Том 65, № 1 (2019): Contemporary Problems in Mathematics and Physics
- Жылы: 2019
- Мақалалар: 12
- URL: https://journals.rcsi.science/2413-3639/issue/view/23547
- DOI: https://doi.org/10.22363/2413-3639-2019-65-1
Бүкіл шығарылым
New Results
1-10
On Formulation of Modified Problems for the Euler-Darboux Equation with Parameters Equalto 1/2 in Absolute Value
Аннотация
We consider the Euler-Darboux equation with parameters equal to 1/2 in absolute value. Since the Cauchy problem in the classical formulation in ill-posed for such values of parameters, we proposeformulations and solutions of modified Cauchy-type problems with the following values of parameters: a)α = β = 1 , b) α = - 1 , β = - 1 , c) α = β = - 1 . In the case а), the modified Cauchy problem is solved2 2 2 2by the Riemann method. We use the obtained result to formulate the analog of the problem Δ1 in the first quadrant with shifted boundary-value conditions on axes and nonstandard conjunction conditions on thesingularity line of the coefficients of the equation y = x. The first condition is gluing normal derivatives of the solution and the second one contains limiting values of combination of the solution and its normal derivatives. The problem is reduced to a uniquely solvable system of integral equations.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):11-20
11-20
Covariant Functors and Shapes in the Category of Compacts
Аннотация
In this paper, we consider covariant functors F : Comp → Comp acting in category of shape-preserving compact sets [2], infinite compact sets, and shape equivalence [9]. Also we study action of compact functors and shape properties of the compact space X consisting of connected components ОX of the compact X as well as shape identity ShX = ShY of infinite compacts X and Y for the space P (X) of probability measures and its subspaces.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):21-32
21-32
Application of A-analytic Functions to the Investigation of the Cauchy Problem for a Stationary Poroelasticity System
Аннотация
In a reversible hydrodynamic approximation, a closed system of second-order dynamic equations with respect to the displacement vector of an elastic porous body and pore pressure has been obtained. The Cauchy problem for the obtained system of poroelasticity equations in the stationary case is considered. The Carleman formula for the Cauchy problem under consideration has been constructed.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):33-43
33-43
A Fuzzy MLP Approach for Identification of Nonlinear Systems
Аннотация
In case of decision making problems, identification of non-linear systems is an important issue. Identification of non-linear systems using a multilayer perceptron (MLP) trained with back propagation becomes much complex with an increase in number of input data, number of layers, number of nodes, and number of iterations in computation. In this paper, an attempt has been made to use fuzzy MLP and its learning algorithm for identification of non-linear system. The fuzzy MLP and its training algorithm which allows to accelerate a process of training, which exceeds in comparing with classical MLP is proposed. Results show a sharp reduction in search for optimal parameters of a neuro fuzzy model as compared to the classical MLP. A training performance comparison has been carried out between MLP and the proposed fuzzy-MLP model. The time and space complexities of the algorithms have been analyzed. It is observed, that number of epochs has sharply reduced and performance increased compared with classical MLP.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):44-53
44-53
Geometry of Orbits of Vector Fields and Singular Foliations
Аннотация
The subject of this paper is the geometry of orbits of a family of smooth vector fields defined on a smooth manifold and singular foliations generated by the orbits. As is well known, the geometry of orbits of vector fields is one of the main subjects of investigation in geometry and control theory. Here we propose some author’s results on this problem. Throughout this paper, the smoothness means C∞-smoothness.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):54-71
54-71
Reductional Method in Perturbation Theory of Generalized Spectral E. Schmidt Problem
Аннотация
In this a paper perturbations of multiple eigenvalues of E. Schmidt spectral problems is considered. At the usage of the reductional method suggested in the articles [10, 11] the investigation of the multiple E. Schmidt perturbation eigenvalues is reduced to the investigation of perturbation of simple ones. At the end, as application of the obtained results the problem about the boundary perturbation for the system of two Sturm-Liouville problems with E. Schmidt spectral parameter is considered.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):72-82
72-82
Continuation of Analytic and Pluriharmonic Functions in the Given Direction by the ChirkaMethod: a Survey
Аннотация
In this paper, we provide a survey of results on analytic and plurisubharmonic continuations of functions that have this set of singularities along a fixed direction. We show the advantages of using the pluripotential theory and the Jacobi-Hartogs series for description of the singular set of such functions.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):83-94
83-94
Carleman’s Formula for Solutions of the Generalized Cauchy-Riemann System in Multidimensional Spatial Domain
Аннотация
In this paper, we consider the restoration problem for solutions of the generalized Cauchy- Riemann system in a multidimensional spatial domain using their values on a piece of the boundary of the domain, i. e., the Cauchy problem. We construct an approximate solution of this problem based on the Carleman matrix method.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):95-108
95-108
109-123
ε-Positional Strategies in the Theory of Differential Pursuit Games and the Invariance of a Constant Multivalued Mapping in the Heat Conductivity Problem
Аннотация
In this paper, we consider two problems. In the first problem, we prove that if the assumption from the paper [1] and one additional condition on the parameters of the game hold, then the pursuit can be finished in any neighborhood of the terminal set. To complete the game, an ε-positional pursuit strategy is constructed.In the second problem, we study the invariance of a given multivalued mapping with respect to the system with distributed parameters. The system is described by the heat conductivity equation containing additive control terms on the right-hand side.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):124-136
124-136
The Cyclical Compactness in Banach C∞(Q)-Modules
Аннотация
In this paper, we study the class of laterally complete commutative unital regular algebras A over arbitrary fields. We introduce a notion of passport Γ(X) for a faithful regular laterally complete A- modules X, which consist of uniquely defined partition of unity in the Boolean algebra of all idempotents in A and of the set of pairwise different cardinal numbers. We prove that A-modules X and Y are isomorphic if and only if Γ(X)= Γ(Y ). Further we study Banach A-modules in the case A = C∞(Q) or A = C∞(Q)+ i · C∞(Q). We establish the equivalence of all norms in a finite-dimensional (respectively, σ-finite-dimensional) A-module and prove an A-version of Riesz Theorem, which gives the criterion of a finite-dimensionality (respectively, σ-finite-dimensionality) of a Banach A-module.
Sovremennaâ matematika. Fundamentalʹnye napravleniâ. 2019;65(1):137-155
137-155