In this article functional approximate equation was get for zeta-function in square form with negative discriminant.

Innovative processes in education, transition to the new state standards of higher education and multi-level system of higher education organization open up new opportunities for the educational community to improve the education system, and in particular, mathematical education. New educational standards provide greater freedom of choice, both for students and for the university. Elective modules which selects the student provide an informed choice on the part of students and a broad spectrum of opportunities from the university. The problem of selecting a specific elective module is quite complicated. Raises the question of the formation of long-term informed choice based on the subsequent post-graduate study and research activities. For serious informed choice requires sufficient awareness, availability of development prospects and the ability to implement intellectual relay. Informatization of society opened opportunities creating problem-oriented educational information systems, to provide necessary conditions for the implementation of such a choice student and his subsequent promotion of successful in their individual educational path. Creating a modern problem-oriented information system involves the provision of necessary and convenient means for educational and, then, and scientific problems. In this paper provides an overview of the step of creation and development issues PODPS—Problem-Oriented Data-Processing System.

In this paper we obtain some arithmetic properties of generalized Fibonacci sequence and consider their applications.

This paper is a survey of results concerning different kinds of Diophantine exponents. Special attention is paid to the transference principle and to generalization of the concept of badly approximable numbers to matrices and lattices.

Given the first correct proof of the reciprocity law in Russian which based on the Zolotarev idea.

Let x ∈ (0, 1) be a real number, x = [0; ε1/b1, . . . , ε1/bn, . . .] be its expansion in Ω− continued fraction. Let An/Bn be its nth convergent and Υn = Υn(x) = B2 n |x − An/Bn|. In this note we prove the analog of the classical theorems by Borel and Hurwitz on the quality of the approximations for Ω− continued fractions: min(Υn−1, Υn, Υn+1) 6 1/ √ 5. The result is best possible.

The lower estimate for number of vectors with real algebraic coordinates near smooth surfaces is obtained. We use a new form of the essential and inessential domains method.

Some examples of domains such that first return time function for twodimensional torus shift has at most three values are constructed. Some applications to bounded remainder sets problem are obtained.

In this paper we study the relationship between representations of abelian groups and representations of abelian n-ary groups. Based on this relationship, described all the representations of abelian semicyclic n-ary groups.

In the work, the family of filtered deformations of Lie algebras of series Z was constructed. Proved that these algebras are new.

In this work is given the complete description of weakly regular unars with standard Mal’tsev operation.

Each magazine has to have presently the web site in the Internet network. But that without message problems his editor needs a workplace where he will be able instantly to operate a content, to prepare new releases, to keep in contact with readers. In article requirements to a magazine site are considered, components of a workplace and their function are listed.

This paper describes construction of a pierce chain of congruences of a semiring - analogue of pierce chains of ideals of a ring, necessary definitions are introduced: a ring of central supplemented idempotents, a congruence of Peirce, a pierce sheaf of semirings, a pierce representation of semirings, a pierce chain of congruences, a horn formula. The basic result of paper is the theorem 1 about equivalence of realizability of horn formulas without negation on a semiring and its factors, additional result is an application of the theorem 1 for the proof of "transposition"of properties of a semiring of a Bezout on its factors and is inverse.

In this paper an inverse boundary problem for the fourth order Boussinesq equation with integral conditions is investigated. First of all the initial problem reduced to the equivalent problem, for which the theorem of existence and uniqueness proved. Then using these facts the existence and uniqueness of the classical solution of initial problem is proved.

The paper describes several algorithms for scalar multiplication over elliptic curves and compares the performance of their implementations.

In this paper we consider the inverse problem. Our goal is to describe classes of semigroups which is isomorphic to the endomorphism semigroup of some monounary algebra. We describe the endomorphism semigroup for certain class of monounary algebras with an one-element cycle.

In this work is given some conditions of strictly simplicity for algebras with operators having one ternary main operation. It is described strictly simple unars with standard and symmetric Mal’tsev operations and with standard majority operation. The description of simple unars with standard majority operation is obtained as well.

It is proved that every periodic abelian n-ary group is isomorphic to the direct product of primary abelian n-ary groups belonging to different primes.