Vol 21, No 2 (2016)
Articles
363-370
ABOUT ANTITONE PERTURBATIONS OF COVERING MAPPINGS OF ORDERED SPACES
Abstract
We consider the problem of existence of a solution x to the equation ψx, x = y , where y is given, the mapping ψ(∙, ∙) acts in ordered spaces, is order-covering with respect to the first argument, and antitone with respect to the second one. The concept of order-covering used in the article was proposed in the joint works of A.V. Arutyunov, E.S. Zhukovskiy, S.E. Zhukovskiy regarding the studies of the mappings’ coincidence points.
Russian Universities Reports. Mathematics. 2016;21(2):371-374
371-374
ON PERTURBATIONS OF COVERING MAPPINGS IN SPACES WITH VECTOR-VALUED METRICS
Abstract
For mappings acting in spaces with vector-valued metrics, the analogues of covering and metric regularity are defined. A theorem on stability of covering property under Lipschitz perturbations is proved. The application of the results obtained to investigation of functional equations is discussed.
Russian Universities Reports. Mathematics. 2016;21(2):375-379
375-379
ONE EXAMPLE OF A VECTOR-VALUED METRIC IN THE SPACE OF NONEMPTY CLOSED SUBSETS OF A METRIC SPACE
Abstract
In the space of nonempty closed subsets of a given metric space, we define a vector-valued metric which differs from the known vector generalizations of the Hausdorff metric. The metric proposed appears in the analysis of multi-valued maps with possibly unbounded images. It allows to get more information about distances between elements of the corresponding sets and turns out to be convenient in fixed point theorems for multi-valued maps.
Russian Universities Reports. Mathematics. 2016;21(2):380-385
380-385
386-391
392-403
DEVELOPMENT OF THE CRITERIA-BASED ASSESSMENT SYSTEM OF THE STUDENTS EDUCATIONAL ACHIEVEMENTS
Abstract
Article is devoted to a problem of estimation of results of the educational activity of school students. The author considers the developed system of the assessment of knowledge, abilities, skills, need of reduction of system in compliance with education goals, suggests to recognize the need to estimate the substantial movement of a student toward the purpose.
Russian Universities Reports. Mathematics. 2016;21(2):404-407
404-407
THE MODIFIED DISCREET FOURIER TRANSFORM BASED ON THE GROUP OF ROOTS OF UNITY
Abstract
In the paper we consider a set of transformations which generalize a standard discreet Fourier transform (DFT). These generalizations are based on permutations for the group of roots of unity. Different permutations define different new DFT’s. On this way we construct transformations with more natural spectral properties. For example in dimension four the standard DFT has incomplete multiple spectrum but almost all newly defined transforms a simple one. We give some numerical computer results and spectral hypotheses. Applications to cryptography is briefly outlined.
Russian Universities Reports. Mathematics. 2016;21(2):408-416
408-416
ON SOLVING LINEAR FUNCTIONAL-DIFFERENTIAL EQUATIONS
Abstract
We consider some linear functional-differential equations the solutions of which can be written analytically. For these equations we derive the Cauchy function, the Green function for a two-point (in particular, for periodic and aperiodic) boundary value problem.
Russian Universities Reports. Mathematics. 2016;21(2):417-431
417-431
432-436
437-440
A BOUNDARY VALUE PROBLEM FOR ONE TYPE IMPULSE FUNCTIONAL-DIFFERENTIAL INCLUSIONS
Abstract
A boundary value problem for one type impulse functional-differential inclusions with a multi-valued map not necessarily convex-valued with respect to switching in the space of summable functions is considered. Concept of a generalized solution is represented. Existence conditions for generalized solutions are obtained and their estimates are found.
Russian Universities Reports. Mathematics. 2016;21(2):441-449
441-449
INTEGRAL REPRESENTATION OF APPROXIMATING INVERSE OPERATORS FOR HYPERBOLIC RIESZ B-POTENTIAL KERNEL
Abstract
The article deals with the special kernel. The limit of the generalized convolution with this kernel is the inverse operator for hyperbolic Riesz potential generated by multidimensional generalized translation. The integral representation containing Appel F4 function was obtained for this kernel.
Russian Universities Reports. Mathematics. 2016;21(2):450-458
450-458
CLUSTERING OF NEIGHBORHOOD STRUCTURE
Abstract
We define a metric on the set of nodes of neighborhood structure and consider the clustering problem for the structure with respect to the metric, or, what is the same, the problem of constructing the factor-structure. Determined metric takes into account both the connections between the nodes of the structure and the experimental data at the nodes.
Russian Universities Reports. Mathematics. 2016;21(2):459-464
459-464
TRILINEAR NEIGHBORHOOD MODEL OF THE PROCESS OF FORMING THE TEMPERATURE OF HOT-ROLLED STRIP COILING
Abstract
The trilinear neighborhood model of the process of forming the temperature of hot-rolled strip coiling where the parameters are a state, control and information is considered. The purpose of the work is to find the values of the components of the model ensuring steady functioning of the system. The technique of defining the structure of the extrema is presented. The existence condition for extrema is received and checked on a concrete example. The suggestion about the area in which it is impossible to speak with definiteness about stability of the system is made. The hypothesis about a condition of the stable balance loss and of the transition of system to a new state is proposed.
Russian Universities Reports. Mathematics. 2016;21(2):465-472
465-472