Astrophysical Bulletin (revtex4-2, maik.rty)

2018A&A...616A...1G
@ARTICLE{Gaia1,
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2013A&A...551A..36N
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2000A&A...355.1164G
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2002A&A...391..647G
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}
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      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
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2017AJ....153..208B
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2019MNRAS.484L...8T
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          doi = {10.1093/mnrasl/sly227},
archivePrefix = {arXiv},
       eprint = {1810.02986},
 primaryClass = {astro-ph.EP},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2019MNRAS.484L...8T},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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\selectlanguage{english}

\keywords{stars: double or binary---stars: individual: ADS\,48}

%\ydk{}
%\titlerunning{}
%\authorrunning{}
%\toctitle{}
%\tocauthor{}

\title{Your paper}

\author{\firstname{I.}~\surname{Author1}}
 \email{[email protected]}
 \affiliation{Main (Pulkovo) Astronomical Observatory
of the RAS, St. Petersburg, 196140 Russia}

\author{\firstname{I.}~\surname{Author2}}
 \affiliation{\saoname}


\begin{abstract}
We study the nearest outskirts ($R<3R_{200c}$) of 40 groups and
clusters of galaxies of the local Universe ($0.02<z<0.045$ and
300~km~s$^{-1}<\sigma<950$~km~s$^{-1}$). Using the SDSS\,DR10
catalog data, we determined the stellar mass of galaxy clusters
corresponding to $K_s$-luminosity (which we determined earlier
based on the 2MASX catalog data) $(M_*/M_{\odot}) \propto
(L_K/L_{\odot})^{1.010\pm0.004}$ (\mbox{$M_K<-21\fm5$},
$R<R_{200c}$). We also found the dependence of the galaxy cluster
stellar mass on halo mass: \mbox{$(M_*/M_{\odot}) \propto
(M_{200c}/M_{\odot})^{0.77\pm0.01}$}\ldots
\end{abstract}

\maketitle

\section{INTRODUCTION}

The multiple star system ADS\,48, discovered by Otto Struve in 1876,
has been repeatedly investigated by various authors~\citep[see,
for example,][]{G-L, Hopman}, but their attention was mainly attracted
by the inner pair AB. According to the identification in the \citet{WDS}
catalog, the three stars---A, B and F---are physically connected
(by common parallax and proper motions). For the inner AB pair,
there has been a long series of observations since its discovery,
and the F component has not been observed for almost a century.


\section{FIRST SECTION}

Here comes some math:
\begin{eqnarray}
\rho&=&\sqrt{x^2+y^2}~,~~~\, \qquad \theta\;=\;\arctan\dfrac{x}{y} \nonumber \\
\mu&=&\sqrt{\mu_{x}'^2+\mu_{y}'^2}~, \qquad
\psi\;=\;\arctan\dfrac{\mu_{x}'}{\mu_{y}'}. \nonumber
\end{eqnarray}
Here
\begin{eqnarray}
x&=&(\alpha_{\rm B}-\alpha_{\rm A})\cos{\delta}\times3600,\nonumber\\
y&=&(\delta_{\rm B}-\delta_{\rm A})\times3600,\nonumber\\
\delta&=&(\delta_{\rm A}+\delta_{\rm B})/2,\nonumber\\
\mu_{x}'&=&\mu_{x{\rm B}}-\mu_{x{\rm A}},\nonumber
\qquad\mu_{y}'=\mu_{y{\rm B}}-\mu_{y{\rm A}}\nonumber.
\end{eqnarray}

%1
\begin{table*}
\caption {Two column table} \label{pvd}
\medskip
\begin{tabular}{c|c|c|c|c|c}
\hline
pair                           & AB             & AB                    & AB--F             & AB--F              & AB--F \\
\hline
\multirow{2}{*}{Instrument}    & $26''$, CCD    & \multirow{2}{*}{GAIA} & $26\arcsec$, photo & $26\arcsec$, photo  & \multirow{2}{*}{GAIA} \\
                               & individual &                       & individual    & smoothed         &    \\
\cline{1-1}
Parameters                      &                &                       &                   &                    &    \\
\hline
$T_1-T_2$                        & $2003$--$2012$ & --           & $1968$--$1995$ & 1971--1992  & -- \\
$T_0$                            & $2008.6$       & $2015.5$     & $1981.5$       & 1981.5      & $2015.5$ \\
  n                              & $48$           & --           & $115$          & 30          & -- \\
 \hline
$\rho$, arcsec.                & $6.0534$       & $6.00768^*$  & $327.3322$     & $327.3339$  & $327.1754$ \\
                                 & $\pm0.0012$    & $\pm0.00008$ & $\pm0.0023$    & $\pm0.0010$ & $\pm0.0002$ \\
\hline
$\theta_{2000}$, degr.         & $185.3604$     & $188.2084$   & $254.2942$     & $254.2943$  & $254.25739$ \\
                                 & $\pm0.0059$    & $\pm0.0010$  & $\pm0.0017$    & $\pm0.0005$ & $\pm0.00001$ \\
\hline
$\mu$, mas/year                   & $43.1$         & $44.94$      & $4.3$          & $3.9$       & $5.4$ \\
                                 & $\pm0.3$       & $\pm0.18$    & $\pm0.5$       & $\pm0.2$    & $\pm0.1$ \\
\hline
$\psi_{2000}$, degr.             & $283.09$       & $288.06$     & $86.4$         & $73.2$      & $37.8$ \\
                                 & $\pm0.7$       & $\pm0.16$    & $\pm19.6$      & $\pm7.4$    & $\pm1.1$ \\
\hline
$\dot{\rho}$, mas/year            & $-6.4$         & $-7.7$       & $-4.2$         & $-3.9$      & $-4.4$ \\
                                 & $\pm0.5$       & $\pm0.1$     & $\pm0.4$       & $\pm0.2$    & $\pm0.1$ \\
\hline $\dot{\theta}$, degr./year & $0.4034$       & $0.4202$     & $-0.0002$      & $-0.0000$   & $-0.00056$ \\
                                 & $\pm0.0024$    & $\pm0.0017$  & $\pm0.0003$    & $\pm0.0001$ & $\pm0.00001$ \\
\hline
\multicolumn{6}{l}{\footnotesize {Here $n$ is the number
of individual or smoothed
observations,}} \\[-5pt]
\multicolumn{6}{l}{\footnotesize {$^*$---the value $\rho$
is given adjusted for Gaia--CCD$=+0\farcs03$.}}\\
\end{tabular}
\end{table*}

\begin{figure*}
\includegraphics[scale=0.3]{Kiyaeva_fig1a.eps}
\includegraphics[scale=0.3]{Kiyaeva_fig1b.eps}
\caption{Two column figure.}
 \label{G-CCD}
\end{figure*}

Table~\ref{pvd} shows AMPs calculated from observations of Gaia\,DR2,
and long-term series of observations of the Pulkovo 26-inch refractor.
For the AB pair, we compare only with the CCD observations of 2003--2012.
For this pair, we found a systematic discrepancy in $\rho$,
which is clearly visible in Fig.~\ref{G-CCD}.



\begin{figure}
\includegraphics[scale=0.3]{Kiyaeva_fig2a.eps}
\includegraphics[scale=0.3]{Kiyaeva_fig2b.eps}
\caption{One column figure.}
 \label{G-photo}
\end{figure}

\section{ANOTHER SECTION}

The text of the Section.



%\begin{figure*}
%\includegraphics[scale=0.33]{Kiyaeva_fig3a.eps}
%\includegraphics[scale=0.33]{Kiyaeva_fig3b.eps}
%\includegraphics[scale=0.35]{Kiyaeva_fig3c.eps}
%\caption{Three-part figure.}
%\label{figAB}
%\end{figure*}


\section{THIRD SECTION}

The motion of the outer pair is in the direction $\rho$, and we can
definitely state that for all orbits of the family,
the inclination of the orbit $i\approx90\degr$,
and the longitude of the ascending node $\Omega\approx\theta-180\degr$.
Therefore, you can calculate the angle between the planes of
the outer and inner orbits. As a result, we get that the planes
of the orbits are non-planar. 


Equations:
\begin{equation}
\label{one} 
v_1=\sqrt{\dfrac{4\pi^2{m_2}^2}{r(m_1+m_2)}}.\nonumber
\end{equation}
Assuming $m_2<<m_1$, we get
\begin{equation}
\label{two} 
m_2=v_1 \times\sqrt{\dfrac{m_1}{4\pi^2}r},\nonumber
\end{equation}

\begin{equation}
\label{three}
\overrightarrow{v_1}=f\times(\overrightarrow{\mu_{\rm
G}}-\overrightarrow{\mu_{\rm ph}})/p_t,\nonumber
\end{equation}
where $\overrightarrow{\mu_{\rm ph}}=(\mu_{\rm ph} \sin\,\psi_{\rm
ph},\mu_{\rm ph} \cos\,\psi_{\rm ph})$is the average orbital motion
obtained from a long series of photographic observations;
$\overrightarrow{\mu_{\rm G}}$ is the instantaneous orbital motion
determined by Gaia observation; \mbox{$p_t=87$}~mas is the parallax; $f$ is the coefficient of transition
from the relative velocity of the orbital motion to the velocity
relative to the center of mass of the hierarchical triple system,
which is motionless. If component F has a satellite,
then $$f_{\rm F}=M_{\rm A+B}/M_{\rm A+B+F}.$$ If the center of mass
of the AB system oscillates, then
\begin{eqnarray}
 f_{\rm C}&=&M_{\rm F}/M_{\rm A+B+F},\nonumber\\
 f_{\rm A}&=&f_{\rm C}\,(M_{\rm A+B}/M_{\rm A}),\nonumber\\
 f_{\rm B}&=&f_{\rm C}\,(M_{\rm A+B}/M_{\rm B}).\nonumber
\end{eqnarray}

If we use the values of $\mu_{ph}$ according to the smoothed series,
then
\begin{eqnarray}
 m_{2,{\rm F}}/\sqrt{r}&=&0.0030\pm0.0006~M_\odot,\nonumber\\
 m_{2,{\rm A}}/\sqrt{r}&=&m_{2,{\rm B}}/\sqrt{r}=0.0027\pm0.0006~M_\odot;\nonumber
\end{eqnarray}
if we use the values of $\mu_{ph}$ according to individual observations, then
\begin{eqnarray}
 m_{2,{\rm F}}/\sqrt{r}&=&0.0039\pm0.0017~M_\odot,\nonumber\\
 m_{2,{\rm A}}/\sqrt{r}&=&m_{2,{\rm B}}/\sqrt{r}=0.0035\pm0.0015~M_\odot.\nonumber
\end{eqnarray}

%4
\begin{table}
\caption {One column table.} \label{orbF}
\medskip
\begin{tabular}{c|c|c|c|c}
\hline
\multirow{2}{*}{Parameters} & \multicolumn{4}{c}{Orbits}  \\
\cline{2-5}
 & 1 & 2 & 3 & 4 \\
\hline
$a_{\rm ph}$,~mas          & 15.0    & 14.3    & 8.2     & 4.0 \\
$P$,~year                   & 11.0    & 11.04   & 9.52    & 10.97 \\
$e$                        & 0.2     & 0.24    & 0.53    & 0.3 \\
$i$,~degr.                 & 97.0    & 96.3    & 179.98  & 44 \\
$\omega$,~degr.            & 235.0   & 258.6   & 79.8    & 56.2 \\
$\Omega$,~degr.            & 147.2   & 143.2   & 12.0    & 217.1 \\
$T$,~year                   & 1980.0  & 1980.56 & 1988.15 & 1982.8 \\
$V_{r\gamma}$,~m\,c$^{-1}$ & --      & --      & $-0.7$  & -- \\
\hline
$p_t$,~mas                 & 87.0    & 87.0    & 87.0    & 86.9\\
$M_1,~M_\odot$             & 0.5     & 0.5     & 0.5     & 0.65 \\
$a_1$,~a.u.                & 0.17    & 0.16    & 0.094   & 0.046 \\
$M_2,~M_\odot$             & 0.023   & 0.022   & 0.013   & 0.007 \\
$a_2$,~a.u.                & 3.82    & 3.82    & 3.50    & 4.28 \\
\hline
$\sigma_x$,~mas            & 2.2     & 2.0     & 3.6     & 5.1 \\
$\sigma_y$,~mas            & 12.3    & 12.0    & 13.5    & 5.4 \\
$\sigma_{V_r}$,~mas/year    & --      & --      & 0.078   & -- \\
\hline
\end{tabular}
\end{table}

The system of equations is solved:
\begin{equation}
\label{four} x(t)=x_0+\dot{x}(t-t_0)+BX_{\varphi}+GY_{\varphi},
\end{equation}
\begin{equation}
\label{five} y(t)=y_0+\dot{y}(t-t_0)+AX_{\varphi}+FY_{\varphi},
\end{equation}
where $x=\rho\sin\theta$, $y=\rho\cos\theta$; phase
$\varphi=(t-t_0)/P$; $X_{\varphi}=\cos\,(E_{\varphi})-e$,
$Y_{\varphi}=\sqrt{1-e^2}\sin\,(E_{\varphi})$are orbital
coordinates corresponding to dynamic orbital elements $P$, $T$
and $e$; $x_0$ and $y_0$ are coordinates of the center of mass
at the moment $t_0$; $A$, $B$, $F$ and $G$ are the Thiele-Innes
elements, from which we obtain the geometric elements of the orbit
($a$, $i$, $\omega$, $\Omega$). In Table~\ref{orbF}, this orbit
is represented by number~2.


\section{CONCLUSION}

This paper demonstrates the possibility\ldots


\begin{acknowledgments}
The authors are grateful\ldots
\end{acknowledgments}

\section*{FUNDING}
This work was supported by the\ldots

\section*{CONFLICT OF INTEREST}
The authors declare no conflicts of interest.

\bibliographystyle{aspb1}
\bibliography{Kiyaeva}

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%I.~S.~{Izmailov}, M.~L.~{Khovricheva}, M.~Y.~{Khovrichev}, et~al.,
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%  (2005).
%
%\bibitem[{Popovi{\'c}} and {Pavlovi{\'c}}(1996)]{Pop}
%G.~M.~{Popovi{\'c}} and R.~{Pavlovi{\'c}}, Bulletin Astronomique
%de Belgrade  \textbf{153}, 57 (1996).
%
%\bibitem[{Tal-Or} et~al.(2019)]{Tal2019}
%L.~{Tal-Or}, T.~{Trifonov}, S.~{Zucker}, et~al., \mnras
%\textbf{484}~(1), L8  (2019).
%
%\bibitem[{Tokovinin}(1990)]{Tok1990}
%A.~A.~{Tokovinin}, \emph{{Catalogue of stellar radial velocities.
%Catalogue of proper motions}} (Moscow State Univ., Moscow, 1990).
%%А.~А.~Токовинин в \emph{Каталог измерений лучевых скоростей звезд.
%%Каталог собственных движений.} (Mоск.Гос.Университет,Москва,1990),
%%92.
%
%\bibitem[{Zhuchkov} and {Orlov}(2005)]{dyst2}
%R.~Y.~{Zhuchkov} and V.~V.~{Orlov}, \arep \textbf{49}~(4), 274
%  (2005).
%
%\end{thebibliography}


\end{document}

%%
%% This is file `aspb1.bst',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% merlin.mbs  (with options: `ay,vonx,nm-init,ed-au,nmlm,x4,m3,mcite,mct-1,mct-x2,blkyear,yr-par,atit-u,jtit-x,jttl-rm,thtit-x,vol-bf,vnum-sp,volp-com,jpg-1,num-xser,numser,ser-vol,ser-ed,jnm-x,pub-date,pre-edn,edpar,blk-com,blknt,pp,ed,abr,ednx,mth-bare,ord,jabr,nfss,')
%% ----------------------------------------
%% ***  ***
%% 
%% Copyright 1994-2011 Patrick W Daly
 % ===============================================================
 % IMPORTANT NOTICE:
 % This bibliographic style (bst) file has been generated from one or
 % more master bibliographic style (mbs) files, listed above.
 %
 % This generated file can be redistributed and/or modified under the terms
 % of the LaTeX Project Public License Distributed from CTAN
 % archives in directory macros/latex/base/lppl.txt; either
 % version 1 of the License, or any later version.
 % ===============================================================
 % Name and version information of the main mbs file:
 % \ProvidesFile{merlin.mbs}[2011/11/18 4.33 (PWD, AO, DPC)]
 %   For use with BibTeX version 0.99a or later
 %-------------------------------------------------------------------
 % This bibliography style file is intended for texts in ENGLISH
 % This is an author-year citation style bibliography. As such, it is
 % non-standard LaTeX, and requires a special package file to function properly.
 % Such a package is    natbib.sty   by Patrick W. Daly
 % The form of the \bibitem entries is
 %   \bibitem[Jones et al.(1990)]{key}...
 % The essential feature is that the label (the part in brackets) consists
 % of the author names, as they should appear in the citation, with the year
 % in parentheses following. There must be no space before the opening
 % parenthesis!
 % In natbib.sty, it is possible to define the type of enclosures that is
 % really wanted (brackets or parentheses), but in either case, there must
 % be parentheses in the label.
 % The \cite command functions as follows:
 %   \citet{key} ==>>                Jones et al. (1990)
 %   \citep{key} ==>>                (Jones et al., 1990)
 %   \citep[chap. 2]{key} ==>>       (Jones et al., 1990, chap. 2)
 %   \citep[e.g.][]{key} ==>>        (e.g. Jones et al., 1990)
 %   \citep[e.g.][p. 32]{key} ==>>   (e.g. Jones et al., 1990, p. 32)
 %   \citeauthor{key} ==>>           Jones et al.
 %   \citeyear{key} ==>>             1990
 %---------------------------------------------------------------------

ENTRY
  { address
    author
    booktitle
    chapter
    edition
    editor
    eid
    howpublished
    institution
    journal
    key
    month
    note
    number
    organization
    pages
    publisher
    school
    series
    title
    type
    volume
    year
  }
  {}
  { label extra.label sort.label short.list }
INTEGERS { output.state before.all mid.sentence after.sentence after.block }
FUNCTION {init.state.consts}
{ #0 'before.all :=
  #1 'mid.sentence :=
  #2 'after.sentence :=
  #3 'after.block :=
}
STRINGS { s t}
FUNCTION {output.nonnull}
{ 's :=
  output.state mid.sentence =
    { ", " * write$ }
    { output.state after.block =
        { add.period$ write$
          newline$
          "\newblock " write$
        }
        { output.state before.all =
            'write$
            { add.period$ " " * write$ }
          if$
        }
      if$
      mid.sentence 'output.state :=
    }
  if$
  s
}
FUNCTION {output}
{ duplicate$ empty$
    'pop$
    'output.nonnull
  if$
}
FUNCTION {output.check}
{ 't :=
  duplicate$ empty$
    { pop$ "empty " t * " in " * cite$ * warning$ }
    'output.nonnull
  if$
}
FUNCTION {fin.entry}
{ add.period$
  write$
  newline$
}

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

FUNCTION {date.block}
{
  skip$
}

FUNCTION {not}
{   { #0 }
    { #1 }
  if$
}
FUNCTION {and}
{   'skip$
    { pop$ #0 }
  if$
}
FUNCTION {or}
{   { pop$ #1 }
    'skip$
  if$
}
STRINGS {z}

FUNCTION {remove.dots}
{ 'z :=
   ""
   { z empty$ not }
   { z #1 #2 substring$
     duplicate$ "\." =
       { z #3 global.max$ substring$ 'z :=  * }
       { pop$
         z #1 #1 substring$
         z #2 global.max$ substring$ 'z :=
         duplicate$ "." = 'pop$
           { * }
         if$
       }
     if$
   }
   while$
}
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$ "" }
    { "\emph{" swap$ * "}" * }
  if$
}
FUNCTION {bolden}
{ duplicate$ empty$
    { pop$ "" }
    { "\textbf{" swap$ * "}" * }
  if$
}
FUNCTION {tie.or.space.prefix}
{ duplicate$ text.length$ #3 <
    { "~" }
    { " " }
  if$
  swap$
}

FUNCTION {capitalize}
{ "u" change.case$ "t" change.case$ }

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

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

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

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

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

FUNCTION {bbl.edition}
{ "ed." }

FUNCTION {bbl.volume}
{ "vol." }

FUNCTION {bbl.of}
{ "of" }

FUNCTION {bbl.number}
{ "no." }

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

FUNCTION {bbl.in}
{ "in" }

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

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

FUNCTION {bbl.chapter}
{ "chap." }

FUNCTION {bbl.techrep}
{ "Tech. Rep." }

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

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

FUNCTION {bbl.first}
{ "1st" }

FUNCTION {bbl.second}
{ "2nd" }

FUNCTION {bbl.third}
{ "3rd" }

FUNCTION {bbl.fourth}
{ "4th" }

FUNCTION {bbl.fifth}
{ "5th" }

FUNCTION {bbl.st}
{ "st" }

FUNCTION {bbl.nd}
{ "nd" }

FUNCTION {bbl.rd}
{ "rd" }

FUNCTION {bbl.th}
{ "th" }

MACRO {jan} {"Jan."}

MACRO {feb} {"Feb."}

MACRO {mar} {"Mar."}

MACRO {apr} {"Apr."}

MACRO {may} {"May"}

MACRO {jun} {"Jun."}

MACRO {jul} {"Jul."}

MACRO {aug} {"Aug."}

MACRO {sep} {"Sep."}

MACRO {oct} {"Oct."}

MACRO {nov} {"Nov."}

MACRO {dec} {"Dec."}

FUNCTION {eng.ord}
{ duplicate$ "1" swap$ *
  #-2 #1 substring$ "1" =
     { bbl.th * }
     { duplicate$ #-1 #1 substring$
       duplicate$ "1" =
         { pop$ bbl.st * }
         { duplicate$ "2" =
             { pop$ bbl.nd * }
             { "3" =
                 { bbl.rd * }
                 { bbl.th * }
               if$
             }
           if$
          }
       if$
     }
   if$
}

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

MACRO {acta} {"Acta Inf."}

MACRO {cacm} {"Commun. ACM"}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


STRINGS  { bibinfo}

FUNCTION {format.names}
{ 'bibinfo :=
  duplicate$ empty$ 'skip$ {
  's :=
  "" 't :=
  #1 'nameptr :=
  s num.names$ 'numnames :=
  numnames 'namesleft :=
    { namesleft #0 > }
    { s nameptr
      "{f.~}{vv~}{ll}{, jj}"
      format.name$
      bibinfo bibinfo.check
      't :=
      nameptr #1 >
        {
          nameptr #3
          #1 + =
          numnames #4
          > and
            { "others" 't :=
              #1 'namesleft := }
            'skip$
          if$
          namesleft #1 >
            { ", " * t * }
            {
              s nameptr "{ll}" format.name$ duplicate$ "others" =
                { 't := }
                { pop$ }
              if$
              numnames #2 >
                { "," * }
                'skip$
              if$
              t "others" =
                {
                  " " * bbl.etal *
                }
                {
                  bbl.and
                  space.word * t *
                }
              if$
            }
          if$
        }
        't
      if$
      nameptr #1 + 'nameptr :=
      namesleft #1 - 'namesleft :=
    }
  while$
  } if$
}
FUNCTION {format.names.ed}
{
  format.names
}
FUNCTION {format.key}
{ empty$
    { key field.or.null }
    { "" }
  if$
}

FUNCTION {format.authors}
{ author "author" format.names
}
FUNCTION {get.bbl.editor}
{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ }

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

FUNCTION {format.title}
{ title
  "title" bibinfo.check
}
FUNCTION {output.bibitem}
{ newline$
  "\bibitem[" write$
  label write$
  ")]{" write$
  cite$ write$
  "}" write$
  newline$
  ""
  before.all 'output.state :=
}

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

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

FUNCTION {format.date}
{ year "year" bibinfo.check duplicate$ empty$
    {
    }
    'skip$
  if$
  extra.label *
  before.all 'output.state :=
  " (" swap$ * ")" *
}
FUNCTION {format.btitle}
{ title "title" bibinfo.check
  duplicate$ empty$ 'skip$
    {
      emphasize
    }
  if$
}
FUNCTION {either.or.check}
{ empty$
    'pop$
    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
  if$
}
FUNCTION {format.bvolume}
{ volume empty$
    { "" }
    { bbl.volume volume tie.or.space.prefix
      "volume" bibinfo.check * *
      series "series" bibinfo.check
      duplicate$ empty$ 'pop$
        { emphasize ", " * swap$ * }
      if$
      "volume and number" number either.or.check
    }
  if$
}
FUNCTION {format.number.series}
{ volume empty$
    { number empty$
        { series field.or.null }
        { series empty$
            { number "number" bibinfo.check }
            { output.state mid.sentence =
                { bbl.number }
                { bbl.number capitalize }
              if$
              number tie.or.space.prefix "number" bibinfo.check * *
              bbl.in space.word *
              series "series" bibinfo.check *
            }
          if$
        }
      if$
    }
    { "" }
  if$
}
FUNCTION {is.num}
{ chr.to.int$
  duplicate$ "0" chr.to.int$ < not
  swap$ "9" chr.to.int$ > not and
}

FUNCTION {extract.num}
{ duplicate$ 't :=
  "" 's :=
  { t empty$ not }
  { t #1 #1 substring$
    t #2 global.max$ substring$ 't :=
    duplicate$ is.num
      { s swap$ * 's := }
      { pop$ "" 't := }
    if$
  }
  while$
  s empty$
    'skip$
    { pop$ s }
  if$
}

FUNCTION {convert.edition}
{ extract.num "l" change.case$ 's :=
  s "first" = s "1" = or
    { bbl.first 't := }
    { s "second" = s "2" = or
        { bbl.second 't := }
        { s "third" = s "3" = or
            { bbl.third 't := }
            { s "fourth" = s "4" = or
                { bbl.fourth 't := }
                { s "fifth" = s "5" = or
                    { bbl.fifth 't := }
                    { s #1 #1 substring$ is.num
                        { s eng.ord 't := }
                        { edition 't := }
                      if$
                    }
                  if$
                }
              if$
            }
          if$
        }
      if$
    }
  if$
  t
}

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

FUNCTION {format.journal.pages}
{ pages duplicate$ empty$ 'pop$
    { swap$ duplicate$ empty$
        { pop$ pop$ format.pages }
        {
          ", " *
          swap$
          first.page
          "pages" bibinfo.check
          *
        }
      if$
    }
  if$
}
FUNCTION {format.journal.eid}
{ eid "eid" bibinfo.check
  duplicate$ empty$ 'pop$
    { swap$ duplicate$ empty$ 'skip$
      {
          ", " *
      }
      if$
      swap$ *
    }
  if$
}
FUNCTION {format.vol.num.pages}
{ volume field.or.null
  duplicate$ empty$ 'skip$
    {
      "volume" bibinfo.check
    }
  if$
  bolden
  number "number" bibinfo.check duplicate$ empty$ 'skip$
    {
      swap$ duplicate$ empty$
        { "there's a number but no volume in " cite$ * warning$ }
        'skip$
      if$
      swap$
      "~(" swap$ * ")" *
    }
  if$ *
  eid empty$
    { format.journal.pages }
    { format.journal.eid }
  if$
}

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

FUNCTION {format.booktitle}
{
  booktitle "booktitle" bibinfo.check
  emphasize
}
FUNCTION {format.in.ed.booktitle}
{ format.booktitle duplicate$ empty$ 'skip$
    {
      format.bvolume duplicate$ empty$ 'pop$
        { ", " swap$ * * }
      if$
      editor "editor" format.names.ed duplicate$ empty$ 'pop$
        {
          " " *
          get.bbl.editor
          "(" swap$ * "), " *
          * swap$
          * }
      if$
      word.in swap$ *
    }
  if$
}
FUNCTION {format.thesis.type}
{ type duplicate$ empty$
    'pop$
    { swap$ pop$
      "t" change.case$ "type" bibinfo.check
    }
  if$
}
FUNCTION {format.tr.number}
{ number "number" bibinfo.check
  type duplicate$ empty$
    { pop$ bbl.techrep }
    'skip$
  if$
  "type" bibinfo.check
  swap$ duplicate$ empty$
    { pop$ "t" change.case$ }
    { tie.or.space.prefix * * }
  if$
}
FUNCTION {format.article.crossref}
{
  word.in
  " \cite{" * crossref * "}" *
}
FUNCTION {format.book.crossref}
{ volume duplicate$ empty$
    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
      pop$ word.in
    }
    { bbl.volume
      swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of space.word *
    }
  if$
  " \cite{" * crossref * "}" *
}
FUNCTION {format.incoll.inproc.crossref}
{
  word.in
  " \cite{" * crossref * "}" *
}
FUNCTION {format.org.or.pub}
{ 't :=
  ""
      add.blank "(" *
      t empty$
        { address "address" bibinfo.check *
        }
        { t *
          address empty$
            'skip$
            { ", " * address "address" bibinfo.check * }
          if$
        }
      if$
      year duplicate$ empty$
        { "empty year in " cite$ * warning$
           pop$ "" }
        { "year" bibinfo.check extra.label * }
      if$
      t empty$ address empty$ and
        { * }
        { ", " swap$ * * }
      if$
      ")" *
}
FUNCTION {format.publisher.address}
{ publisher "publisher" bibinfo.warn format.org.or.pub
}

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

FUNCTION {article}
{ output.bibitem
  format.authors "author" output.check
  author format.key output
  crossref missing$
    {
      journal
      "journal" bibinfo.check
      "journal" output.check
      add.blank
      format.vol.num.pages output
      format.date "year" output.check
    }
    { format.article.crossref output.nonnull
      format.pages output
    }
  if$
  new.sentence
  format.note 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$
  format.btitle "title" output.check
  crossref missing$
    { format.bvolume output
      format.edition output
      format.number.series output
      format.publisher.address output
    }
    {
      format.book.crossref output.nonnull
      format.date "year" output.check
    }
  if$
  new.sentence
  format.note output
  fin.entry
}
FUNCTION {booklet}
{ output.bibitem
  format.authors output
  author format.key output
  format.title "title" output.check
  howpublished "howpublished" bibinfo.check output
  address "address" bibinfo.check output
  format.date "year" output.check
  new.sentence
  format.note 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$
  format.btitle "title" output.check
  crossref missing$
    {
      format.bvolume output
      format.chapter.pages "chapter and pages" output.check
      format.edition output
      format.number.series output
      format.publisher.address output
    }
    {
      format.chapter.pages "chapter and pages" output.check
      format.book.crossref output.nonnull
      format.date "year" output.check
    }
  if$
  new.sentence
  format.note output
  fin.entry
}

FUNCTION {incollection}
{ output.bibitem
  format.authors "author" output.check
  author format.key output
  crossref missing$
    { format.in.ed.booktitle "booktitle" output.check
      format.edition output
      format.chapter.pages output
      format.number.series output
      format.publisher.address output
    }
    { format.incoll.inproc.crossref output.nonnull
      format.chapter.pages output
    }
  if$
  new.sentence
  format.note output
  fin.entry
}
FUNCTION {inproceedings}
{ output.bibitem
  format.authors "author" output.check
  author format.key output
  crossref missing$
    { format.in.ed.booktitle "booktitle" output.check
      format.pages output
      format.number.series output
      publisher empty$
        { format.organization.address output }
        { organization "organization" bibinfo.check output
          format.publisher.address output
        }
      if$
    }
    { format.incoll.inproc.crossref output.nonnull
      format.pages output
    }
  if$
  new.sentence
  format.note output
  fin.entry
}
FUNCTION {conference} { inproceedings }
FUNCTION {manual}
{ output.bibitem
  format.authors output
  author format.key output
  format.btitle "title" output.check
  organization "organization" bibinfo.check output
  address "address" bibinfo.check output
  format.edition output
  format.date "year" output.check
  new.sentence
  format.note output
  fin.entry
}

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

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

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

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

FUNCTION {unpublished}
{ output.bibitem
  format.authors "author" output.check
  author format.key output
  format.title "title" output.check
  format.date "year" output.check
  new.sentence
  format.note "note" output.check
  fin.entry
}

FUNCTION {default.type} { misc }
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 :=
 "" 't :=
  #1 'nameptr :=
  s num.names$ 'numnames :=
  numnames 'namesleft :=
    { namesleft #0 > }
    { s nameptr
      "{vv~}{ll}" format.name$
      't :=
      nameptr #1 >
        {
          nameptr #2 =
          numnames #2 > and
            { "others" 't :=
              #1 'namesleft := }
            'skip$
          if$
          namesleft #1 >
            { ", " * t * }
            {
              s nameptr "{ll}" format.name$ duplicate$ "others" =
                { 't := }
                { pop$ }
              if$
              t "others" =
                {
                  " " * bbl.etal *
                }
                {
                  numnames #2 >
                    { "," * }
                    'skip$
                  if$
                  bbl.and
                  space.word * t *
                }
              if$
            }
          if$
        }
        't
      if$
      nameptr #1 + 'nameptr :=
      namesleft #1 - 'namesleft :=
    }
  while$
}

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.short.authors}
{ type$ "book" =
  type$ "inbook" =
  or
    'author.editor.key.label
    { type$ "proceedings" =
        'editor.key.label
        'author.key.label
      if$
    }
  if$
  'short.list :=
}

FUNCTION {calc.label}
{ calc.short.authors
  short.list
  "("
  *
  year duplicate$ empty$
     { pop$ "" }
     { purify$ #-1 #4 substring$ }
  if$
  *
  'label :=
}

FUNCTION {sort.format.names}
{ 's :=
  #1 'nameptr :=
  ""
  s num.names$ 'numnames :=
  numnames 'namesleft :=
    { namesleft #0 > }
    { s nameptr
      "{ll{ }}{  f{ }}{  jj{ }}"
      format.name$ 't :=
      nameptr #1 >
        {
          nameptr #3
          #1 + =
          numnames #4
          > and
            { "others" 't :=
              #1 'namesleft := }
            'skip$
          if$
          "   "  *
          namesleft #1 = t "others" = and
            { "zzzzz" 't := }
            'skip$
          if$
          t sortify *
        }
        { 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 last.extra.num.extended last.extra.num.blank number.label }
FUNCTION {initialize.extra.label.stuff}
{ #0 int.to.chr$ 'last.label :=
  "" 'next.extra :=
  #0 'last.extra.num :=
  "a" chr.to.int$ #1 - 'last.extra.num.blank :=
  last.extra.num.blank 'last.extra.num.extended :=
  #0 'number.label :=
}
FUNCTION {forward.pass}
{ last.label label =
    { last.extra.num #1 + 'last.extra.num :=
      last.extra.num "z" chr.to.int$ >
       { "a" chr.to.int$ 'last.extra.num :=
         last.extra.num.extended #1 + 'last.extra.num.extended :=
       }
       'skip$
      if$
      last.extra.num.extended last.extra.num.blank >
        { last.extra.num.extended int.to.chr$
          last.extra.num int.to.chr$
          * 'extra.label := }
        { last.extra.num int.to.chr$ 'extra.label := }
      if$
    }
    { "a" chr.to.int$ 'last.extra.num :=
      "" 'extra.label :=
      label 'last.label :=
    }
  if$
  number.label #1 + 'number.label :=
}
FUNCTION {reverse.pass}
{ next.extra "b" =
    { "a" 'extra.label := }
    'skip$
  if$
  extra.label 'next.extra :=
  extra.label
  duplicate$ empty$
    'skip$
    { "{\natexlab{" swap$ * "}}" * }
  if$
  'extra.label :=
  label extra.label * 'label :=
}
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}{" number.label int.to.str$ * "}" *
  write$ newline$
  "\providecommand{\natexlab}[1]{#1}"
  write$ newline$
}
EXECUTE {begin.bib}
EXECUTE {init.state.consts}
ITERATE {call.type$}
FUNCTION {end.bib}
{ newline$
  "\end{thebibliography}" write$ newline$
}
EXECUTE {end.bib}
%% End of customized bst file
%%
%% End of file `aspb1.bst'.

\def\saoname{Special Astrophysical Observatory,  Russian Academy of Sciences,
              Nizhnii Arkhyz, 369167 Russia}
\def\saonamer{Специальная астрофизическая обсерватория РАН, Нижний Архыз, 369167
Россия}

%******* SPECIAL SIGNS AND CHARACTERS FOR MATH MODE *******
%
\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}

\def\sq{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
\penalty50\hskip1em\null\nobreak\hfil\squareforqed
\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}

\def\sun{\hbox{$\odot$}}

\def\la{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\sim\cr}}}}}

\def\ga{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\sim\cr}}}}}

\def\degr{\hbox{$^\circ$}}

\def\arcmin{\hbox{$^\prime$}}

\def\arcsec{\hbox{$^{\prime\prime}$}}

\def\utw{\smash{\rlap{\lower5pt\hbox{$\sim$}}}}

\def\udtw{\smash{\rlap{\lower6pt\hbox{$\approx$}}}}

\def\fa{\hbox{$\,.\!\!^{\rm a}$}}

\def\fd{\hbox{$\,.\!\!^{\rm d}$}}

\def\fh{\hbox{$\,.\!\!^{\rm h}$}}

\def\fm{\hbox{$\,.\!\!^{\rm m}$}}

\def\fs{\hbox{$\,.\!\!^{\rm s}$}}

\def\fdg{\hbox{$\,.\!\!^\circ$}}

\def\farcm{\hbox{$\,.\mkern-4mu^\prime$}}

\def\farcs{\hbox{$\,.\!\!^{\prime\prime}$}}

\def\fp{\hbox{$\,.\!\!^{\scriptscriptstyle\rm p}$}}

\def\cor{\mathrel{\mathchoice {\hbox{$\widehat=$}}{\hbox{$\widehat=$}}
{\hbox{$\scriptstyle\hat=$}}
{\hbox{$\scriptscriptstyle\hat=$}}}}

\def\sol{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr\sim\cr<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\sim\cr
<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\sim\cr
<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\sim\cr<\cr}}}}}

\def\sog{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr\sim\cr>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\sim\cr
>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
\sim\cr>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\sim\cr>\cr}}}}}

\def\lse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\simeq\cr}}}}}

\def\gse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\simeq\cr}}}}}

\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.5pt}<\cr}}}}}

\def\leogr{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip-1.5pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\noalign{\vskip-1.5pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\noalign{\vskip-1pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\noalign{\vskip-0.5pt}>\cr}}}}}

\def\loa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\approx\cr}}}}}

\def\goa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\approx\cr}}}}}

\def\diameter{{\ifmmode\mathchoice
{\ooalign{\hfil\hbox{$\displaystyle/$}\hfil\crcr
{\hbox{$\displaystyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\textstyle/$}\hfil\crcr
{\hbox{$\textstyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\scriptstyle/$}\hfil\crcr
{\hbox{$\scriptstyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\scriptscriptstyle/$}\hfil\crcr
{\hbox{$\scriptscriptstyle\mathchar"20D$}}}}
\else{\ooalign{\hfil/\hfil\crcr\mathhexbox20D}}%
\fi}}

\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr\gets\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\gets\cr\to\cr}}}}}

\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr
\noalign{\vskip0.9pt}=\cr}}}}}

\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr
\noalign{\vskip0.9pt}=\cr}}}}}

%********** ABBREVIATIONS OF THE OFT-REFERENCED JOURNALS ***********

% *** Астрофизические исследования % русск. версия журнала САО до 1993 г.
\newcommand{\air}{Астрофиз. исслед. (Известия Спец. астрофиз. обс.) }
% *** Astrophysical Bulletin % англ. версия журнала САО с 2007 г.
\newcommand{\ab}{Astrophysical Bulletin }
% *** Астрофизический бюллетень % русск. версия журнала САО с 2007 г.
\newcommand{\abr}{Астрофизический бюллетень }
% *** Astronomy and Astrophysics
\newcommand{\aaa}{Astron. and Astrophys. }
\newcommand{\aap}{Astron. and Astrophys. }
% *** Astronomy and Astrophys. Supplement Series
\newcommand{\aas}{Astron. and Astrophys. Suppl. }
\newcommand{\aaps}{Astron. and Astrophys. Suppl. }
% *** Astronomy and Astrophysics Review
\newcommand{\aar}{Astron. Astrophys. Rev. }
% *** Astronomical Journal
\newcommand{\aj}{Astron.~J. }
% *** Astrophysical Journal
\renewcommand{\apj}{Astrophys.~J. }
% *** Astrophysical Journal Supplement Series
\newcommand{\apjs}{Astrophys.~J. Suppl. }
% *** Astrophysics and Space Science
\newcommand{\apss}{Astrophys. and Space Sci. }
% *** Annual Review of Astronomy and Astrophys.
\newcommand{\araa}{Annual Rev. Astron. Astrophys. }
% *** Astronomicekij Zhurnal
\newcommand{\azh}{Astron.~Zh. }
% *** Bulletin of the American Astron. Society
\newcommand{\baas}{Bull. Amer. Astron. Soc. }
% *** Bulletin of the Special Astrophysical Observatory % англ. версия до 2007 г.
\newcommand{\bsao}{Bull. Spec. Astrophys. Obs. }
% *** Бюллетень Спец. астрофизич. обсерватории % русск. версия до 2007 г.
\newcommand{\bsaor}{Бюлл. Спец. астрофиз. обсерв. }
% *** Inform. Bul. Var. Stars
\newcommand{\ibvs}{Inform. Bull. Var. Stars }
% *** Journal of Astronomy and Astrophysics
\newcommand{\jaa}{J.~Astron. Astrophys. }
% *** Monthly Notices of the Roy. Astron. Society
\newcommand{\mnras}{Monthly Notices Royal Astron. Soc. }
% *** Publ. of the Astron. Society of Australia
\newcommand{\pasa}{Publ. Astron. Soc. Australia }
% *** Publ. Astronom. Soc. Japan
\newcommand{\pasj}{Publ. Astron. Soc. Japan }
% *** Publ. of the Astron. Society of the Pacific
\newcommand{\pasp}{Publ. Astron. Soc. Pacific }
% *** Astronomy Reports (АЖ)
\newcommand{\arep}{Astronomy Reports }
% *** Astronomy Letters (ПАЖ)
\newcommand{\alet}{Astronomy Letters }
% *** Astronomische Nachrichten
\newcommand{\an}{Astronomische Nachrichten }
% *** Pis'ma v Astronomicekij Zhurnal
\newcommand{\pazh}{Pis'ma Astron. Zh. }
% *** Письма в АЖ
\newcommand{\pazhr}{Письма в АЖ }
% *** Астрон. ж.
\newcommand{\azhr}{Астрон.~ж. }
% *** Soviet Astronomy
\newcommand{\sovast}{Sov. Astron. }
% *** Scientific American
\newcommand{\sca}{Scientific American }
% *** Sky and Telescope
\newcommand{\skytel}{Sky Telesc. }
% *** Space Science Reviews
\newcommand{\spsrev}{Space Sci.~Rev. }
% Revista Mexicana de Astronomia y Astrofisica
%\newcommand{\rmxaa}{Revista Mexicana de Astronom\'{\i}a y Astrof\'{\i}sica}
\newcommand{\rmxaa}{Revista Mexicana Astronom. Astrof\'{\i}s. }
%\newcommand{\nat}{Nature }
% *** Physical Review D
%\newcommand{\prd}{Phys. Rev.~D }
\newcommand{\memsai}{Memorie della Societ\`a Astronomica Italiana }
% *** Nature
\renewcommand{\nat}{Nature }
\newcommand{\aatrans}{Astronomical and Astrophysical Transactions }
\newcommand{\qjras}{Quarterly Journal of the Royal Astronomical Society }
\newcommand{\actaa}{Acta Astronomica}
% *** SPIE Conference Proceedings
\newcommand{\procspie}{SPIE Conf. Proc. }
\newcommand{\na}{New Astronomy}
\newcommand{\apjl}{Astrophys.~J.}
\newcommand{\aapr}{Astron. and Astrophys.}
%
\newcommand{\bain}{Bull. Astron. Inst. Netherlands }
\newcommand{\memras}{Memoirs of the Royal Astronomical Society }
\newcommand{\jqsrt}{Journal of Quantitative Spectroscopy and Radiative Transfer }
%
\newcommand{\jcap}{Journal of Cosmology and Astroparticle Physics }
\newcommand{\physrep}{Physics Reports }
\newcommand{\solphys}{Sol. Phys. }