Vol 22, No 3 (2017)
- Year: 2017
- Articles: 16
- URL: https://ogarev-online.ru/2686-9667/issue/view/24810
Articles
ON VOLTERRA OPERATOR INCLUSIONS AND DIFFERENTIAL INCLUSIONS WITH DEVIATING ARGUMENT
Abstract
We obtained conditions for solvability of operator inclusions with abstract Volterra operators and continuous dependence of the solutions on a parameter. These results were implemented to investigation of a Cauchy problem for a functional-differential inclusion with deviating argument.
Russian Universities Reports. Mathematics. 2017;22(3):501-507
501-507
LIPSCHITZ CONTINUITY OF THE MEASURE LAGRANGE MULTIPLIER FROM THE MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS OF EQUALITY AND INEQUALITY TYPE
Abstract
Properties of regular extremals in optimal control problems with equality and inequality state constraints are studied. It is proved that, under the regularity conditions, the strengthened Legendre condition implies Lipschitz continuity of the measure Lagrange multiplier from the maximum principle.
Russian Universities Reports. Mathematics. 2017;22(3):508-516
508-516
APPLICATION OF THE ESTIMATION OF SOLUTIONS OF PERTURBED INCLUSION TO DIFFERENTIAL INCLUSIONS
Abstract
In the article, the statement about the estimation of closeness of solutions for perturbed inclusion to a given continuous function is obtained. The application of this statement to differential inclusions is considered.
Russian Universities Reports. Mathematics. 2017;22(3):517-522
517-522
ABOUT THE SOLVABILITY OF THE CAUCHY PROBLEM FOR NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS
Abstract
The Cauchy problem for a nonlinear functional-differential equation of general type with Volterra mappings is considered. Conditions of existence of a unique global solution and conditions of existence of a unique limitary prolonged solution are derived. The reduction to an operator equation with the Volterra operator in the space of continuous functions is used.
Russian Universities Reports. Mathematics. 2017;22(3):523-532
523-532
ON QUADRATIC MAPPINGS PROPERTIES AND CONDITIONS FOR INVERSE FUNCTIONS EXISTENCE
Abstract
Some properties of quadratic mappings are studied It is proved that if a quadratic mapping have no nontrivial zeroes then it has nontrivial fixed points. Sufficient conditions for inverse function existence are obtained for smooth mappings in the case when the first derivative vanishes.
Russian Universities Reports. Mathematics. 2017;22(3):533-538
533-538
SINGULARITIES OF GEODESIC FLOWS AND LINES IN PSEUDO-FINSLER SPACES. III
Abstract
This is a third paper in the series devoted to singularities of geodesic flows in generalized Finsler (pseudo-Finsler) spaces. In two previous papers, we defined geodesics as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional, and studied generic singularities of so-defined geodesic flows in the case the pseudo-Finsler metric is given by a generic form of degree 3 on a two-dimensional manifold. In the present paper, we consider an important non-generic case: singularities of geodesic flows on two-dimensional surfaces embedded into the Berwald-Moor space of arbitrary dimension.
Russian Universities Reports. Mathematics. 2017;22(3):539-551
539-551
552-557
PARAMETRIC IDENTIFICATION OF NEIGHBORHOOD SYSTEMS NEAR NOMINAL MODES
Abstract
The paper discusses the problem of parametric identification of a structurally identified static polynomial system near the nominal mode in the case when only allowable limits are specified for states, controls and coefficients of the model.
Russian Universities Reports. Mathematics. 2017;22(3):558-564
558-564
ON CONVERGENCE IN THE SPACE OF CLOSED SUBSETS OF A METRIC SPACE
Abstract
We consider the space closX of closed subsets of unbounded (not necessarily separable) metric space X, ϱ X endowed with the metric ρ X cl introduced in [ Zhukovskiy E.S., Panasenko E.A. // Fixed Point Theory and Applications. 2013:10]. It is shown that if any closed ball in the space X, ϱ X is totaly bounded, then convergence in the space clos X , ρ X cl of a sequence F i i=1 ∞ to F is equivalent to convergence in the sense of Wijsman, that is to convergence for each x∈X of the distances ϱ X x, F i to ϱ X x, F .
Russian Universities Reports. Mathematics. 2017;22(3):565-570
565-570
ABOUT IMPLICIT DIFFERENTIAL INEQUALITIES WITH DEVIATING ARGUMENT
Abstract
Assertion about existence and evaluation of solutions to equations Yx, x =y , where the mapping Y acting in partially ordered spaces is covering by the first argument and antitone by the second argument is derived. This result is used for the proof of the Chaplygin’s type theorem on differential inequality with deviating argument.
Russian Universities Reports. Mathematics. 2017;22(3):571-578
571-578
CONTINUOUS DEPENDENCE ON PARAMETERS OF SOLUTIONS TO BOUNDARY-VALUE PROBLEMS FOR A SYSTEM OF IMPLICIT DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT
Abstract
Conditions are offered that ensure a continuous dependence on the parameters solutions of the boundary value problem for a system of implicit differential equations with a deviating argument. The method used in this paper is based on the results on vector-covering mappings obtained by E.S. Zhukovsky.
Russian Universities Reports. Mathematics. 2017;22(3):579-584
579-584
BOUNDARY VALUE PROBLEMS FOR FUNCTIONAL-DIFFERENTIAL INCLUSIONS WITH THE MULTIVALUED IMPULSES
Abstract
The boundary value problems for a functional-differential inclusion generated by a multivalued map not necessarily convex-valued with respect to switching in the space of summable functions and with multi-valued impulses are considered. Concept of a generalized solution of such a problem is introduced. Existence conditions for a generalized solution of the boundary value problem are found. The effective estimates of generalized solutions are derived.
Russian Universities Reports. Mathematics. 2017;22(3):585-590
585-590
591-595
NEIGHBORHOOD MODELING OF WASTEWATER TREATMENT PROCESSES
Abstract
The article presents the definition of industrial and domestic sewage, their principal and staff are listed. The main task of the wastewater treatment facilities are described, the sewage treatment plant, its components are given. The purpose of the writing of this work lies in the prediction of the composition of mixed waste water, which is coming from households and industrial enterprises in a centralized system of water removal, after cleaning on the basis of dynamic linear and quadratic neighborhood models. The work is relevant because before draining waste waters into the pond, you must ensure that the information contained in their composition of impurities and contaminants do not exceed acceptable norms. In the article is presented the wastewater treatment process in the form neighborhood dynamic model, consisting of five nodes. The dynamic linear and quadratic neighborhood models are reviewed. The equations of recalculation of conditions and outputs for the intermediate and output nodes neighborhood models are given. The identification of dynamic linear and quadratic neighborhood models of wastewater treatment are performed, calculated average absolute errors for identification. The comparison of the results of dynamic linear and quadratic neighborhood models and the conclusion are produced.
Russian Universities Reports. Mathematics. 2017;22(3):596-604
596-604
PARAMETRIC IDENTIFICATION OF THE NEIGHBORHOOD MODEL OF AIR EXCHANGE PROCESS IN THE INDUSTRIAL PREMISE
Abstract
A system of automatic climate control was considered in the industrial premise: rotary kiln remote plant control room. To control the air conditioning system, a mathematical model of the microclimate with the use of neighborhood systems was constructed, which makes it possible to achieve resource saving and to ensure microclimate parameters corresponding to the norms.
Russian Universities Reports. Mathematics. 2017;22(3):605-610
605-610
611-614