REMARKS CONCERNING PAPERS ARRANGMENT


The arrangement of theorems, lemmas, propositions, corollaries and definitions, which are to be numerated, in papers written in English should be carried out in the following way:

\begin{theorem}
{\sl Formulation text }
\end{theorem}
\begin{proof}
Proof text
\end{proof}

\begin{lemma}
{\sl Formulation text }
\end{lemma}
\begin{proof}
Proof text
\end{proof}

\begin{proposition}
{\sl Formulation text }
\end{proposition}
\begin{proof}
Proof text
\end{proof}

\begin{corollary}
{\sl Formulation text }
\end{corollary}
\begin{proof}
Proof text
\end{proof}

\begin{definition}
Definition text {\it the term which is defined} the continuation of definition text
\end{definition}



I n the case, when the paper is written in Ukrainian (Russian), the theorems, lemmas, propositions, corollaries and definitions, which are to be numerated, should be arranged in the following way:

\begin{theorem}
{\sl Formulation text }
\end{theorem}
\begin{proof}[Доведення.] ( [Доказательство.] )
Proof text
\end{proof}

\begin{lemma}
{\sl Formulation text }
\end{lemma}
\begin{proof}[Доведення.] ( [Доказательство.] )
Proof text
\end{proof}

\begin{proposition}
{\sl Formulation text }
\end{proposition}
\begin{proof}[Доведення.] ( [Доказательство.] )
Proof text
\end{proof}

\begin{corollary}
{\sl Formulation text }
\end{corollary}
\begin{proof} ( [Доказательство.] )
Proof text
\end{proof}

\begin{definition}
Definition text {\it the term which is defined} the continuation of definition text
\end{definition}



I f there is no numeration, use

theorem*, lemma*, proposition*, corollary*, definition*

everywhere instead of

theorem, lemma, proposition, corollary, definition

respectively.


T he arrangement of ordered lists should be carried out using the environment itemize, for example:
\begin{itemize}
\item[1.] text 1
\item[2.] text 2
\item[3.] text 3
\end{itemize}
or
\begin{itemize}
\item[a)] text a
\item[b)] text b
\item[c)] text c
\end{itemize}.



I n order to organize complicated formulae and relations, which occupy more than one line, use the environment gather, for instance:
\begin{gather}
\nonumber line 1 of the formula \\
line 2 of the formula \\
\nonumber line 3 of the formula
\end{gather}
The above example reflects the formula, which occupies three lines. Besides, line 1 and line 3 are not numerated, and line 2 is numerated automatically.

If the author wants to arrange a formula, which is not numerated, he or she is supposed to use the environment
gather* :
\begin{gather*}
line 1 of the formula \\
line 2 of the formula \\
...
the last line of the formula
\end{gather*}



T he references items should be arranged in one of the following ways:

I.
a) \bibitem{1.} Бицадзе А.В., Самарский А.А. {\it О некоторых простейших обобщениях линейных эллиптических краевых задач} \sep Докл. АН СССР -- 1969. -- \No 4. -- C. 739--740.

б) \bibitem{3.} Шеремета М.М. Цілі ряди Діріхле. -- К.: ІСДО, 1993. -- 168 с.
II.
a) \bibitem{2.} T. Banach, {\it Characterization of spaces admitting a homotopy dense embedding into a Hilbert manifold, Topology Appl. {\bf 86} (1998), 123--131.

б)\bibitem{5.} A. Chigogidze, Inverse Spectra, North Holland, Amsterdam, 1996.



I n case, when the paper has to contain pictures, they are to be created in bmp-format.



I f possible, try to avoid using too many definitions of new commands (\def).