### Lobachevskii Journal of Mathematics

Related subjects: Algebra - Analysis - Geometry & Topology - Mathematics - Probability Theory and Stochastic Processes
Kazan Federal University

Lobachevskii Journal of Mathematics considers all manuscripts on the strict condition that

• the manuscript is your own original work, and does not duplicate any other previously published work, including your own previously published work;
• the manuscript has been submitted only Lobachevskii Journal of Mathematics; it is not under consideration or peer review or accepted for publication or in press or published elsewhere.

The manuscript should be prepared in LaTeX-2e, style Revtex. It should contain abstract, keywords, 2010 Mathematical Subject Classification, author's affiliation and email. Please use LJMs LaTeX macro package ljm.sty.

﻿The manuscript should be prepared in LaTeX-2e, style Revtex. It should contain abstract, keywords, 2010 Mathematical Subject Classification, author's affiliation
and ljm.sty).

Please, do not use your own TeX-tricks. In fact, revtex style has sufficiently many tools (environments, fonts, etc.) to express any mathematical idea.

%%%%%%%% %%%%%%%%% %%%%%% file template-ljm.tex %%%%%%%%%%% %%%%%%%%% %%%%%
%
% This is a general template file for the LaTeX package ljm-sty
% for Lobachevskii Journal of Mathematics 2017/12/06
%
% Copy it to a new file with a new name and use it as the basis
% for your article. Delete % signs as needed.
%%
\documentclass[
11pt,%
tightenlines,%
twoside,%
onecolumn,%
nofloats,%
nobibnotes,%
nofootinbib,%
noshowpacs,%
centertags]%
{revtex4}
\usepackage{ljm}

\begin{document}

\titlerunning{Short form of the title} % for running heads
\authorrunning{First-Author at al.} % for running heads
%\authorrunning{First-Author, Second-Author} % for running heads

\title{Title of the Article,\\
Broken into Lines}
% Splitting into lines is performed by the command \\
% The title is written in accordance with the rules of capitalization.

\author{\firstname{A.~A.}~\surname{First-Author}}
\email[E-mail: ]{First.Author@email.com}
\affiliation{Place of work and/or the address of the first and second authors}
\affiliation{Example: N.I. Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008 Russia}

\author{\firstname{B.}~\surname{Second-Author}}
\email[E-mail: ]{Second.Author@email.com}
\affiliation{Place of work and/or the address of the first and second authors}
\affiliation{Place of work and/or the address of second authors}
%\noaffiliation % If the author does not specify a place of work.

\firstcollaboration{(Submitted by A.~A.~Editor-name)} % Add if you know submitter.
%\lastcollaboration{ }

\received{December 06, 2017} % The date of receipt to the editor, i.e. December 06, 2017

\begin{abstract} % You shouldn't use formulas and citations in the abstract.
In this example, the article contains some required author
information and examples of how to gain an article in the REV\TeX~4
for \ljm. You shouldn't use formulas and citations in the abstract.
\end{abstract}

\subclass{12345, 54321} % Enter 2010 Mathematics Subject Classification.

\keywords{Keyword1, Keyword2} % Include keywords separeted by comma.

\maketitle

% Text of article starts here.

\section{Introduction}

The process of processing an article using REV\TeX{} is described in detail in the package manuals \cite{RTeX}. Great help in resolving technical
issues on \TeX{} can be found in books \cite{GG,L}.
Use the House Style Guide: Version 2.0'' \cite{hsg} for more help on how to format article.

broken into lines}

There are three levels of Headings that are set by the commands
\verb|\section|, \verb|\subsection|, and \verb|\subsubsection|
(Chapter, subchapter, subsection). Split header into lines
is done with the command \verb+\protect\\+.
Second level heading as the title of article is written in accordance with the rules of capitalization \cite{cap}.

References in the text are by using the commands
\verb+\cite{#1}+ or \verb+\onlinecite{#1}+. Label \verb+#1+
can have a name consisting of both letters and numbers. In
the bibliography section\footnote{See the end of the article.} this link also has a label \verb+#1+ and starts the command \verb+\bibitem{#1}+.

With the command \verb+\cite{GG}+ get a reference \cite{GG},
if you need to refer to several sources:
\cite{GG,L}, the curly brackets indicate references
separated by commas: \verb+\cite{GG,L}+. When
use the command \verb|\onlinecite{#1}| link will not be
in brackets: see~\onlinecite{RTeX}, p.~8.
If there is a link to the sources with serial numbers,
e.g. [1,2,3,6,7,8], then print automatically following links will take
[1--3,6--8].

\section{Standalone formulae}

In \LaTeX, there are many ways to embed standalone formulas
on the page and align them. By default, formulas always
centered.

\subsubsection{One-line formulas}

Below are examples of one-line equations:
\begin{eqnarray}
\chi_+(p)\alt{\bf [}2|{\bf p}|(|{\bf p}|+p_z){\bf ]}^{-1/2}
\left(
\begin{array}{c}
|{\bf p}|+p_z\\
px+ip_y
\end{array}\right)\;,
\\
\left\{%
\openone234567890abc123\alpha\beta\gamma\delta1234556\alpha\beta
\frac{1\sum^{a}_{b}}{A^2}%
\right\}%
\label{one}.
\end{eqnarray}
The second formula has the number~(\ref{one}), which is set by command
\verb|\label{one}|. The first formula is assigned a number~(1), but
it cannot be applied with the help of automatic links,
as it has no label.

If the formula number is not necessary, use the environment
\verb+$+, \verb+$+, (or \$...\$) which obtained the following formula:
$g^+g^+ \rightarrow g^+g^+g^+g^+ \dots ~,~~q^+q^+\rightarrow q^+g^+g^+ \dots ~.$ % You also can use the dollar sign ($). \subsubsection{Multiline formulae} Multiline formulas are typed using the environment eqnarray: \begin{eqnarray} {\cal M}=&&ig_Z^2(4E_1E_2)^{1/2}(l_i^2)^{-1} \delta_{\sigma_1,-\sigma_2} (g_{\sigma_2}^e)^2\chi_{-\sigma_2}(p_2)\nonumber\\ &&\times [\epsilon_jl_i\epsilon_i]_{\sigma_1}\chi_{\sigma_1}(p_1), \end{eqnarray} \begin{eqnarray} \sum \vert M^{\rm viol}_g \vert ^2&=&g^{2n-4}_S(Q^2)~N^{n-2} (N^2-1)\nonumber \\ & &\times \left( \sum_{i\sum_{\rm perm} \frac{1}{S_{12}} \frac{1}{S_{12}} \sum_\tau c^f_\tau~. \end{eqnarray} If the formula number is not necessary, then at the end of the row in front of the sign \verb|\\| you need to put the command \verb|\nonumber|. Never use one line command \verb|\nonumber| and \verb|\label{#1}|, as this may cause error in automatic the numbering of references. If you want to gain a few formulas without number, use the eqnarray environment* (the asterisk means the abolition numbering): \begin{eqnarray*} \sum \vert M^{\rm viol}_g \vert ^2&=&g^{2n-4}_S(Q^2)~N^{n-2} (N^2-1)\\ & &\times \left( \sum_{i\left( \sum_{\rm perm}\frac{1}{S_{12}S_{23}S_{n1}} \right) \frac{1}{S_{12}}~. \end{eqnarray*} To add numbers to the formula manually, use the command \verb+\tag{#1}+, where \verb+#1+~--- the desired equation number. Here how is the formula with the number of~(\ref{eq:mynum}): g^+g^+ \rightarrow g^+g^+g^+g^+ \dots ~,~~q^+q^+\rightarrow q^+g^+g^+ \dots ~. \tag{2.6$'}\label{eq:mynum} When you enable single-line and multi-line formulas are surrounded by subequations, each formula numbered" with a letter, as shown in equations~(\ref{mlett:1}) and (\ref{mlett:2}): \begin{subequations} \label{generallabel} \left\{ abc123456abcdef\alpha\beta\gamma\delta1234556\alpha\beta \frac{1\sum^{a}_{b}}{A^2} \right\},\label{mlett:1} \begin{eqnarray} {\cal M}=&&ig_Z^2(4E_1E_2)^{1/2}(l_i^2)^{-1} (g_{\sigma_2}^e)^2\chi_{-\sigma_2}(p_2)\nonumber\\ &&\times [\epsilon_i]_{\sigma_1}\chi_{\sigma_1}(p_1).\label{mlett:2} \end{eqnarray} \end{subequations} If you put the label right after the \verb+\begin{subequations}+, it can be used further as a reference to all the equations in this environment. For example, you can refer to equation~(\ref{generallabel}) this example. To set multi-line formulas you can use the environment multline, gather and align. The multline environment is good to use for a set of standalone long formulas that do not fit on one line: \begin{multline} \int_{a_1}^{a_2} f(x)\,dx+\int_{a_2}^{a_3} f(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} f(x)\,dx\\ +\int_{a_1}^{a_2} g(x)\,dx+\int_{a_2}^{a_3} g(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} g(x)\,dx\\ +\int_{a_1}^{a_2} h(x)\,dx+\int_{a_2}^{a_3} h(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} h(x)\,dx\\ =\int_{a_1}^{a_n} f(x)+g(x)+h(x)\,dx. \end{multline} This formula is automatically numbered, if the formula number is not need, you have to use the environment multline*. Environment gather centers included in the formula: \begin{gather} \int_{a_1}^{a_2} f(x)\,dx+\int_{a_2}^{a_3} f(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} f(x)\,dx\\ +\int_{a_1}^{a_2} g(x)\,dx+\int_{a_2}^{a_3} g(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} g(x)\,dx\notag\\ +\int_{a_1}^{a_2} h(x)\,dx+\int_{a_2}^{a_3} h(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} h(x)\,dx\\ =\int_{a_1}^{a_n} f(x)+g(x)+h(x)\,dx. \end{gather} Each line is automatically numbered, if the line number it is not necessary, before \verb+\\+ in this line, you need to put the command \verb+\notag+. When you use the environment gather* formula will not be numbered. The align environment allows you to align formulas on your discretion: \begin{align} \int_{a_1}^{a_2} f(x)\,dx &+\int_{a_2}^{a_3} f(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} f(x)\,dx\notag\\ &+\int_{a_1}^{a_2} g(x)\,dx +\int_{a_2}^{a_3} g(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} g(x)\,dx\\ &+\int_{a_1}^{a_2} h(x)\,dx+\int_{a_2}^{a_3} h(x)\,dx +\dots+\int_{a_{n-1}}^{a_n} h(x)\,dx\notag\\ &=\int_{a_1}^{a_n} f(x)+g(x)+h(x)\,dx. \end{align} Read more about working with these environments can be found in the book \cite{GG}. \section{Variables} For the writing of definitions, theorems, lemmas and their proofs use the following variables. If necessary, you can add your variables in the sample. \begin{definition}\label{D:1} Define ... \end{definition} \begin{lemma}\label{L:1} If ... \end{lemma} \begin{theorem}\label{Th:1} Let ... \end{theorem} \begin{proof} Consider... \end{proof} \section{Figures and tables} REV\TeX~4 will automatically number sections, equations, tables, and drawings. Figure captions are made after the image and the signature tables~--- before a table, as shown in the examples at the end. In tables footnotes \footnote{Footnotes in tables, you can try to do this manually.} not working. Graphics and diagrams should be monochrome in black-and-white color and saved in EPS format. %You can include a picture in the article using the figure environment: \begin{figure}[h] \setcaptionmargin{5mm} %\onelinecaptionsfalse % if the caption is multiline \onelinecaptionstrue % if the caption is one-line \includegraphics[width=0.85\textwidth]{deform.eps} \captionstyle{normal}\caption{Please write your figure caption here.}\label{fig:1} \end{figure} \begin{table}[!h] \setcaptionmargin{0mm} \onelinecaptionsfalse \captionstyle{flushleft} \caption{ For the insertion of tables, the table environment is used, the signatures to the tables are made in the same way as the captions for the figures. This is an example of a table whose multi-line name is decorated with the \textbf{caption2} package.} \bigskip \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline &r_c$(\AA)&$r_0$(\AA)&$\kappa r_0$& &$r_c$(\AA) &$r_0$(\AA)&$\kappa r_0\$\\
\hline
Cu& 0.800 & 14.10 & 2.550 &Sn
& 0.680 & 1.870 & 3.700 \\
Ag& 0.990 & 15.90 & 2.710 &Pb
& 0.450 & 1.930 & 3.760 \\
Au& 1.150 & 15.90 & 2.710 &Ca
& 0.750 & 2.170 & 3.560 \\
Mg& 0.490 & 17.60 & 3.200 &Sr
& 0.900 & 2.370 & 3.720 \\
Zn& 0.300 & 15.20 & 2.970 &Li
& 0.380 & 1.730 & 2.830 \\
Cd& 0.530 & 17.10 & 3.160 &Na
& 0.760 & 2.110 & 3.120 \\
Hg& 0.550 & 17.80 & 3.220 &K & 1.120 & 2.620 & 3.480 \\
Al& 0.230 & 15.80 & 3.240 &Rb & 1.330 & 2.800 & 3.590 \\
Ga& 0.310 & 16.70 & 3.330 &Cs & 1.420 & 3.030 & 3.740 \\
In& 0.460 & 18.40 & 3.500 &Ba & 0.960 & 2.460 & 3.780 \\
Tl& 0.480 & 18.90 & 3.550 & & & & \\[1mm]
\hline
\end{tabular}
\end{table}

\begin{table}[!htb]
\setcaptionmargin{0mm}
\onelinecaptionstrue
\captionstyle{flushleft}
\caption{The name of this table is --- one-line.}
\bigskip
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
& 1 & 2 & 3 & 4 & 5 & 6\\
\hline
1 & 1 & 2 & 3 & 4 & 5 & 6\\
2 & 2 & 4 & 6 & 8 & 10 & 12\\
3 & 3 & 6 & 9 & 12 & 15 & 18\\[1mm]
\hline
\end{tabular}
\end{table}

\section{Bibliography}
The following rules apply for references to books:

\begin{itemize}
\item Author’s initials go before the surname with a space between the initials. Use and between the last two authors. All authors listed in the original reference should be cited.
\item The title of the book is written in italics. If the book is originally published in Russian, only the English translation of the title is cited and after citation the original language may be indicated in square brackets, e.g.: [in Russian].
\end{itemize}

\begin{acknowledgments}
At the end of the articles are written thanks.\\
For example:\\
We thank A.~A.~Surname1 and B.~B.~Surname2 for their participation in discussions of the results.\\
We are grateful to C.~C.~Surname3 and the reviewers for careful reading of the manuscript and helpful remarks.

Links to grants are also listed here.
\end{acknowledgments}

% Text of article ends here.

\appendix

\section{Applications}

To switch to the tab application, you need to use the command
\verb+\appendix+. After all the sections will be referred to the word
The application and the corresponding letter in the command \verb+\section+
you don't specify, then the application will have
names.

\section{}

The application may contain subchapters and subsections.

%
% The Bibliography
%
\begin{thebibliography}{99}
\bibitem{RTeXHome}
\url{https://journals.aps.org/revtex}.

\bibitem{RTeX}
REV\TeX~4.1 Author's Guide\\
\url{https://d22izw7byeupn1.cloudfront.net/files/revtex/auguide4-1.pdf}

APS Author Guide for REV\TeX~4.1 (Version 1.0)\\
\url{https://d22izw7byeupn1.cloudfront.net/files/revtex/apsguide4-1.pdf}

Author's Guide to AIP Substyles for REV\TeX~4.1\\
\url{https://d22izw7byeupn1.cloudfront.net/files/revtex/aipguide4-1.pdf}

REV\TeX~4.1 Command and Options Summary\\
\url{https://d22izw7byeupn1.cloudfront.net/files/revtex/summary4-1.pdf}.
\bibitem {GG}
\refitem{book}
{\it Grjetcer G.} // Pervye shagi v \LaTeX'e. M.: Mir, 2000.

\bibitem{RTeXHome}
\url{https://journals.aps.org/revtex}.

\bibitem{L}
\refitem{book}
{\it L'vovskij S.M.} // Nabor i verstka v pakete \LaTeX, 2-e izdanie. M.: Kosmosinform, 1995.

\bibitem{cap}
\refitem{url}
Capitalization in Titles 101\\
\url{https://www.grammarcheck.net/capitalization-in-titles-101/}.

\bibitem{hsg}
\refitem{url}
House Style Guide: Version 2.0\\
\url{http://ojs.kpfu.ru/files/HSG2013.pdf}.

\bibitem{K}
\refitem{book}
{\it Knut D.} // Vse pro \TeX. Protvino: AO RDTeX, 1993.

\bibitem{S}
\refitem{book}
{\it Spivak M.} // Voshititel'nyj TeX. M.: Mir, 1993.

\bibitem{KCh}
\refitem{book}
{\it Kotel'nikov I., Chebotaev P.} //
Izdatel'skaja sistema \LaTeXe. Novosibirsk: Sibirskij hronograf, 1998.

\bibitem{GMS}
\refitem{book}
{\it Gussens M., Mittel'bah F., Samarin A.} //
Putevoditel' po paketu \LaTeX. M.: Mir, 1999.

\bibitem{KD}
\refitem{book}
{\it Kopka H. and Daly P.} // A Guide to \LaTeXe.

\bibitem{GRM}
\refitem{book}
{\it Goossens M., Rahtz S., and Mittelbach F.} //
The \LaTeXe Graphics Companion.

\bibitem{RG}
\refitem{book}
{\it Goossens M., Rahtz S. et al.} //
The \LaTeXe Web Companion:Integrating \TeX, HTML and XML.

\bibitem{R}
\refitem{misc}
{\it Reckdahl K.} //
Using Imported Graphics in \LaTeXe. Version 2.0, 1997.
\url{\texmf\doc\latex\graphics\epslatex.pdf}

\bibitem{babel}
\refitem{misc}
{\it J. Braams.} Babel, a multilingual package for use with \LaTeX{}'s
standard document class. \url{\texmf\doc\generic\babel\user.dvi}
%
\bibitem{1}
\refitem{article}
N.~Cabibbo, Phys. Rev. Lett. \textbf{10}, 531 (1963);
\refitem{article}
M.~Kobayashi and T.~Maskawa, Prog. Theor. Phys. \textbf{49}, 652 (1973).

\bibitem{37:Landsberg_n}%[37]%
S.~L.~Glashow, J.~Iliopoulos, and L.~Maiani, Phys. Rev. D \textbf{2}, 1285 (1970).
\bibitem{38:Landsberg_n}%[38]%
\refitem{article}
T.~D.~Lee and C.~S.~Wu, Annu. Rev. Nucl. Part. Sci. \textbf{15}, 381 (1965);
\refitem{article;ibid}
\textbf{16}, 471 (1966).

\bibitem{2}
\refitem{report}
A.~R.~Barker and S.~H.~Kettell, hep-ex/0009024;
\refitem{article;prevau}
Annu. Rev. Nucl. Part. Sci. \textbf{50}, 249 (2000).

\bibitem{3}
\refitem{article}
A.~I.~Va\u{\i}nshte\u{\i}n \emph{et al.}, Pis'ma Zh. \'{E}ksp. Teor. Fiz. \textbf{22}, 123 (1975)
\refitem{article;rusjou}
[JETP Lett. \textbf{22}, 55 (1975)];
\refitem{article;prevau}
Nucl. Phys. B \textbf{120}, 316 (1977).

\bibitem{4}
\refitem{article}
A.~ Vainshtein, Int. J. Mod. Phys. A \textbf{14}, 4705 (1999).
\bibitem{5}
\refitem{article}
NA-31 Collab. (H. Burkhardt \emph{et al.}), Phys. Lett. B \textbf{206}, 169 (1988);
\refitem{article}
NA-31 Collab. (G. D. Barr \emph{et al.}), Phys. Lett. B \textbf{317}, 233 (1993).

\bibitem{06}
\refitem{book}
L.~B.~Okun, \emph{Leptons and Quarks} (Nauka, Moscow, 1990; North-Holland, Amsterdam, 1984);
\refitem{book}
L.~B.~Okun, \emph{Particle Physics} (Nauka, Moscow, 1988; Harwood, Chur, 1985).

\bibitem{7}
\refitem{article}
Yu.~R.~Rivin, Int.~J.~Geomagn. Aeron. \textbf{1} (3), (1998);
\end{thebibliography}
\end{document}

The paper should be written in good English. If author's native language is not English, we strongly recommend to

• use standard English sentences;
• check if you use terms correctly (consult dictionaries!);
• use a spell-check program.
• SpringerPlus. Instructiion for Authors (http://www.springerplus.com/authors/instructions/research)
• Mathematical English Usage - a Glossary by Jerzy Trzeciak (http://www.emis.de/monographs/Trzeciak/)
• 2010 Mathematics Subject Classification (http://www.ams.org/msc/msc2010.html)
A manuscript with spelling and grammar errors will be immediately rejected.
The list of references should only include works that are cited in the text and that have been published or accepted for publication. The entries in the list should be numbered consecutively. Bibliography items should be ordered by citation order.kage
﻿

The following rules apply for references to books:

• Author’s initials go before the surname with a space between the initials. Use and between the last two authors. All authors listed in the original reference should be cited.
• The title of the book is written in italics. If the book is originally published in Russian, only the English translation of the title is cited and after citation the original language may be indicated in square brackets, e.g.: [in Russian].
Examples:

TEX-code:
    \bibitem{Adams}


TEX-code:
    \bibitem{elizarov:mathml}
A.~M.~Elizarov, E.~K.~Lipachev, and M.~A.~Malakhaltsev, \textit{Web Technologies for Mathematicians: The Basics of MathML. A Practical Guide} (Fizmatlit, Moscow, 2010) [In Russian].

The following rules apply for references to journals:
• Author’s initials go before the surname with a space between the initials. Use and between the last two authors. All authors listed in the original reference should be cited.
• The title of the book is written in italics.
• The name of the journal is written in the standard abbreviated form in plain text instead of italics.Always use the standard abbreviation of a journal’s name (AMS. Abbreviations of Names of Serialshttp://www.ams.org/msnhtml/serials.pdf; ISSN.org “List of Title Word Abbreviations”http://www.issn.org/services/online-services/access-to-the-ltwa/).If you are unsure, please use the full journal title.
• The volume number follows the journal title in bold without a preceding comma and without the word vol.
• If the page numbering is continuous throughout the volume, the issue number is not indicated. In this case, the first page number of the article follows the volume number separated by a comma but without the word p. If the page numbering is not continuous, the issue number is written in parentheses in plain text following the volume number with a comma placed after the issue number, followed by the page number. In both cases, the year of publication follows the page number in parentheses.
Examples:

TEX-code:
    \bibitem{Zhizhchenko}
A.~B.~Zhizhchenko and  A.~D.~Izaak, \textit{The information system Math-Net.Ru.  Application  of  contemporary  technologies  in  the scientific  work of mathematicians}, Russian Math. Surveys \textbf{62} (5), 943--966 (2007).


Manual formatting of bibliographies is accomplished with the thebibliography environment, using \bibitem to set an individual reference.
Submissions to our Journal are made using Open Journal Systems, the online submissions and peer review system available on the website of our Journal at http://ojs.kpfu.ru/index.php/ljm/user/register. If you do not have an account, please click here to create an account (Registration ).

﻿Submitting to LJMrequires :
For Submitting a Manuscript use "Submit Article"
Full information and guidance on using Open Journal Systems is available on the websites OJS Documentation and the website PKP | School.

Having completed the registration procedure, the author shall upload the .ZIP archive containing: the manuscript in .PDF format and .TEX format, the pictures and graphics in .EPS format, the scanned documents, including the Author's Agreement: