D. N. Azarov On the residuality a finite p-group of groups on the finite rank

It is proved that any group of finite rank is nilpotent if it is residually a finite p-group for every prime p. This generalized the similar result of Sexsenbayev about polycyclic groups.

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E. P. Baranovskii Simplexes of 8-multiple relative volume in the L-partitions of 12-dimensional lattices

An examples of 12-dimensional lattices having L-simplexes of 8-dimensional relative volume are given.

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A. S. Belov On properties of non-negative trigonometric polynomials with monotone coefficients

For arbitrary non-negative even trigonometric polynomial of the degree n with monotone positive coefficients and the free term a₀ and for each natural number m = 1, ..., 2n the method of construction of non-negative even trigonometric polynomial of the degree m with monotone positive coefficients the free term of which does not exceed 3a₀ is given. In this case some properties of the coefficients as, for instance, to be integers, are conserved. The applications of the results of such kind are indicated.

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S. R. Kogalovskii Simple remarks on a groups with multiple operators

It is proved that any group with a finite set of multiple operators (in the sense of P. Higgins) is equivalent to an algebra with an unique operation. This implies the following: let A be a group with a countable set of multiple operators. Then Con A  Con B for some algebra B with an unique operation.

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D. I. Korovin Simulation on the random variables in construction of stochastic measures on the algebraic spaces

The distribution of the product of random matrixes g(n) = g₁g₂...g_n from unimodular group G of third order is considered. For the analysis some analog of Fourier transform is constructed and by means of this transform the random variables with corresponding stochastic measures in the Euclidean space are simulated.

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Yu. I. Maslyakov On some bound of final Laplace transformation

The bound of final Laplace transformation under some restrictions on the original is obtained.

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M. A. Parinov One method of obtaining the first integrals of the generalized Lorentz equations

The author's method of the first integrals of the Lorentz equations (1981 y.) is generalized for all dimensions. The ground of this method in particular case is presented.

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S. V. Puhov On the polynomials of the least deviation from zero in metric of the space L([-1; 1]) with fixed higher coefficients

The extremal problem on algebraic polynomials of the least deviation from zero in metric of the space L([-1; 1]) with fixed higher coefficients is considered. Depending of alternance process of construction of such polynomial is analyzed. The theorem on the polynomial dependence of lower coefficients of polynomial from the higher ones is brought in the case when four higher coefficients are fixed and alternance of the polynomial is maximal.

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