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Rules and Examples

 General requirements for entry preparation: FORMAT: Latex 2e (with AmS fonts and/or AMS math optional). Any standard package may be included. Send only after correct latexing. In exceptional cases also Latex 2.09 is OK. The entry will be translated. Bibliography: without \bibitem command till 3-4 entries. Bibliography - if cited, then hard citations (without \cite command !!!). Please take into account all details below up to spaces. Equations: with \tag or \eqno command for numbering (only if needed) and \nonumber command. No \newcommand please!!! No \ref please!!! It is very much desirable that terms and articles have to be with corresponding _formulas_ on a strong mathematical level. The statements should be concise, but have to be made as inside body of an article, not as in introduction (several sentences without formulas with citations, as in Example 3 below). Please, add formulas to every word which implies them. For well-known notions and terms it would be desirable to cite an article where it has appeared for the first time. Size of entries is not very much restricted: till 1 page for shortest entry; 3-4 pages for longest entry; till 5 pages for review and bio/historical articles. Entries can be written with coauthors (1 entry - till 2 authors, for review articles - till 3 authors).

 EXAMPLES Example 1. General structure of entry. %%%%%%%%%Begin of Entry%%%%%%%%%% \documentclass{article} \usepackage{amssymb} \usepackage{amsfonts} \begin{document} % Your name TERM, definition [1], also [2]... BIBLIOGRAPHY. [1] A.B. Author, A.B. Author Abbr.Journal volume (year) page; [2] A.B. Authors Abbr.Journal volume (year) page; [3] A.B. Authors hep-th/0000000; [4] A.B. Authors Title of Book, Edition 1999. \end{document} %%%%%%%%%End of Entry%%%%%%%%%%% Example 2. Simple example of a term. %%%%%%%%%Begin of Entry%%%%%%%%%% \documentclass{article} \usepackage{amssymb} \usepackage{amsfonts} \begin{document} % Ivanov SUPERSPACE, an extended space in supersymmetric theories [1] which has in addition to usual spacetime [2] bosonic coordinates $x^{\mu}$ also fermionic coordinates $\theta^{\alpha}$. A real superspace $$\mathbb{R}^{4|4}=\left\{ x^{\mu},\theta^{\alpha},\theta^{\overset{.}{\alpha} }\right\} \tag{1}$$ contains (1) additional spinorial coordinates $\theta^{\alpha},\theta ^{\overset{.}{\alpha}}\left( \alpha,\overset{.}{\alpha}=1,2\right)$. BIBLIOGRAPHY. [1] S.J. Gates et al. Superspace, Benjamin 1983; [2] J. Wess, B. Zumino PL B66 (1977) 361. \end{document} %%%%%%%%%End of Entry%%%%%%%%%%% Example 3. Undesirable and desirable styles of entry. Please save as text and latexing2e the below approximate example (or download ready postscript version of this file example.ps) %%%%%%%%%Begin of example%%%%%%%%%% \documentclass{article} \usepackage{amssymb} \usepackage{amsfonts} \begin{document} \begin{center} \textbf{Undesirable entry }(very short simple) \textbf{example:} \end{center} K\"{A}HLER MANIFOLD, a complex manifold which admits a K\"{a}hler metric [1] BIBLIOGRAPHY. [1] E.K\"{a}hler Abh. Math. Semin. Univ. Hamburg 9(1933)173. \bigskip \begin{center} \textbf{Desirable entry }(very short simple) \textbf{example:} \end{center} K\"{A}HLER MANIFOLD, a complex manifold $K$ having $U\left( N\right)$ holonomy admitting a Hermitian metric $g_{i\bar{j}}$ (called a \textit{K\"{a}hler metric} and can be written in complex coordinates $z_{i}$ through the K\"{a}hler potential $\varphi$ as $g_{i\bar{j}}=\frac{\partial ^{2}\varphi }{\partial z^{i}\partial \bar{z}^{j}}$) for which the fundamental form $\Omega =g_{i\bar{j}}dz_{i}\wedge d\bar{z}^{j}$ is closed $d\Omega =0$ [1]. Examples: any one-dimensional complex manifold, complex $N$-space, a projective manifold $CP_{N}$ and any its submanifold are K.M. The only nonvanishing Christoffel symbol of a K.M. is $\Gamma _{ij}^{k}=g^{k\bar{k}}\partial g_{i\bar{k}}/\partial z^{j}$ and the only nonvanishing component of the curvature tensor is $R_{ij\bar{k}}^{l}=-\partial \Gamma _{ij}^{l}/\partial \bar{z}^{j}$. The theorem of Calabi-Yau: K.M. of vanishing first \textit{Chern class} $c_{1}\left( K\right) =0$ admits a \textit{K\"{a}hler metric} of $SU\left( N\right)$ holonomy. Such K.M. is Ricci flat $R_{ij}=0$ and admits nonvanishing covariantly constant spinor $% D_{i}\varepsilon =0$ which allows to exploit 6-dimensional K.M. $K_{6}$ in superstring phenomenology [2] based on compactification scheme $M_{10}\rightarrow M_{4}\times K_{6}$, where $M_{4}$ is 4D maximally symmetric (de Sitter, anti-de Sitter or Minkowski) manifold [3]. BIBLIOGRAPHY. [1] A. Weil Introduction to the theory of K\"{a}hler manifolds, NY 1957. [2] M. Kaku Introduction to superstrings and M-Theory, Berlin 1999. [3] P.Candelas et al. NP B258 (1985) 46. \end{document} %%%%%%%%%End of example%%%%%%%%%%%