "" }
        { "there's a month but no year in " cite$ * warning$
          month
        }
      if$
    }
    { month empty$
        { year }
        { month " " * year * }
      if$
    }
  if$
}


FUNCTION {format.address.date}
{ address empty$
    {year empty$ 
        { "" }
        { push.date *} 
        if$
    }
    { "(" address * ", " * year * ")" * }
  if$
}

FUNCTION {format.school.date}
{ school empty$
    {"school is missing " cite$ * warning$
    year empty$ 
        { "" }
        { push.date *} 
        if$
    }
    { "(" school * ", " * year * ")" * }
  if$
}

FUNCTION {push.address.publisher.year}
% the whole imprint
{ address empty$
    { publisher empty$
        { url empty$
            { year empty$ 
                { "" }
                { push.date } 
              if$
            }
            { 
              push.url
              year empty$
                { skip$ }
                { ", " * push.date * ")" * }
              if$
            }
          if$
        }
      { "(" publisher *
      year empty$
            { skip$ }
            { ", " * push.date * ")" * }
          if$
        }
      if$
    }
    { 
      publisher empty$
        { skip$ }
        { "(" publisher * ", " * address * }
      if$
      year empty$
    { ")" * }
    { ", " * push.date * ")" * }
      if$
    }
  if$
}

FUNCTION {article}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  crossref missing$
    { format.journal.volume.number output
      blank.sep
      format.date "year" output.check
      blank.sep
      format.pages output
    }
    { format.article.crossref output.nonnull
      format.pages output
    }
  if$
  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.edition output
      blank.sep
      push.address.publisher.year "publisher" output.check
    }
    { new.block
      format.book.crossref output.nonnull
    }
  if$
  new.block
  note output
  fin.entry
}

FUNCTION {booklet}
{ output.bibitem
  format.authors output
  title empty$
    { "empty title in " cite$ * warning$
      howpublished new.sentence.checka
    }
    { howpublished empty$ not
      address empty$ month empty$ year empty$ and and
      or
    { format.title.p output.nonnull }
    { format.title output.nonnull }
      if$
    }
  if$
  howpublished output
  publisher empty$
  {format.address.date output}
  {push.address.publisher.year "publihser" output.check}
  if$
  new.block
  note output
  fin.entry
}

FUNCTION {inbook}
{ output.bibitem
  author empty$
    { format.editors "author and editor" output.check }
    { format.authors output.nonnull}
  if$
  format.btitle "title" output.check
  blank.sep
  format.in.ed.booktitle "booktitle" output.check
  crossref missing$
    { format.bvolume output
      new.block
      format.number.series output
      push.address.publisher.year "publisher" output.check
      address output
      format.chapter.ppages "chapter and pages" output.check      
    }
    { format.chapter.ppages "chapter and pages" output.check
      new.block
      format.book.crossref output.nonnull
    }
  if$
  format.edition output
  note output
  fin.entry
}

FUNCTION {incollection}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  crossref missing$
    {
    format.in.ed.booktitle "booktitle or editor" output.check
     format.series.volume.number output
      blank.sep
      push.address.publisher.year "publisher" output.check
      %%%blank.sep
      format.ppages output
      format.edition output
    }
    { format.incoll.inproc.crossref output.nonnull
      blank.sep
      format.ppages output
    }
  if$
  new.block
  note output
  fin.entry
}

FUNCTION {inproceedings}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  crossref missing$
    { format.in.ed.booktitle "booktitle" output.check
      format.bvolume output
      format.number.series output
      blank.sep
	  publisher output
	  format.date "year" output.check
      %%%blank.sep
      format.ppages output
    }
    { format.incoll.inproc.crossref output.nonnull
      format.ppages output
    }
  if$
  %%%new.block
  note output
  fin.entry
}

FUNCTION {conference} { inproceedings }

FUNCTION {manual}
{ output.bibitem
  author empty$
    { organization empty$
    'skip$
    { organization output.nonnull
      address output
    }
      if$
    }
    { format.authors output.nonnull }
  if$
  format.btitle "title" output.check
  author empty$
    { organization empty$
    { address new.block.checka
      address output
    }
    'skip$
      if$
    }
    { organization address new.block.checkb
      organization output
      address output
    }
  if$
  format.edition output
  format.date output
  new.block
  note output
  fin.entry
}

FUNCTION {mastersthesis}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  "Master's thesis" format.thesis.type output.nonnull
  %format.school.date "school" output.check
  school output
  blank.sep
  format.date output
  new.block
  note output
  fin.entry
}

FUNCTION {misc}
{ output.bibitem
  format.authors output
  title empty$
    { howpublished new.sentence.checka }
    { howpublished empty$ not
      month empty$ year empty$ and
      or
    { format.title.p output.nonnull }
    { format.title output.nonnull }
      if$
      blank.sep
    }
  if$
  howpublished output
  format.date output
  note output
  fin.entry
  empty.misc.check
}

FUNCTION {phdthesis}
{ output.bibitem
  format.authors "author" output.check
  format.btitle "title" output.check
  "PhD thesis" format.thesis.type output.nonnull
  school "school" output.check
  publisher empty$
  {format.address.date output}
  {push.address.publisher.year "publihser" output.check}
  if$
  format.ppages output
  new.block
  note output
  fin.entry
}

FUNCTION {proceedings}
{ output.bibitem
  editor empty$
    { organization output }
    { format.editors output.nonnull }
  if$
  format.btitle "title" output.check
  blank.sep  
  format.series.volume.number output   
  editor empty$
    'skip$
    { organization output }
  if$
   push.address.publisher.year "publisher" output.check
  new.block
  note output
  fin.entry
}

FUNCTION {techreport}
{ output.bibitem
  format.authors "author" output.check
  format.title "title" output.check
  format.tr.number output.nonnull
  institution "institution" output.check
  blank.sep
  address empty$
  {format.mdate output}
  {format.address.date output}
  if$
  note output
  fin.entry
  new.block  
}

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

FUNCTION {default.type} { misc }

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 Computing Surveys"}

MACRO {acta} {"Acta Informatica"}

MACRO {cacm} {"Communications ACM"}

MACRO {ibmjrd} {"IBM J. Research and Development"}

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

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

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

MACRO {ieeetcad} {"IEEE Trans. Computer-Aided Design"}

MACRO {ipl} {"Information Processing Letters"}

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

MACRO {jcss} {"J.~Computer and System Sciences"}

MACRO {scp} {"Science of Computer Programming"}

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

MACRO {tocs} {"ACM Trans. Computer Systems"}

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

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

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

MACRO {toois} {"ACM Trans. Office Information Systems"}

MACRO {toplas} {"ACM Trans. Programming Languages and Systems"}

MACRO {tcs} {"Theoretical Computer Science"}

READ

EXECUTE {type.msg}

FUNCTION {sortify}
{ purify$
  "l" change.case$
}

INTEGERS { len }

FUNCTION {chop.word}
{ 's :=
  'len :=
  s #1 len substring$ =
    { s len #1 + global.max$ substring$ }
    { s }
  if$
}

FUNCTION {sort.format.names}
{ 's :=
  #1 'nameptr :=
  ""
  s num.names$ 'numnames :=
  numnames 'namesleft :=
    { namesleft #0 > }
    { nameptr #1 >
        { "   " * }
        { skip$ }
      if$
      s nameptr "{vv{ } }{ll{ }}{  ff{ }}{  jj{ }}" format.name$ 't :=
      nameptr numnames = t "others" = and
        { "et al" * }
        { t sortify * }
      if$
      nameptr #1 + 'nameptr :=
      namesleft #1 - 'namesleft :=
    }
  while$
}

FUNCTION {sort.format.title}
{ 't :=
  "A " #2
    "An " #3
      "The " #4 t chop.word
    chop.word
  chop.word
  sortify
  #1 global.max$ substring$
}

FUNCTION {author.sort}
{ author empty$
    { key empty$
        { "to sort, need author or key in " cite$ * warning$ "" }
        { key sortify }
      if$
    }
    { author sort.format.names }
  if$
}

FUNCTION {author.editor.sort}
{ author empty$
    { editor empty$
        { key empty$
            { "to sort, need author, editor, or key in " cite$ * warning$ "" }
            { key sortify }
          if$
        }
        { editor sort.format.names }
      if$
    }
    { author sort.format.names }
  if$
}

FUNCTION {author.organization.sort}
{ author empty$
    { organization empty$
        { key empty$
            { "to sort, need author, organization, or key in " cite$ * warning$ "" }
            { key sortify }
          if$
        }
        { "The " #4 organization chop.word sortify }
      if$
    }
    { author sort.format.names }
  if$
}

FUNCTION {editor.organization.sort}
{ editor empty$
    { organization empty$
        { key empty$
            { "to sort, need editor, organization, or key in " cite$ * warning$ "" }
            { key sortify }
          if$
        }
        { "The " #4 organization chop.word sortify }
      if$
    }
    { editor sort.format.names }
  if$
}

FUNCTION {author.organization.institution.sort}
{ author empty$
    { organization empty$
        { institution empty$
            { key empty$
                { "to sort, need author, organization, institution or key in " cite$ * warning$ "" }
                { key sortify }
              if$
            }
            { "The " #4 institution chop.word sortify }
          if$
        }
        { "The " #4 organization chop.word sortify }
      if$
    }
    { author sort.format.names }
  if$
}


FUNCTION {presort}
{ type$ "ieeetranbstctl" =
    { key empty$
        { "_" }
        { key sortify }
      if$
    }
    { type$ "book" =
      type$ "inbook" =
      or 
        { author.editor.sort }
        { type$ "proceedings" =
          type$ "periodical" =
          or
            { editor.organization.sort }
            { type$ "manual" =
              type$ "electronic" =
              type$ "misc" =
              or or
                { author.organization.sort }
                { type$ "standard" =
                   { author.organization.institution.sort }
                   { author.sort }
                 if$ 
                }
              if$
            }
          if$
        }
      if$
      "    "
      *
      year empty.field.to.null.string sortify
      *
      "    "
      *
      title empty.field.to.null.string
      sort.format.title
      *
    }
  if$
  #1 entry.max$ substring$
  'sort.key$ :=
}

ITERATE {presort}

SORT

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$
}

EXECUTE {begin.bib}

EXECUTE {init.state.consts}

ITERATE {call.type$}

FUNCTION {end.bib}
{ newline$
  "\end{thebibliography}" write$ newline$
}

EXECUTE {end.bib}

%%
%% End of file
%% For Support: [email protected], [email protected]
%% ws-ijac.bst (C) World Scientific Publishing Co.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Text Area: 8in (include Runningheads) x 5in
%% ws-ijac.cls   :   23-06-2026
%% Class file to use with ws-ijac.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 2026 by World Scientific Publishing Co. 
%% All rights are reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%

\NeedsTeXFormat{LaTeX2e}[1995/06/01]
\ProvidesClass{ws-ijac}[2026/06/23 v1.5g Standardized LaTeX document class]
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\newif\if@openright
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\ProcessOptions
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               \parsep 2\p@ \@plus\p@ \@minus\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip}
%
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   \@setfontsize\footnotesize\@viiipt{10}%
   \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@
   \abovedisplayshortskip \z@ \@plus\p@
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               \parsep 2\p@ \@plus\p@ \@minus\p@
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\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}
\newcommand\large{\@setfontsize\large\@xiipt{14}}%
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\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}
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          {\mbox{\boldmath$\scriptscriptstyle#1$}}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%% Article FM %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\title#1{\gdef\@title{{{#1}}}}
\def\subtitle#1{\titlefont :~#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
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  \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}
	\addvspace{-2pt plus-2pt minus-2pt}}
	{
   	\end{center}
	\addvspace{15pt plus2pt minus2pt}
		}
%
\def\email#1{\it #1\par}
\def\http#1{\it http://#1\par}
\def\urrll#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{\par\addvspace{1\baselineskip}Communicated\ by~#1\par}
%
\def\@clinebuf{}
\def\catchline#1#2#3#4#5{\expandafter\def\expandafter\@clinebuf\expandafter
	{\@clinebuf\catchlinefont
	\noindent International Journal of Algebra and Computation\par
%	\noindent Vol.\ {#1}, \No\ {#2} (#3)\ \thebepage--\theeepage\par
	\noindent \copyright\ World Scientific Publishing Company\par
	\noindent\vskip-\baselineskip \hphantom{#4 \hskip2em #5}
	}\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\ccode#1{\par
	\vspace*{8pt}
	{\authorfont{\leftskip18pt\rightskip\leftskip
	\noindent #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}
%
\newenvironment{otherinfo}{%
	\addvspace{-2pt plus-2pt minus-2pt}
   \authorfont\begin{center}%\vskip-\lastskip
}{%
   \end{center}
	\addvspace{15pt plus2pt minus2pt}
}
%
\newenvironment{dedication}{%
	\addvspace{-2pt plus-2pt minus-2pt}
   \authorfont\begin{center}%\vskip-\lastskip
}{%
   \end{center}
	\addvspace{15pt plus2pt minus2pt}
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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{\alph{enumii}}%
  \def\labelenumi{(\theenumi)}\def\labelenumii{(\theenumii)}%
		\let\item\Item
  \begin{enumerate}%
}{%
  \end{enumerate}}
%
\newenvironment{arabiclist}{%
	\def\theenumi{\arabic{enumi}}\def\theenumii{\arabic{enumii}}
	\def\labelenumi{\theenumi.}\def\labelenumii{(\theenumii)}%
	\let\item\Item
	\begin{enumerate}
	}{%
	\end{enumerate}}
%
\newenvironment{romanlist}{%
	\def\theenumi{\roman{enumi}}\def\theenumii{\roman{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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%

\@addtoreset{equation}{section}
\renewcommand\theequation{\thesection.\arabic{equation}}

%
\def\bstrut{\vrule width0pt depth5pt}
\def\tstrut{\vrule width0pt height10pt}
\jot=3pt
%
%
\renewcommand{\[}{\relax\ifmmode\@badmath\else\bgroup\let\eqnnum\relax\let\refstepeqcnt\relax\@equation\fi}
\renewcommand{\]}{\relax\ifmmode\end@equation\egroup\@endparenv\@doendpe\else\@badmath\fi}
%
\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\alttext#1{\relax}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\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}
%
\def\ArtDir{\jobname/}
%
%%%%%%%%%%%%%%%%%%%%%%%%%% 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}
%
%%
\newenvironment{tabfootnote}{%
   \par\addvspace{2pt}
   \setbox\tempbox\vbox\bgroup\hsize\tabledim\parindent12pt
   \tabnotefont
}{%
		\par\egroup
   \tableformat{\box\tempbox}}
%
%%
\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\\[-7.5pt]}
\def\colrule{\\[-7.5pt]\hline\\[-7.5pt]}
\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 %%%%%%%%%%%%%%%%%%%%%%%
%
\def\@xthm#1#2{\@begintheorem{#2}{\csname the#1\endcsname}{}\ignorespaces}
%

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

%
\let\Definitionfont\itshape%
\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}
%

\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 SOORAN - 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}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newtheorem{theorem}{Theorem}[section]   %Theorem 1.  
\newtheorem{corollary}[theorem]{Corollary}%[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{question}[theorem]{Question}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conjecture}[theorem]{Conjecture}%[section]
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newif\if@cghi
\def\cite{\@cghitrue\@ifnextchar [{\@tempswatrue\@citex}{\@tempswafalse\@citex[]}}
\def\@citex[#1]#2{%
  \let\@citea\@empty
  \@cite{\@for\@citeb:=#2\do
    {\@citea\def\@citea{,\penalty\@m}%
     \edef\@citeb{\expandafter\@firstofone\@citeb}%
     \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
     \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%
       \G@refundefinedtrue\@latex@warning
       {Citation `\@citeb' on page \thepage \space undefined}}%
     {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}
%
%
\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}    %connect to {theorem}
        %\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{Group 1 Journals}}
\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
\usepackage[figuresright]{rotating}  
\RequirePackage{amsfonts}
\RequirePackage{amssymb}
\RequirePackage{amsmath}
\RequirePackage{graphicx}
\endinput
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%End of file%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Text Area: 8in (include Runningheads) x 5in
%% ws-ijac.tex   :   23-06-2026
%% Tex file to use with ws-ijac.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 2026 by World Scientific Publishing Co.
%% All rights are reserved.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass{ws-ijac}

\usepackage{xcolor}
\usepackage[verbose]{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. Use footnote to indicate permanent address of 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.}\\
\email{author\_id@domain\_name\footnote{Typeset author's e-mail
address in 8pt italic.}} }

\author{Second Author}

\address{Group, Laboratory, Address\\
City, State ZIP/Zone, Country\\
author\_id@domain\_name }

\maketitle

\begin{history}
\received{(Day Month Year)}
\revised{(Day Month Year)}
\accepted{(Day Month Year)}
\published{(Day Month Year)}
\comby{}
\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 reference
citations or displayed equations. Typeset the abstract in 8 pt roman
with baselineskip of 10 pt, making an indentation of 0.25 inches on
the left and right margins.
\end{abstract}

\keywords{Keyword1; keyword2; keyword3.}

\ccode{Mathematics Subject Classification 2020: 81Q10, 81Q15, 35J10}

\section{General Appearance}	
Contributions to the {\it International Journal of Algebra and Computation}
will be processed by using the authors' source files. The format of
the files must be\break LaTeX/TeX.  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}
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).

Typeset text in 10 pt roman, single spaced with baselineskip of 13~pt.
Text area (excluding running title) is 5 inches across and 7.7 inches deep.
Final pagination and insertion of running heads will be done by
the publisher.

\section{Running Heads}
Please provide a shortened running head (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{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. Capitalize the
first letter of the first word only. Section number 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 presented with bullets or numbers.

\subsubsection{Bulleted items}

\begin{itemize}
\item First item in the first level
\item Second item in the first level
\begin{itemize}
\item First item in the second level
\item Second item in the second level
\begin{itemize}
\item First item in the third level
\item Second item in the third level
\end{itemize}
\item Third item in the second level
\item Fourth item in the second level
\end{itemize}
\item Third item in the first level
\item Fourth item in the first level
\end{itemize}

\subsubsection{Numbered items}

\begin{arabiclist}
\item First item in the first level
\item Second item in the first level
\begin{alphlist}[(a)]
\item First item in the second level
\item Second item in the second level
  \begin{romanlist}[(iii)]
\item[(i)] First item in the third level
\item[(ii)] Second item in the third level
\item[(iii)] Third item in the third level
\end{romanlist}
\item Third item in the second level
\item Fourth item in the second level
\end{alphlist}
\item Third item in the first level
\item Fourth item in the first level
\end{arabiclist}

\section{Equations}
Displayed equations should be numbered consecutively in each section,
with the number set flush right and enclosed in parentheses:
\begin{equation}
\mu(n, t) = \frac{\sum^\infty_{i=1} 1(d_i < t, N(d_i) = n)}{
\int^t_{\sigma=0} 1(N(\sigma) = n)d\sigma}\, .\label{eq1}
\end{equation}

In multiple-line equations, the number should be given on the last
line. Displayed equations are to be centered on the page width.
Punctuation marks are used at the end of equations as if they
appeared directly in the text.

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}

Equations should be referred to in the abbreviated form,
e.g.~``$\ldots$ in Eq.~(\ref{eq1})'' or
``$\ldots$ in (\ref{eq1})'' or
``$\ldots$ in Eqs.~(\ref{eq1}) and (6.2)''. Where the
word ``Equation'' begins a sentence, it should be spelled in full.

\section{Theorem Environments\label{sfive}}

\begin{theorem}\label{thm1}
Theorems, lemmas, corollaries, propositions, remarks,
examples, etc. are to be numbered consecutively in each section.
Use an extra one line space before and after each theorem,
lemma, etc.
\end{theorem}

\begin{lemma}\label{lem1}
The headings are in boldface; the statements of theorem,
lemmas, corollaries and propositions in italics, and the
remarks and examples in roman.
\end{lemma}

\begin{proof}
The heading is in boldface, while the proof is in roman.
Proofs should end with a box.
\end{proof}

\begin{figure}[b]
\centerline{\includegraphics[width=1.5in]{ijacf1}}
\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}
\alttext{Description of the figure}
\end{figure}

\section{Illustrations and Photographs}
Figures are to be inserted in the text nearest their first reference. 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 photo\-graphs are to be used, only black and white ones are acceptable.

Figures are to be numbered sequentially 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.

Figures should be referred to in the abbreviated form,
e.g.~``$\ldots$ in Fig.~\ref{fig1}'' or ``$\ldots$ in
Figs.~\ref{fig1} and 2''. Where the word ``Figure'' begins a
sentence, it should be spelled in full.

\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
table text and captions in 8 pt roman with baselineskip of 10 pt.

\begin{table}[ht]
\tbl{Comparison of acoustic for frequencies for piston-cylinder problem.}
{\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}}
\end{table}

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

\section*{Acknowledgments}
This section should come before the References. Dedications and 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}
Use only when absolutely necessary. They should come before the References. If there is more than one appendix, number them alphabetically. Number displayed equations occurring in the Appendix as follows: (\ref{app1}), (A.2), etc.
\begin{equation}
\mu(n, t) = \frac{\sum^\infty_{i=1} 1(d_i < t,
N(d_i) = n)}{\int^t_{\sigma=0} 1(N(\sigma) = n)d\sigma}\,.
\label{app1}
\end{equation}

\section*{References}
References are to be listed in alphabetical order with Arabic numerals
within square brackets. They can be referred to indirectly,
e.g.~``$\ldots$ in the statement \cite{2}.'' or used directly,
e.g.~``$\ldots$ see [2] for examples.'' List references 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{1} A. Alekseev, A. Malkin and E. Meinrenken, Lie group valued
moment maps, {\it J. Differential Geom.} {\bf 48}(3) (1998) 445-495.

\bibitem{2} F. Bouchut, On zero pressure gas dynamics, in
{\it Advances in Kinetic Theory and Computing}, ed.~B. Perthame,
Series on Advances in Mathematics for Applied Sciences, Vol.~22 (World Scientific, 1994),
pp.~171--190, \url{https://doi.org/10.1142/9789814354165_0006}.

\bibitem{3} S. K. Godunov and E. Romenskii, {\it Elements of Continuum
Mechanics and Conservation Laws} (Kluwer Academic/Plenum Publishers,
2003), \url{https://doi.org/10.1007/978-1-4757-5117-8}.

\bibitem{4} J. Li and T. Zhang, On the initial-value problem for
zero-pressure gas dynamics, in {\it Proc. 7th Intl. Conf. on Hyperbolic
Problems}, ed. R. Jeltsch (Birkhauser Verlag, 1998), pp.~629--640, \url{https://doi.org/10.1007/978-3-0348-8724-3_14}.
\end{thebibliography}

\end{document} 

\documentclass{ws-ijac}

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

\begin{document}

\def\bib{B\kern-.05em{I}\kern-.025em{B}\kern-.08em}
\def\btex{B\kern-.05em{I}\kern-.025em{B}\kern-.08em\TeX}

\title{\large B\kern-.05em{\large I}\kern-.025em{\large B}\kern-.08em\TeX ing\\[.5ex] in \\[.5ex] WSPC \bib\/
Style}

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

\maketitle

\enlargethispage{-13pt}

\section{Usage}

\begin{verbatim}
\documentclass{ws-ijac}
\usepackage{url}

\begin{document}

\section{Output}
Sample output using ws-ijac bibliography style file ...
text\cite{best,pier,jame} ...

\bibliographystyle{ws-ijac}
\bibliography{sample}
\end{document}
\end{verbatim}

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

\begin{enumerate}[(14)]
\item article: text\cite{best,pier,jame}
\item proceedings: text\cite{Weiss94}
\item inproceedings: text\cite{conftypical,Moss94}
\item book: text\cite{ArmsRace1}
\item edition: text\cite{ComplexVariables}
\item editor: text\cite{ColBenh:93}
\item series: text\cite{inbook}
\item tech report: text\cite{hobby1992,CSTR116}
\item unpublished: text\cite{VoQS}
\item phd thesis: text\cite{Brown:1988:IEL}
\item masters thesis: text\cite{segms}
\item incollection: text\cite{Jones:Phoneme}
\item booklet: text\cite{URW:kerning}
\item misc: see Ref.~\refcite{netpbm} for examples
\end{enumerate}

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

\end{document}