Vol 22, No 6 (2017)
- Year: 2017
- Articles: 20
- URL: https://ogarev-online.ru/2686-9667/issue/view/24812
Articles
1218-1228
ON POSITIVITY OF THE GREEN FUNCTION FOR POISSON PROBLEM FOR A LINEAR FUNCTIONAL DIFFERENTIAL EQUATION
Abstract
For the Poisson problem -∆u+p x u- Ωu s r x, ds=ρf, u | Γ( Ω )=0 equivalence of positivity of the Green function and other classical properties is showed. Here Ω is an open set in R n , and Γ( Ω ) is the boundary of the Ω . For almost all x∈ Ω , r(x, ∙) is a measure satisfying certain symmetry condition. In particular this equation involves integral differential equation and the equation -∆u+p x u(x)- i=1 m p i x u h i x =ρf, where h i : Ω→Ω is a measurable mapping.
Russian Universities Reports. Mathematics. 2017;22(6):1229-1234
1229-1234
BEREZIN QUANTIZATION AS A PARTOF THE REPRESENTATION THEORY
Abstract
We present an approach to polynomial quantization (a variant of quantization in the spirit of Berezin) on para-Hermitian symmetric spaces using the notion of an "overgroup". This approach gives covariant and contravariant symbols and the Berezin transform in a highly natural and transparent way.
Russian Universities Reports. Mathematics. 2017;22(6):1235-1246
1235-1246
ABOUT EXISTENCE AND ESTIMATION OF SOLUTION TO ONE INTEGRAL INCLUSION
Abstract
An inclusion with multi-valued mapping acting in spaces with vector-valued metrics is under discussion. It is shown that, if a multi-valued mapping F can be written as F(x)= Y(x, x), where the mapping Y is closed and metrically regular with some operator coefficient K with respect to one argument, Lipschitz with operator coefficient Q with respect to the other argument, and the spectral radius of the operator KQ is less than one, then the inclusion F(x) ∋ y is solvable. The estimations of the vector-valued distance from a solution x of the inclusion to a given element x 0 are derived. In the second part of the paper, these results are used to investigate an integral inclusion of the implicit type with respect to the unknown integrable function.
Russian Universities Reports. Mathematics. 2017;22(6):1247-1254
1247-1254
ONE ESTIMATE OF FIXED POINTS AND COINCIDENCE POINTS OF MAPPINGS OF METRIC SPACES
Abstract
For single-valued and multi-valued mappings acting in a metric space X and satisfying the Lipschitz condition, we propose a lower estimate of the distance from a given element x 0 ∈ X to a fixed point. Thus, we find r >0 such that there are no fixed points in the ball with center at x 0 of radius r . The proof follows directly from the triangle inequality. The result is extended to (q 1 , q 2 ) - metric spaces. An analogous estimate is obtained for coincidence points of covering and Lipschitz mappings of metric spaces.
Russian Universities Reports. Mathematics. 2017;22(6):1255-1260
1255-1260
ON ONE INVERSE PROBLEM OF SOURCES DENSITY DISTRIBUTION RECONSTRUCTION IN A MIXED BOUNDARY VALUE PROBLEM FOR THE POISSON EQUATION
Abstract
An inverse problem with mixed boundary value conditions for the Poisson equation for bodies of constant thickness is considered, aiming to reconstruct the sources density distribution. A stable solution of the problem is obtained.
Russian Universities Reports. Mathematics. 2017;22(6):1261-1267
1261-1267
THE SYMBOLIC SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS IN THE COMPUTER ALGEBRA SYSTEM MATH PARTNER
Abstract
The article deals with algorithms of symbolic solution of ordinary differential equations, their software implementation in the computer algebra system Math Partner. Classes are described for solving differential equations with separable variables, homogeneous differential equations, and equations in complete differentials.
Russian Universities Reports. Mathematics. 2017;22(6):1268-1276
1268-1276
APPLICATION OF THE EXISTENCE THEOREM AND ESTIMATE OF SOLUTIONS OF THE PERTURBED INCLUSION TO THE STUDY OF THE PERTURBED LINEAR PROBLEM
Abstract
In the article, a statement about estimation of the closeness of solutions of the perturbed inclusion to a given continuous function is formulated. An application of this statement to the study of perturbation of a linear boundary value problem for functional-differential equations is considered.
Russian Universities Reports. Mathematics. 2017;22(6):1277-1284
1277-1284
ABOUT ONE QUASI-METRIC SPACE
Abstract
The M -space (X, ρ) is defined as a non-empty set X with distance ρ :X 2 →R+ satisfying the axiom of identity and the weakened triangle inequality. The M -space (X, ρ) belongs to the class of f -quasi-metric spaces, and the map ρ may not be ( c1 , c2 ) -quasi-metric for any values of c 1 , c 2 ; and ( c1 , c2 ) -quasi-metric space may not be an M -space. The properties of the M -space are investigated. An extension of the Krasnosel’skii theorem about a fixed point of a generally contracting map to the M -space is obtained.
Russian Universities Reports. Mathematics. 2017;22(6):1285-1292
1285-1292
1293-1297
ON MINIMA OF FUNCTIONALS AND IMPLICIT DIFFERENTIAL EQUATIONS
Abstract
The stability of Caristi-like conditions under small Lipschitz perturbations is proved for functionals on metric spaces. The result obtained is used for the investigation of implicit differential equation. Sufficient conditions for solvability of Cauchy problem for implicit ordinary differential equations are obtained.
Russian Universities Reports. Mathematics. 2017;22(6):1298-1303
1298-1303
ON THE APPLICATION OF THE RESULTS OF COVERING MAPPINGS THEORY FOR THE STUDY OF DYNAMICAL MODELS OF ECONOMIC PROCESSES
Abstract
The paper is a study of the existence of equilibruim points in the dynamic Walrasian-Evans-Samuelson model. Sufficient conditions for the existence of the vector-function of equilibruim prices are derived from the existence theorems for coincidence points of Lipschitz continuous and covering mappings.
Russian Universities Reports. Mathematics. 2017;22(6):1304-1308
1304-1308
ON COINCIDENCE POINTS OF TWO MULTI-VALUED MAPPINGS IN SPACES WITH VECTOR-VALUED METRICS
Abstract
Spaces with vector-valued metrics are considered. The values of a vector-valued metric are elements of a cone in some linear normed space. The concept of covering (metric regularity) for multi-valued mappings in spaces with vector-valued metrics is formulated. A statement about coincidence points of a metrically regular and a Lipschitz multi-valued mappings in spaces with vector-valued metrics is obtained.
Russian Universities Reports. Mathematics. 2017;22(6):1309-1313
1309-1313
ON ONE METHOD OF STUDYING IMPLICIT SINGULAR DIFFERENTIAL INCLUSIONS
Abstract
We propose a method of studying singular differential inclusions based on the representation of such an inclusion in the form of an operator inclusion in some space of measurable functions depending on the type of a given singularity. To the operator inclusion we apply the results on Lipschitz perturbations of multi-valued covering mappings. The article consists of three sections. In the first one we give the necessary definitions and formulate the theorem [A. Arutyunov, V.A. de Oliveira, F.L. Pereira, E. Zhukovskiy, S. Zhukovskiy // Applicable Analysis, 2015, 94, № 1] on the Lipschitz perturbations of multi-valued covering mappings. In the second section we introduce special metric spaces of integrable functions and obtain sufficient conditions of covering for the multi-valued Nemytskii operator in such spaces. Finally, using the mentioned results, we derive the existence conditions for the Cauchy problem for an implicit singular differential inclusion.
Russian Universities Reports. Mathematics. 2017;22(6):1314-1320
1314-1320
1321-1324
1325-1328
1329-1334
METHOD OF ANALYSIS OF HIERARCHIES AND CONSTRUCTION INTEGRATED PARAMETERS FOR MULTIPLE SYSTEMS
Abstract
In article the method of construction of integrated parameters for the systems having hierarchical structure is offered. Feature of researched systems will be their multidimensionality and heterogeneity of characteristics making them. The problem of construction of a complex estimation of a condition of such objects or processes is actual for various branches of knowledge (economy, ecology, medicine). From the mathematical point of view construction of integrated parameters concerns to problems multicriteria the analysis of hierarchies, therefore a first step at construction of an integrated parameter is decomposition of object on parts making it. Such decomposition is convenient for representing as the graph. We use a linear function - the enclosed linear convolution with weight factors of the importance of each criterion to make a scalar function from vector criterion. Weight factors are in turn determined by method of hierarchy’s analysis, allowing to translate qualitative gradation of a condition of system in quantitative. Further the integrated parameter is considered as the criterion function subject to improvement in some optimum image.
Russian Universities Reports. Mathematics. 2017;22(6):1335-1340
1335-1340
1341-1345
AGGREGATION OF NEIGHBORHOOD SYSTEMS IN THE MODEL OF VENTILATION OF CEMENT PRODUCTION WORKSHOP
Abstract
The article considers an example of aggregation (merging) of neighborhood systems in the problem of mathematical modeling of the ventilation system of the cement production workshop. The aim of simulation is to optimize the operation of the ventilation system according to the criteria of energy consumption and environmental friendliness.
Russian Universities Reports. Mathematics. 2017;22(6):1346-1354
1346-1354