Vol 23, No 121 (2018)
- Year: 2018
- Articles: 8
- URL: https://journal-vniispk.ru/2686-9667/issue/view/19683
Articles
ON DISCRETENESS OF SPECTRUM OF A SECOND ORDER FUNCTIONAL DIFFERENTIAL OPERATOR
5-9
ON THE CONDITIONS OF EXISTENCE COINCIDENCE POINTS FOR MAPPING IN PARTIALLY ORDERED SPACES
Abstract
A.V. Arutyunov, E.S. Zhukovskiy, S.E. Zhukovskiy studied the coincidence points for mappings of partially ordered spaces in particular, it was proved that an covering and monotone mapping, acting from a partially ordered space X , ≽ X to a partially ordered space Y , ≽ Y , have a coincidence point. It is shown that the conditions of this assertion can be weakened: the binary relation ≽ Y should not be in order. We give an appropriate result and demonstrate an example of mappings satisfying its conditions, but to which the results of the cited work are not applicable.
Russian Universities Reports. Mathematics. 2018;23(121):10-16
10-16
ON CONNECTION BETWEEN CONTINUOUS AND DISCONTINUOUS NEURAL FIELD MODELS WITH MICROSTRUCTURE I. GENERAL THEORY
Abstract
We suggest a method allowing to investigate existence and the measure of proximity between the stationary solutions to continuous and discontinuous neural fields with microstructure. The present part involves a theorem on solvability of such equations based on topological degree theory, and a theorem on continuous dependence of the solutions under the transition from continuous to discontinuous activation function using compactness in a special topology.
Russian Universities Reports. Mathematics. 2018;23(121):17-30
17-30
INTEGRAL GUIDING POTENTIALS IN THE PROBLEM OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS
Abstract
The new method to solving the problem of the asymptotic behavior of trajectories for control systems governed by functional differential inclusions with convexvalued and nonconvex-valued right-hand sides is introduced. As the main tool of solving the problem the method of integral guiding potentials is applied. The application of this method makes it possible to establish estimates for the norms of trajectories for above systems.
Russian Universities Reports. Mathematics. 2018;23(121):31-43
31-43
A GENERALIZED BOUNDARY VALUE PROBLEM FOR A FEEDBACK CONTROL SYSTEM WITH INFINITE DELAY
Abstract
We consider a non-local boundary value problem for a feedback control system governed by a semilinear functional differential inclusion with infinite delay in a separable Banach space. As the example we present a generalized Cauchy problem and periodic problem.
Russian Universities Reports. Mathematics. 2018;23(121):44-64
44-64
ON ARUTYUNOV THEOREM OF COINCIDENCE POINT FOR TWO MAPPING IN METRIC SPACES
Abstract
In the famous theorem of Arutyunov, it is asserted that the mappings ψ, φ, acting from the complete metric space X , ρ X to the metric space Y , ρ Y , one of which is α -covering and the second is β -Lipschitz, α> β, have the coincidence point is the solution of the equation ψx =φx . We show that this assertion remains valid also in the case when the space Y is not metric it is sufficient that the function ρ Y :Y 2 →R + satisfies only the axiom of identity. The function ρ Y may not be symmetric and does not correspond to the triangle inequality; moreover, it does not have to satisfy the f -triangle inequality (that is, it is possible that the space Y is not even f -quasimetric).
Russian Universities Reports. Mathematics. 2018;23(121):65-73
65-73
ON THE STUDY OF SPECTRAL PROPERTIES OF DIFFERENTIAL OPERATORS OF EVEN ORDER WITH DISCONTINUOUS WEIGHT FUNCTION
Abstract
The boundary value problem for a differential operator of high even order, whose coefficients are discontinuous functions at some interior point of the segment on which the operator is considered, is studied. At the point of discontinuity of the coefficients, certain conditions of «conjugation» that follow from the physical conditions are required. The boundary conditions of the considered boundary value problem are separated and depend on several parameters. Thus simultaneously the spectral properties of a family of differential operators are studied. The weight function of the operator is piecewise constant on the interval of the definition of the differential operator. For large values of the spectral parameter, the asymptotics of the solutions of the differential equations determining the operator under investigation is derived. Using this asymptotics, the conditions of “conjugation” are studied. The obtained formulas allow to investigate the boundary conditions of the considered boundary value problem. As a result, we have derived an equation for the eigenvalues of the studied operator. It is proved that the eigenvalues of the operator are the roots of some entire function. The indicator diagram of the equation for the eigenvalues of the operator is studied. It is proved that the spectrum of the operator is discrete. In different sectors of the indicator diagram, the asymptotics of the eigenvalues of the studied operator is found, depending on the parameters of the boundary conditions. The found formulas allow us to find the asymptotics of the eigenfunctions of the operator and to calculate the regularized traces of this operator.
Russian Universities Reports. Mathematics. 2018;23(121):74-99
74-99
PARALLEL INVERSION OF INTEGER MATRIX: THE RESULTS OF THE EXPERIMENTS
Abstract
We focuses on results of experiments of the parallel algorithm for finding the inverse matrix through the adjoint matrix and determinant. A parallel algorithm based on the use of the Chinese remainder theorem and sequential algorithms implemented in the computer algebra system MathPartner. Graph of algorithm has a two-tier structure, achieved a uniform distribution between processors.
Russian Universities Reports. Mathematics. 2018;23(121):100-108
100-108