E. P. Baranovskii On the completeness of the list of L-conditions for simplexes of 6-dimensional lattices

This work can be considered as a supplement to the autors' paper [*] where was given a full list of the L-conditions for simplexes of 6-dimensional lattices in the E ⁶. In this work it was shown that in E ⁶ do not occur lattices which have L-simplexes of volume 4pv and 5pv, where v is the volume of a basic simplex of the lattice and p = 1, 2, ... This fact is a basic of the proof in [*] of completeness of the list of L-conditions.

Recently the L-conditions for simplexes of 6-dimensional lattices were obtained by M. Dutour and M. Deza [**] (Mathieu Dutour, Michel Deza. The hypermetric cone on seven vertices // 2001. Preprint in Laboratore interdisciplinaire de geometrie appliquee, CNRS/ENS, Paris.) when they investigated the hypermetric cone on seven vertices. The ways of solution of the problem in works [*] and [**] are quite different.

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D. I. Moldavanskii The residual p-finiteness of some HNN-extensions of groups

Sufficient conditions for HNN-extension to be residually a finite p-group are obtained. One of this conditions implies that if the base group G of HNN-extension G^* is residually a finite p-group and associated subgroups are central and finite and their intersection is equal to identity then the group G^* is residually a finite p-group.

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S. V. Puhov, E. A. Sukhareva The system of functions with limited number of roots and the generalization of Gauss quadrature formula

The generalization of Gauss quadrature formula for system of functions such that the number of roots of any generalized polynomial on it is bounded is given.

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E. V. Sokolov The structure of finitely generated bounded solvable groups

It is proved that finitely generated solvable group bounded in the sense of Mal'cev is polycyclic.

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S. I. Khashin 17-dot interpolation formula

The interpolational formula with 2 variables constructed on 17 points of interpolation is found. The comparison of it with bilinear and bicubic interpolation formulas is given. The received formula can be used for compression of graphic files by methods of Boolean algebra.

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S. I. Khashin, Yu. A. Khashina Optimization of the algorithm of Boolean algebra compression methods

The way of optimization of algorithm of compression by methods of Boolean algebra is offered. Preliminary transformation of initial data allows to simplify considerably the kind of the transformed information.

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N. I. Yatskin Algebraic statics: problems setting

In this article the theory of systems of sliding vectors on modules over commutative rings is developed. Equivalence classes of such systems are described by means of sliders (spicially constructed objects in the exteior algebra of the module).

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