Vol 21, No 1 (2016)
- Year: 2016
- Articles: 17
- URL: https://journals.rcsi.science/2686-9667/issue/view/24815
Articles
EQUILIBRIUM PRICES IN ECONOMIC EQUILIBRIUM MODELS WITH TRANSACTION COSTS
Abstract
In this paper, we generalize the results obtained in [1] for the case of different shares of transaction costs. As a corollary of the theory of metric regular maps (theorems about the existence of coincidence points), we obtain sufficient conditions of the existence of equilibrium price vector in the considered models.
Russian Universities Reports. Mathematics. 2016;21(1):9-16
9-16
ON WELL-POSEDNESS OF GENERALIZED NEURAL FIELD EQUATIONS WITH IMPULSIVE CONTROL
Abstract
We formulate and prove the theorem on well-posedness of abstract Volterra equations in metric spaces. We consider nonlinear nonlocal integral Volterra equation involving generalizing equations typically used in mathematical neuroscience. We investigate solutions that tend to zero at any moment with unbounded growth of the spatial variable. In the literature such solutions are called «spatially localized solutions» or «bumps». They correspond to normal brain functioning. For the main equation, we consider an impulsive control problem, where the control parameters are moments, when the solution discontinue, and corresponding jumps’ values. Such control systems model electrical stimulation used in the presence of various diseases of central nervous system. We define suitable complete metric (not linear) space. Using the aforementioned theorem, we obtain conditions for existence and uniqueness of solution to this equation and continuous dependence of this solution on the control.
Russian Universities Reports. Mathematics. 2016;21(1):16-27
16-27
THE CONTINUITY OF THE MEASURE LAGRANGE-MULTIPLIER FROM THE MAXIMUM PRINCIPLE FOR AN OPTIMAL CONTROL PROBLEM WITH EQUALITY AND INEQUALITY STATE CONSTRAINTS UNDER WEAK REGULARITY CONDITIONS OF THE EXTREMAL PROCESS
Abstract
Under weak regularity assumptions, the continuity of the measure Lagrange multiplier from the maximum principle for control problems with state constraints of equality and inequality types is investigated. Appropriate assertions are proved.
Russian Universities Reports. Mathematics. 2016;21(1):28-39
28-39
CLARIFICATION OF THE OPTIMALITY CONDITIONS IN CONTROL PROBLEMS WITH STATE CONSTRAINTS OF EQUALITY AND INEQUALITY TYPES
Abstract
The continuity of the measure Lagrange multiplier from the maximum principle for control problems with state constraints is investigated. It is proved, under certain regularity assumptions, that the distribution function of the measure is H¨older continuous with exponent 1/2.
Russian Universities Reports. Mathematics. 2016;21(1):40-55
40-55
INTEGRAL GUIDING FUNCTIONS AND PERIODIC SOLUTIONSFOR INCLUSIONS WITH CAUSAL MULTIOPERATORS
Abstract
In the present paper the method of guiding functions is applied to study the periodic problem for a differential inclusion with a causal multioperator. At first we consider the case when the multioperator is closed and convex-valued. Then the case of a non-convex-valued and lower semicontinuous right-hand part is considered.
Russian Universities Reports. Mathematics. 2016;21(1):55-65
55-65
SINGULARITIES OF GEODESIC FLOWS AND GEODESIC LINES IN PSEUDO-FINSLER SPACES. I
Abstract
This is a first paper in the series devoted to singularities of geodesic flows in generalized Finsler (pseudo-Finsler) spaces. Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional. This allows to consider isotropic lines as (unparametrized) geodesics, similarly to pseudo-Riemannian metrics. In the next forthcoming paper we study generic singularities of sodefined geodesic flows in the case when the pseudo-Finsler metric is given by a generic 3-form on a two-dimensional manifold.
Russian Universities Reports. Mathematics. 2016;21(1):66-75
66-75
POISSON PROBLEM FOR A LINEAR FUNCTIONAL DIFFERENTIAL EQUATION
Abstract
The solvability, existence and positiveness of the Green function of the Poisson problem -∆u- Ωu y -u x r x,dy =ρf, u | Γ( Ω) =0 are showed. The spectral properties of corresponding eigenvalue problem are considered. Here Ω is an open set in R N and ΓΩ is the boundary of the Ω . For almost all x ϵ Ω, r x,∙ is a measure satisfying certain symmetry condition. The function ρ is a positive weight. This problem has a clear mechanical interpretation.
Russian Universities Reports. Mathematics. 2016;21(1):76-81
76-81
82-88
COVERING MAPPINGS IN THE SPACES WITH VECTOR-VALUED METRICS
Abstract
The concepts of covering mapping and of metric regularity are extended to mappings in the spaces with vector-valued metrics (such a «metric» is understood as a function with the standard metric’s properties which values are elements of a cone in a linear normed space). The theorem on points of coincidence of a covering and a Lipschitz continuous (with respect to a vector-valued metric) mappings is formulated and proved. This statement is an analog of the theorem about coincidence points due to A.V. Arutyunov. Some applications of the obtained results are illustrated on the example of studying one class of difference equations in the space of measurable essentially bounded functions.
Russian Universities Reports. Mathematics. 2016;21(1):88-95
88-95
А COMPOSITION METHOD FOR CONSTRUCTING TRANSMUTATIONS FOR DIFFERENTIAL EQUATIONS
Abstract
The paper is devoted to transmutation theory for ordinary and partial differential operators. It has many applications to inverse problems, spectral theory, nonlinear and soliton problems, singular equations, generalized analytic functions, singular boundary-value problems, fractional integrals and function spaces embedding. In this survey paper the most important classes of transmutations in modern theory is introduced and the new method is proposed to find transmutations via integral transform compositions.
Russian Universities Reports. Mathematics. 2016;21(1):95-108
95-108
THE REMOVABLE SINGULARITY THEOREM FOR HARMONIC FUNCTION ON A TWO-DIMENSIONAL STRATIFIED SET
Abstract
We prove the removable singularity theorem for harmonic function on a two-dimensional stratified set. It is shown that harmonic and bounded function defined on the twodimensional stratified set, except the zero-dimensional strata, is harmonic extendable over all stratified set. This theorem plays an important role in the proof of the solvability of the Dirichlet problem for the Laplace equation on stratified set and in the implement of Poincar-Perron method on a stratified set. In proof we use analogues of divergence theorem and Harnack’s inequality on a stratified set. We provide basic information from the theory of differential equations on the stratified sets, which are necessary for the formulation and proof of main result.
Russian Universities Reports. Mathematics. 2016;21(1):108-116
108-116
116-121
THE METHODOLOGY OF ASSESSMENT OF HEALTH-RELATED QUALITY OF LIFE
Abstract
The article is dedicated to using the methods of cognitive analysis and analysis of hierarchy for study such complex object, as with health-related quality of life of the population. Interconnected concepts of cognitive map are used for building of the hierarchical model of quality of life and shaping the matrixes of the fresh comparisons - a bases of all computing procedures of the method of the analysis hierarchy for transformation of qualitative information on under investigation object in quantitative - an weight factors for all its descriptions. The analysis hierarchy method and cognitive analysis have independent importance, but, as it is shown, in combination, they will complement each other and become the new instrument of the study complex and bad formalized object with a set interacting heterogeneous subjective and objective factor. The Main result of our research is the description of methods for studying health-related quality of life with the combined use of cognitive maps and the basic procedures of hierarchy’s analysis method.
Russian Universities Reports. Mathematics. 2016;21(1):121-130
121-130
Derivatives of interval elementary functions
Abstract
The problems related to calculation of derivatives of interval-specified functions are considered. These problems are relevant in study of systems with any level of uncertainty (nondeterministic systems). Specifically we speak about simple systems described by elementary interval-specific functions. Accordingly we solved problem of calculating derivatives of elementary interval-specified functions. Previously obtained formulas and methods of finding derivatives of any intervally defined functions are used. Basic definitions related to derivatives of the interval-specified functions are given and formulas of two types that allow you to calculate interval derivatives are presented. The first type formulae express derivatives in the closed interval form, which requires to compute using the apparatus of interval mathematics. But formulae of the second type can express derivatives in the open interval form, i. e. in form of two formulas. Formulas above expresses the lower and the upper limits of the interval representing the derivative. Here finding the derivative of interval-defined function is reduced to computation of two ordinary certain functions. Using above mathematical apparatus we find the derivatives of all elementary interval functions: interval constant, interval power function, interval exponential function, interval logarithmic function, interval natural-logarithmic function, interval trigonometric functions (sine, cosine, tangent, cotangent), interval inverse trigonometric functions (arcsine, arccosine, arctangent and arccotangent). Formulae of all the derivatives are shown in form of an open interval. The difference between derivatives of interval elementary functions and the derivatives of normal (i.e. non-interval) elementary functions is discussed.
Russian Universities Reports. Mathematics. 2016;21(1):131-141
131-141
142-145
146-149
150-153