E. P. Baranovskii, V. P. Grishuchin An algorithm of the calculation of the non-rigidity degree of L-partitions of the lattices

Non-rigidity degree of L-partition of a lattice is defined as dimension of the L-type domain containing the positive quadratic form corresponding to a basis of the lattice. In this note an algorithm of the calculation of the non-rigidity degree of L-partition of a lattice is constructed. The nonstruction of this algorithm is based on the theory of the repartioning complexes.

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S. V. Kolesnikov On the classification similar to baire classification for boundary values of analitic functions

In this article, for ordinal numbers \alpha of the first or second class, classes of functions on the unit circle \Gamma are defined. These classes are defined similar to well-known Baire classes of functions. Class of polynomials of complex variable is considered as a zero class. Class is the class of functions which are point-wise limits of uniformly bounded sequences of functions from and do not belong to preceding classes. It is proved here that is the class of functions which are boundary values of bounded analytic functions on unit disk and belong to ordinary Baire \alpha-class.

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D. I. Moldavanskii Residuality of HNN-extensions by a class of finite p-groups

The criterion for HNN-extension with a finite p-group base to be residually a finite p-group is given and the sufficient condition for any HNN-extensions to be residually a finite p-group based on this criterion is proved. These results are applied to describe all groups from two classes of one-relator groups which are residually a finite p-group.

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M. A. Parinov Einstein - Maxwell spaces and Lorentz equations

We introduce the concept "Einstein - Maxwell space" as a natural base for description of electromagnetic fields in presence of gravity. We present the survey of results on classification of Maxwell spaces and on finding the first integrals of Lorentz equations by the author's method.

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S. V. Puhov The natural splines on a sphere

The construction based on the M. Atteia - P. M. Anselone - P.-J. Laurent theory of a natural interpolated splines on the unit sphere is given as a solution of some extremal problem.

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S. I. Khashin The numerical solution of Butcher equations

The program for numerical solution of Butcher equations (for obtaining Runge-Kutta methods) is described. Some received Runge-Kutta methods of high order are fulfilled.

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