Mathematics

About generating set of the invariant subalgebra of free restricted Lie algebra

Authors: Petrogradsky V. M., Subbotin I. A.

Suppose that L=L(X) is the free Lie p-algebra of finite rank k with free generating set X={x1,…,xk} on a field of positive characteristic. Let G is nontrivial finite group of homogeneous automorphisms L(X). Our main purpose to prove that LG subalgebra of invariants is is infinitely generated. We have more strongly result. Let Y=∪∞n=1Yn be homogeneous free generating set for the algebra of invariants LG, elements Yn are of degree n relatively X, n≥1. Consider the corresponding generating function H(Y,t)=∑∞n=1|Yn|tn.

Parameters Recovering Algorithm for One Class of Irrationalities

Authors: Nesterenko A. Y.
In this article we study one class of irrationalities whichmay be defined as covergent series with rational coefficients. This class contain a lot of well known constants such as ln 2, ¼, e.t.c. We consider the problem of determination parameters of rational coefficients by rational approximation of irrationality. We deduced the lower and upper bounds and present an algorithm for determination of unknown parameters. Also, we present some results of practical calculations.

On the A. V. Mikhalev’s Problem for Lie Algebras

Authors: Mescherina E. V., Pikhtilkov S. A., Pikhtilkova O. A.

Weakened A. V. Mikhalev’ sproblem about the prime radical of artinian Lie algebras is solved.

On a Particular Equivalent of Extended Riemann Hypothesis for Dirichlet L-functions on Numerical Fields

Authors: Matveev O. A., Matveev V. A.
A condition on summatory function over a set of prime ideals for Dirichlet L-functions on numerical fields is obtained. This condition is equivalent to extended Riemann hypothesis. Analytical properties of Euler products associated with this equivalent are studied

An Estimate of a Certain Summatory Functions Class

Authors: Matveev V. A.
In this paper summatory functions of form P n·x h(n)nit, 1 · |t| · T for finite-valued functions h(n) of natural argument with bounded sum function are estimated

Approximation Polynomials and Dirichlet L-functions Behavior in the Critical Strip

Authors: Matveev O. A.
In this paper a sequence of Dirichlet polynomials that approximate Dirichlet L-functions is constructed. This allows to calculate zeros of L-functions in an effective way and make an assumptions about Dirichlet L-function behavior in the critical strip.

On Universality of Certain Zeta-functions

Authors: Laurinˇcikas A. P., Macaitiene R. .., Mokhov D. .., Siauciunas D. ..
It is well known that a generalization of the Hurwitz zeta-function—the periodic Hurwitz zeta-function with transcendental parameter is universal in the sense that its shifts approximate any analytic function. In the paper, the transcendence condition is replaced by a simpler one on the linear independence of a certain set.

On Combinatorial Problem, Related with Fast Matrix Multiplication

Authors: Kuznetsov Y. V.
The group-theoretical approach to fast matrix multiplication generates specific combinatorial objects, named Uniquely Solvable Puzzles (briefly USP). In the paper some numerical characteristic of the USP was discussed and the relation of USPs to famous combinatorial problem named «Cap set problem» was investigated.

Конгруэнции полигонов над группами

Authors: Халиуллина А. Р.

Получено полное описание конгруэнций полигонов над группами.

On Congruence Lattices of Direct Sums of Strongly Connected Commutative Unary Algebras

Authors: Kartashova A. V.
A union of mutually disjoint unary algebras is called their direct sum. A unary algebra is said to be strongly connected if it is generated by its arbitrary element. In the present paper we investigate congruence lattices of the class of all algebras with finitely many operations whose every connected component is strongly connected. We give a necessary and sufficient condition for an algebra from this class to have a distributive congruence lattice (Theorem 1). Besides, all distributive congruence lattices of algebras from the above class are discribed (Theorem 2).

Pages