Philosophical Transactions of the Royal Society B

%% This is file `RS.bst'

ENTRY
  { address
    author
    booktitle
    chapter
    edition
    editor
    howpublished
    institution
    journal
    key
    month
    note
    number
    organization
    pages
    publisher
    school
    series
    title
    type
    volume
    year
    doi
  }
  {}
  { label extra.label sort.label }

INTEGERS { output.state before.all mid.sentence after.sentence after.block }

INTEGERS { no.comma}

FUNCTION {init.state.consts}
{ #0 'before.all :=
  #1 'mid.sentence :=
  #2 'after.sentence :=
  #3 'after.block :=
  #4 'no.comma :=
}

STRINGS { s t }

FUNCTION {output.nonnull}
{ 's :=
 output.state no.comma = 
 {  " " * write$ before.all 'output.state := }
 {  output.state mid.sentence =
    { " " * write$ }
    { output.state after.block =
        { add.period$ write$
          newline$
          "" write$
        }
        { output.state before.all =
            'write$
            { add.period$ " " * write$ }
          if$
        }
      if$
  }
 if$
 mid.sentence 'output.state :=
 }  
 if$    
  s
}

FUNCTION {bookoutput.nonnull}
{ 's :=
 output.state no.comma = 
 {  " " * write$ before.all 'output.state := }
 {  output.state mid.sentence =
    { ": " * write$ }
    { output.state after.block =
        { add.period$ write$
          newline$
          "" write$
        }
        { output.state before.all =
            'write$
            { add.period$ " " * write$ }
          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 {bookoutput.check}
{ 't :=
  duplicate$ empty$
    { pop$ "empty " t * " in " * cite$ * warning$ }
    'bookoutput.nonnull
  if$
}


FUNCTION {output.year.check}
{ year empty$
    { "empty year in " cite$ * warning$ }
    { write$
      ". " year * extra.label * " " *
      before.all 'output.state :=
    }
  if$
}

FUNCTION {output.bibitem}
{ newline$
  "\bibitem{" write$
  cite$ write$
  "}" write$
  newline$
  ""
  before.all 'output.state :=
}


FUNCTION {fin.entry}
{ doi empty$
    { add.period$ }
    'skip$
  if$
  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 {not}
{   { #0 }
    { #1 }
  if$
}

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

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

FUNCTION {new.block.checkb}
{ empty$
  swap$ empty$
  and
    'skip$
    'new.block
  if$
}

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

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

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


INTEGERS { nameptr namesleft numnames }

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

FUNCTION {format.key}           
{ empty$
    { key field.or.null }
    { "" }
  if$
}

FUNCTION {format.editors}
{ editor empty$
    { "" }
    { editor format.names
      editor num.names$ #1 >
    { ", editors" * }
    { ", editor" * }
      if$
    }
  if$
}

FUNCTION {format.title}
{ title empty$
    { "" }
    { title
      "" swap$ * ". " *
    }
no.comma 'output.state :=   
  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.btitle}
{ title emphasize
}

FUNCTION {format.bintitle}
{ "In " title emphasize * "," *
}

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

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

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

FUNCTION {format.binvolume}
{ volume empty$
    { "" }
    { "vol." volume tie.or.space.connect  ", " * 
      series empty$
    'skip$
    { "" * series emphasize * }
      if$
      "volume and number" number either.or.check
    }
  if$
}

FUNCTION {format.bincvolume}
{ volume empty$
    { ", " }
    {series empty$
    'skip$
    { ", " * series * ", " * 
    "vol." volume tie.or.space.connect ", " * }
      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 =
        { "number" }
        { "Number" }
      if$
      number tie.or.space.connect
      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$ " edition" * }
    { edition "t" change.case$ " edition" * }
      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 {format.pages}
{ pages empty$
    { "" }
    { pages multi.page.check 
    { "pp." pages n.dashify tie.or.space.connect }
    { "p." pages tie.or.space.connect }
      if$
    }
  if$
}

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


FUNCTION {format.vol.num.pages}
{ volume bold field.or.null
  number empty$
    'skip$
    { "" "" * *
      volume empty$
        { "there's a number but no volume in " cite$ * warning$ }
        'skip$
      if$
    }
  if$
  pages empty$
    'skip$
    { duplicate$ empty$
        { pop$ format.pages }
        { ", " * pages n.dashify * }
      if$
    }
  if$
}

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

FUNCTION {format.inchapter.pages}
{ chapter empty$
    'format.pages
    { type empty$
    { "" }
    { type "l" change.case$ }
      if$
      chapter tie.or.space.connect
      pages empty$
    'skip$
    {}
      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$
      type "t" change.case$
    }
  if$
}

FUNCTION {format.tr.number}
{ type empty$
    { "Technical Report" }
    'type
  if$
  number empty$
    { "t" change.case$ }
    { number tie.or.space.connect }
  if$
}

FUNCTION {format.article.crossref}
{ "In"                          
  " \cite{" * crossref * "}" *
}

FUNCTION {format.book.crossref}
{ volume empty$
    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
      "In "
    }
    { "Volume" volume tie.or.space.connect
      " of " *
    }
  if$
  "\cite{" * crossref * "}" *               
}

FUNCTION {format.incoll.inproc.crossref}
{ "In"                          
  " \cite{" * crossref * "}" *
}

FUNCTION {format.doi}
{ doi empty$
    { "" }
    {
      "(\href{http://dx.doi.org/" doi * "}{" * doi * "})" *
    }
  if$
}

FUNCTION {article}
{ output.bibitem
  format.authors "author" output.check
  author format.key output              
  output.year.check                 
  format.title "title" output.check 
  crossref missing$
    { journal emphasize "journal" output.check 
      format.vol.num.pages output
    }
    { format.article.crossref output.nonnull
      format.pages output
    }
  if$
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {book}
{ output.bibitem
  author empty$
    { format.editors "author and editor" output.check
      editor format.key output
    }
    { format.authors output.nonnull
      crossref missing$
    { "author and editor" editor either.or.check }
    'skip$
      if$
    }
  if$
  output.year.check             
  new.block
  format.btitle "title" output.check
  crossref missing$
    { format.bvolume output
      new.block
      format.number.series output
      new.sentence
      address output
      publisher "publisher" bookoutput.check
    }
    { new.block
      format.book.crossref output.nonnull
    }
  if$
  format.edition output
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {booklet}
{ output.bibitem
  format.authors output
  author format.key output              
  output.year.check                 
  new.block
  format.title "title" output.check
  new.block
  howpublished output
  address output
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {inbook}
{ output.bibitem
  author empty$
    { format.editors "author and editor" output.check
      editor format.key output
    }
    { format.authors output.nonnull
      crossref missing$
    {"author and editor" editor either.or.check }
    'skip$
      if$
    }
  if$
  output.year.check             
  new.block
  format.inchapter.pages "chapter and pages" output.check
  new.block
  format.bintitle "title" output.check
  crossref missing$
    { format.binvolume output
      format.number.series output
      format.inpages output 
      new.sentence
      address output
      publisher "publisher" bookoutput.check
    }
    { format.chapter.pages "chapter and pages" output.check
      new.block
      format.book.crossref output.nonnull
    }
  if$
  format.edition output
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {incollection}
{ output.bibitem
  format.authors "author" output.check
  author format.key output              
  output.year.check                 
  new.block
  format.title "title" output.check
  new.block
  crossref missing$
    { format.in.ed.booktitle "booktitle" output.check
      format.bincvolume output
      format.number.series output
      format.inpages output
      new.sentence
      address output
      publisher "publisher" bookoutput.check
      format.edition output
    }
    { format.incoll.inproc.crossref output.nonnull
      format.chapter.pages output
    }
  if$
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {inproceedings}
{ output.bibitem
  format.authors "author" output.check
  author format.key output              
  output.year.check                 
  new.block
  format.title "title" output.check
  new.block
  crossref missing$
    { format.in.ed.booktitle "booktitle" output.check
      format.bvolume output
      format.number.series output
      format.pages output
      address output                    
      new.sentence                  
      organization output               
      publisher output                  
    }
    { format.incoll.inproc.crossref output.nonnull
      format.pages output
    }
  if$
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {conference} { inproceedings }

FUNCTION {manual}
{ output.bibitem
  format.authors output
  author format.key output              
  output.year.check                 
  new.block
  format.btitle "title" output.check
  organization address new.block.checkb
  organization output
  address output
  format.edition output
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {mastersthesis}
{ output.bibitem
  format.authors "author" output.check
  author format.key output              
  output.year.check                 
  new.block
  format.title "title" output.check
  new.block
  "Master's thesis" format.thesis.type output.nonnull
  school "school" output.check
  address output
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {misc}
{ output.bibitem
  format.authors output
  author format.key output              
  output.year.check                 
  new.block
  format.title output
  new.block
  howpublished output
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {phdthesis}
{ output.bibitem
  format.authors "author" output.check
  author format.key output              
  output.year.check                 
  new.block
  format.btitle "title" output.check
  new.block
  "PhD thesis" format.thesis.type output.nonnull
  school "school" output.check
  address output
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {proceedings}
{ output.bibitem
  format.editors output
  editor format.key output              
  output.year.check                 
  new.block
  format.btitle "title" output.check
  format.bvolume output
  format.number.series output
  address output                
  new.sentence                  
  organization output               
  publisher output              
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {techreport}
{ output.bibitem
  format.authors "author" output.check
  author format.key output              
  output.year.check                 
  new.block
  format.title "title" output.check
  new.block
  format.tr.number output.nonnull
  institution "institution" output.check
  address output
  new.block
  note output
  format.doi output
  fin.entry
}

FUNCTION {unpublished}
{ output.bibitem
  format.authors "author" output.check
  author format.key output              
  output.year.check                 
  new.block
  format.title "title" output.check
  new.block
  note "note" output.check
  format.doi 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 of the ACM"}

MACRO {ibmjrd} {"IBM Journal of Research and Development"}

MACRO {ibmsj} {"IBM Systems Journal"}

MACRO {ieeese} {"IEEE Transactions on Software Engineering"}

MACRO {ieeetc} {"IEEE Transactions on Computers"}

MACRO {ieeetcad}
 {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"}

MACRO {ipl} {"Information Processing Letters"}

MACRO {jacm} {"Journal of the ACM"}

MACRO {jcss} {"Journal of Computer and System Sciences"}

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

MACRO {sicomp} {"SIAM Journal on Computing"}

MACRO {tocs} {"ACM Transactions on Computer Systems"}

MACRO {tods} {"ACM Transactions on Database Systems"}

MACRO {tog} {"ACM Transactions on Graphics"}

MACRO {toms} {"ACM Transactions on Mathematical Software"}

MACRO {toois} {"ACM Transactions on Office Information Systems"}

MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"}

MACRO {tcs} {"Theoretical Computer Science"}

READ

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 {format.lab.names}
{ 's :=
  s #1 "{vv~}{ll}" format.name$
  s num.names$ duplicate$
  #2 >
    { pop$ " et~al." * }
    { #2 <
    'skip$
    { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
        { " et~al." * }
        { " \& " * s #2 "{vv~}{ll}" format.name$ * }
      if$
    }
      if$
    }
  if$
}

FUNCTION {author.key.label}
{ author empty$
    { key empty$
    { cite$ #1 #3 substring$ }
    'key                    
      if$
    }
    { author format.lab.names }
  if$
}

FUNCTION {author.editor.key.label}
{ author empty$
    { editor empty$
    { key empty$
        { cite$ #1 #3 substring$ }
        'key                
      if$
    }
    { editor format.lab.names }
      if$
    }
    { author format.lab.names }
  if$
}

FUNCTION {editor.key.label}
{ editor empty$
    { key empty$
    { cite$ #1 #3 substring$ }
    'key            
      if$
    }
    { editor format.lab.names }
  if$
}

FUNCTION {calc.label}
{ type$ "book" =
  type$ "inbook" =
  or
    'author.editor.key.label
    { type$ "proceedings" =
    'editor.key.label           
    'author.key.label           
      if$
    }
  if$
  ", "                          
  *                         
  year field.or.null purify$ #-1 #4 substring$      
  *
  'label :=
}

FUNCTION {sort.format.names}
{ 's :=
  #1 'nameptr :=
  ""
  s num.names$ 'numnames :=
  numnames 'namesleft :=
    { namesleft #0 > }
    { nameptr #1 >
    { "   " * }
    'skip$
      if$                       
      s nameptr "{vv{ } }{ll{ }}{  f{ }}{  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 {editor.sort}
{ editor empty$
    { key empty$
    { "to sort, need editor or key in " cite$ * warning$
      ""
    }
    { key sortify }
      if$
    }
    { editor sort.format.names }
  if$
}

FUNCTION {presort}
{ calc.label
  label sortify
  "    "
  *
  type$ "book" =
  type$ "inbook" =
  or
    'author.editor.sort
    { type$ "proceedings" =
    'editor.sort
    'author.sort
      if$
    }
  if$
  #1 entry.max$ substring$  
  'sort.label :=        
  sort.label            
  *
  "    "
  *
  title field.or.null
  sort.format.title
  *
  #1 entry.max$ substring$
  'sort.key$ :=
}

ITERATE {presort}

%SORT        

STRINGS { last.label next.extra }   %

INTEGERS { last.extra.num }     % 

FUNCTION {initialize.extra.label.stuff} % 
{ #0 int.to.chr$ 'last.label :=
  "" 'next.extra :=
  #0 'last.extra.num :=
}

FUNCTION {forward.pass}
{ last.label label =
    { last.extra.num #1 + 'last.extra.num :=
      last.extra.num int.to.chr$ 'extra.label :=
    }
    { "a" chr.to.int$ 'last.extra.num :=
      "" 'extra.label :=
      label 'last.label :=
    }
  if$
}

FUNCTION {reverse.pass}
{ next.extra "b" =
    { "a" 'extra.label := }
    'skip$
  if$
  label extra.label * 'label :=
  extra.label 'next.extra :=
}

EXECUTE {initialize.extra.label.stuff}

ITERATE {forward.pass}

REVERSE {reverse.pass}

FUNCTION {bib.sort.order}
{ sort.label
  "    "
  *
  year field.or.null sortify
  *
  "    "
  *
  title field.or.null
  sort.format.title
  *
  #1 entry.max$ substring$
  'sort.key$ :=
}

ITERATE {bib.sort.order}

%SORT        %

FUNCTION {begin.bib}
{ preamble$ empty$              %
    'skip$
    { preamble$ write$ newline$ }
  if$
  "\begin{thebibliography}{99}" write$ newline$       %
}

EXECUTE {begin.bib}

EXECUTE {init.state.consts}

ITERATE {call.type$}

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

EXECUTE {end.bib}

%% Author_tex.tex
%% V1.0
%%  2022/08/16
%% developed by Techset
%%
%% This file describes the coding for rsproca.cls

\documentclass[openacc]{rstb}%%%%where rsproca is the template name

%%%% *** Do not adjust lengths that control margins, column widths, etc. ***

%%%%%%%%%%% Defining Enunciations  %%%%%%%%%%%
\newtheorem{theorem}{\bf Theorem}[section]
\newtheorem{condition}{\bf Condition}[section]
\newtheorem{corollary}{\bf Corollary}[section]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%% Please insert respective article type here %%%%
\titlehead{Research}

\begin{document}

%%%% Article title to be placed here
\title{Your paper}

\author{%%%% Author details
X. X. First author$^{1}$, X. Second author$^{2}$ and X. Third author$^{3}$
X. X. Fourth author$^{4}$, X. Fifth author$^{5}$ and X. Sixth author$^{6}$
X. X. Seventh author$^{7}$, X. Eighth author$^{8}$ and X. Ninth author$^{9}$
X. X. Tenth author$^{10}$, X. Eleventh author$^{11}$ and X. twelfth author$^{12}$
X. X. Thirteenth author$^{13}$, X. Fourteenth author$^{14}$ and X. Fifteenth author$^{15}$}

%%%%%%%%% Insert author address here
\address{$^{1}$First author address\\
$^{2}$Second author address\\
$^{3}$Third author address\\
$^{4}$Fourth author address\\
$^{5}$Fifth author address\\
$^{6}$Sixth author address\\
$^{7}$Seventh author address\\
$^{8}$Eighth author address\\
$^{9}$Ninth author address\\
$^{10}$Tenth author address\\
$^{11}$Eleventh author address\\
$^{12}$Twelfth author address\\
$^{13}$Thirteenth author address\\
$^{14}$Fourteenth author address\\
$^{15}$Fifteenth author address}

%%%% Subject entries to be placed here %%%%
\subject{xxxxx, xxxxx, xxxx}



%%%% Insert corresponding author and its email address}
\corres{Insert corresponding author name\\
\email{[email protected]}}

%%%% Abstract text to be placed here %%%%%%%%%%%%
\begin{abstract}
Para 1 The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.

Para 2 The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.

Para 3 The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.

Para 4 The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
The abstract text goes here. The abstract text goes here. The abstract text goes here. The abstract text goes here.
\end{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%% Keyword entries to be placed here %%%%
\keywords{xxxx, xxxx, xxxx}

\rsbreak

%%%%%%%%%% Insert the texts which can accomdate on firstpage in the tag "fmtext" %%%%%

\section{Insert A head here}
%%%% Insert A head here

This demo file is intended to serve as a ``starter file''
for rsproca journal papers produced under \LaTeX\ using
rsproca\_new.cls v1.0.

\subsection{Insert B head here}
%%%% Insert B head here
Subsection text here.

\subsubsection{Insert C head here}
%%%% Insert C head here
Subsubsection text here.

\section{Equations}

Sample equations.

%%% Numbered equation
\begin{align}\label{1.1}
\begin{split}
\frac{\partial u(t,x)}{\partial t} &= Au(t,x) \left(1-\frac{u(t,x)}{K}\right)-B\frac{u(t-\tau,x) w(t,x)}{1+Eu(t-\tau,x)},\\
\frac{\partial w(t,x)}{\partial t} &=\delta \frac{\partial^2w(t,x)}{\partial x^2}-Cw(t,x)+D\frac{u(t-\tau,x)w(t,x)}{1+Eu(t-\tau,x)},
\end{split}
\end{align}

\begin{align}\label{1.2}
\begin{split}
\frac{dU}{dt} &=\alpha U(t)(\gamma -U(t))-\frac{U(t-\tau)W(t)}{1+U(t-\tau)},\\
\frac{dW}{dt} &=-W(t)+\beta\frac{U(t-\tau)W(t)}{1+U(t-\tau)}.
\end{split}
\end{align}

%%%% Unnumbered equation
\begin{eqnarray}
\frac{\partial(F_1,F_2)}{\partial(c,\omega)}_{(c_0,\omega_0)} = \left|
\begin{array}{ll}
\frac{\partial F_1}{\partial c} &\frac{\partial F_1}{\partial \omega} \\\noalign{\vskip3pt}
\frac{\partial F_2}{\partial c}&\frac{\partial F_2}{\partial \omega}
\end{array}\right|_{(c_0,\omega_0)}\notag\\
=-4c_0q\omega_0 -4c_0\omega_0p^2 =-4c_0\omega_0(q+p^2)>0.
\end{eqnarray}

%%%%%%%%%%%%%%% End of first page %%%%%%%%%%%%%%%%%%%%%

\maketitle

\section{Enunciations}

\begin{theorem}\label{T0.1}
Assume that $\alpha>0, \gamma>1, \beta>\frac{\gamma+1}{\gamma-1}$.
Then there exists a small $\tau_1>0$, such that for $\tau\in
[0,\tau_1)$, if $c$ crosses $c(\tau)$ from the direction of
to  a small amplitude periodic traveling wave solution of
(2.1), and the period of $(\check{u}^p(s),\check{w}^p(s))$ is
\[
\check{T}(c)=c\cdot \left[\frac{2\pi}{\omega(\tau)}+O(c-c(\tau))\right].
\]
\end{theorem}


\begin{condition}\label{C2.2}
From (0.8) and (2.10), it holds
$\frac{d\omega}{d\tau}<0,\frac{dc}{d\tau}<0$ for $\tau\in
[0,\tau_1)$. This fact yields that the system (2.1) with delay
$\tau>0$ has the periodic traveling waves for smaller wave speed $c$
than that the system (2.1) with $\tau=0$ does. That is, the
delay perturbation stimulates an early occurrence of the traveling waves.
\end{condition}


\section{Figures \& Tables}

The output for figure is:\vspace*{-7pt}

\begin{figure}[!h]
%\centering\includegraphics[width=2.5in]{xxxxxx.eps}
%%% where xxxxxx name represents "figurename.eps"
\caption{Insert figure caption here}
\label{fig_sim}
\end{figure}

\vspace*{-5pt}

\noindent The output for table is:\vspace*{-7pt}

\begin{table}[!h]
\caption{An Example of a Table}%%%Table caption goes here
\label{table_example}
\begin{tabular}{llll}%%%The number of columns has to be defined here
\hline
date &Dutch policy &date &European policy \\
\hline
1988 &Memorandum Prevention &1985 &European Directive (85/339) \\
1991--1997 &{\bf Packaging Covenant I} & & \\
1994 &Law Environmental Management &1994 &European Directive (94/62) \\
1997 &Agreement Packaging and Packaging Waste & & \\\hline
\end{tabular}
\vspace*{-4pt}
\end{table}%%%End of the table

\section{Conclusion}
The conclusion text goes here.\vskip6pt

\enlargethispage{20pt}

\ack{Insert acknowledgment text here.}


%%%%%%%%%% Insert bibliography here %%%%%%%%%%%%%%

\vskip2pc

\noindent {\bf Please follow the coding for references as shown below.}

\begin{thebibliography}{9}

\bibitem{1} Allwood JM, Cullen JM. 2011 \textit{Sustainable materials:  with both eyes open}.
Cambridge, UK: UIT Cambridge. See \href{http://www.withbotheyesopen.com}{http://www.withbotheyesopen.com}.

\bibitem{2}  MacKay DJC. 2008  \textit{Sustainable energy:  without the hot air}.
 Cambridge, UK: UIT Cambridge. See \href{http://www.withouthotair.com}{http://www.withouthotair.com}.

\bibitem{3} Gallman PG. 2011  \textit{Green alternatives and national energy strategy: the facts
 behind the headlines}.  Baltimore,\ MD: Johns Hopkins University Press.

\bibitem{4} MacKay DJC. 2013.  Solar energy in the context of energy use, energy transportation, and
 energy storage. \textit{Proc. R. Soc. A} \textbf{371}.

\end{thebibliography}

\noindent If maintaining .bib file for references, then please use "RS.bst" to generate the references.

\noindent Example:

\verb+\bibliographystyle{RS}+ %%%% .BST file

\verb+\bibliography{sample}+ %%%%% .Bib file

\end{document}

51 KB — too long to show here. It arrives with the project.

@book {Lannes,
AUTHOR = {Lannes, David},
TITLE = {The Water Waves Problem: Mathematical Analysis and Asymptotics},
SERIES = {Mathematical Surveys and Monographs},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2013},
ISBN = {9780821894705},
}


@article {HJ2,
AUTHOR = {Hur, Vera Mikyoung and Johnson, Mathew A.},
TITLE = {Modulational instability in the {W}hitham equation for water waves},
JOURNAL = {Stud. Appl. Math.},
FJOURNAL = {Studies in Applied Mathematics},
VOLUME = {134},
YEAR = {2015},
NUMBER = {1},
PAGES = {120--143},
ISSN = {0022-2526},
MRCLASS = {35Q53 (35B10 35C07)},
MRNUMBER = {3298879},
MRREVIEWER = {Thierry Cazenave},
}

@article {BF,
AUTHOR = {Benjamin, T. B. and Feir, J. E.},
TITLE = {The disintegration of wave trains on deep water. {P}art 1. {T}heory},
JOURNAL = {J. Fluid Mech.},
FJOURNAL = {Journal of Fluid Mechanics},
VOLUME = {27},
YEAR = {1967},
NUMBER = {3},
PAGES = {417--437},
ISSN = {0022-1120},
}

@article{Benjamin1967,
AUTHOR={Benjamin, T. Brooke and Hasselmann, K},
TITLE={Instability of Periodic Wavetrains in Nonlinear Dispersive Systems [and Discussion]},
JOURNAL = {Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.},
FJOURNAL = {Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences},
VOLUME={299},
YEAR={1967},
NUMBER={1456},
PAGES={59--76},
ISSN = {1364-5021}
}

@article {HJ3,
AUTHOR = {Hur, Vera Mikyoung and Johnson, Mathew A.},
TITLE = {Modulational instability in the {W}hitham equation with surface tension and vorticity},
JOURNAL = {Nonlinear Anal.},
FJOURNAL = {Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods},
VOLUME = {129},
YEAR = {2015},
PAGES = {104--118},
ISSN = {0362-546X},
MRCLASS = {Preliminary Data},
MRNUMBER = {3414922},
}

@article{HP2,
AUTHOR={Hur, Vera Mikyoung and Pandey, Ashish Kumar},
TITLE={Modulational instability in a shallow water model},
JOURNAL={Preprint},
PAGES={1608.04685},
YEAR={2016}
}

@incollection{BHJ,
AUTHOR={Bronski, Jared C. and Hur, Vera Mikyoung and Johnson, Mathew A.},
TITLE={Modulational instability in equations of {K}d{V} type},
BOOKTITLE={New Approaches to Nonlinear Waves},
EDITORS={Tobiscnh, Elena},
SERIES={Lecture Notes in Physics},
VOLUME={908},
YEAR={2016},
PAGES={83--133},
PUBLISHER={Springer International Publishing},
ADDRESS={Berlin, Germany}
}

@book {K,
    AUTHOR = {Kato, Tosio},
     TITLE = {Perturbation theory for linear operators},
   EDITION = {Second},
      NOTE = {Grundlehren der Mathematischen Wissenschaften, Band 132},
 PUBLISHER = {Springer-Verlag, Berlin-New York},
      YEAR = {1976},
     PAGES = {xxi+619},
   MRCLASS = {47-XX},
  MRNUMBER = {0407617 (53 \#11389)},
}

@article{Hur-blowup,
AUTHOR = {Hur, Vera Mikyoung},
TITLE = {On the formation of singularities for surface water waves},
JOURNAL = {Commun. Pure Appl. Anal.},
FJOURNAL = {Communications on Pure and Applied Analysis},
VOLUME = {11},
YEAR = {2012},
NUMBER = {4},
PAGES = {1465--1474},
ISSN = {1534-0392},
MRCLASS = {35R11 (35B44 35Q53 35R37 76B15)},
MRNUMBER = {2900797},
MRREVIEWER = {Francesco Petitta},
}

@article{Hur-breaking,
AUTHOR = {Hur, Vera Mikyoung},
TITLE={Wave breaking in the {W}hitham equation for shallow water},
JOURNAL={Preprint},
PAGES={arxiv:1506.04075},
YEAR={2015}
}

@article{BJ1,
AUTHOR = {Bronski, Jared C. and Johnson, Mathew A.},
TITLE = {The modulational instability for a generalized {K}orteweg-de {V}ries equation},
JOURNAL = {Arch. Ration. Mech. Anal.},
FJOURNAL = {Archive for Rational Mechanics and Analysis},
VOLUME = {197},
YEAR = {2010},
NUMBER = {2},
PAGES = {357--400},
ISSN = {0003-9527},
MRCLASS = {35Q53 (35B10 35B35 35C07 76B25)},
MRNUMBER = {2660515 (2012f:35456)},
MRREVIEWER = {John Albert},
}