Vol 21, No 6 (2016)

Lagrange’s quadratic bound, LQ , on the values of the positive roots of polynomials consists of two parts. Sorting of one-dimensional arrays is used in the second part of the Lagrange algorithm in all known implementations. We propose to change this part of the algorithm and to avoid the sort. The computing time of the second part as is currently implemented is O(n∙ log⁡(n)) . With our improvement we reduce the computing time of the second step of LQ to O(n) .

In the work examines some problems for the linearized equations of hemodynamics on simple graphs. By the method of propagating waves and by the continuation method obtained exactsolutions of these problems.

For canonical representations on a Lobachevsky space, a description of distributions concentrated at the boundary is given.

The study of covering mappings of partially ordered spaces, initiated in the works of A.V. Arutyunov, E.S. Zhukovskiy, S.E. Zhukovskiy (Topology and its Applications. 2015. V. 179. №1. P. 13-33; 2016. V. 201. P. 330-343), is continued. For multi-valued mappings, the conditions of preserving the property of ordered covering under antitone disturbances are derived.

A boundary value problem for an implicit differential inclusion is considered Sufficient conditions for solvability of this problem are obtained.

We propose two algorithms for particular cases of block-recursive LU -decomposition of matrices over idempotent semifields. We consider the cases in which the band width of the block is equal to 1 or 2. For each of them we will get the decomposition algorithm and give an example.

A linear inverse problem for the Newtonian potential for bodies of constant thickness is considered, the field of potential is defined on a non-linear surface. A stable solution of the problem is obtained.

We discuss the problem of constructing an effective algorithm for computing the inverse matrix for an integer matrix. One of the way, for obtaining the inverse matrix, is based on the matrix Smith form. Known probabilistic algorithm can find the Smith form with the computational bit complexity which has cubic dependence of the matrix sizes. We propose a deterministic extension of this approach to calculating the inverse matrix.

This paper contain results of numerical calculations which prove the effectiveness of the method of approximation for digital signals by integer shifts of the Gauss function. The method is based on usage of nodal functions and approximations of infinite systems of linear equations by finite ones. It is demonstrated that by this method an effective approximation of signals of different nature is attained: normal distributions, Cauchy distributions, triangular and trapezoid signals, meanders of complex forms. We specially recall that this method is effective for mixtures of different distributions, their identification and expansions, including so-called «heavy-tailed» signals, such as Cauchy distribution. At the end of the paper author’s results are briefly outlined together with some generalizations and applications.

This paper addresses the question of recoverability in the three-dimensional Euclidean space with C 3 -regular surface explicitly specified by the equation z=z ( x, y ) on the entire plane of R 2 on its specified negative Gaussian curvature. The solution to this problem is reduced to the proof of existence and uniqueness of the R 2 of the classical solving differential equations of Monge-Ampere equations of hyperbolic type. Formulated the conditions for the existence of such a decision as a whole.

We present a new approach to the definition of covariant and contravariant symbols in polynomial quantization on para-Hermitian symmetric spaces.

We propose method of studying implicit singular differential equations based on the results of the covering mapping theory. The article consists of three sections. In the first section we give the necessary designations and definitions and formulate the theorem on Lipcshitz perturbations of covering mappings. In the second section we introduce special spaces of measurable functions making it possible to study singular equations by methods of functional analysis and formulate the results about the Nemytskii operator in those spaces. In the last section we provide conditions for the resolubility of the Cauchy problem for implicit singular differential equations.

The article deals with greedy, «semigreedy» Kaczmarz algorithms and an algorithm for the identification of the Neighbor neural network model and examples of their implementation.

We prove the uniqueness of the weak solution of the third initial-boundary value problem for hyperbolic equations with distributed parameters on a limited oriented graph, the boundary conditions which are reduced to a uniform.

We give a solution of the general Euler-Poisson-Darboux equation when the parameter of the Bessel operator acting by time variable is real.