http://dspace.nbuv.gov.ua:80/handle/123456789/140537 2026-04-18T23:17:09Z 2026-04-18T23:17:09Z Tieplova, D. http://dspace.nbuv.gov.ua:80/handle/123456789/140566 2018-07-10T22:23:21Z 2017-01-01T00:00:00Z

Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples Tieplova, D. We consider the n² × n² real symmetric and hermitian matrices Mₙ, which are equal to the sum mn of tensor products of the vectors Xμ = B(Yμ ⊗ Yμ), μ = 1, . . . ,mn, where Yμ are i.i.d. random vectors from Rⁿ(Cⁿ) with zero mean and unit variance of components, and B is an n² × n² positive definite non-random matrix. We prove that if mₙ / n² → c ∊ [0,+∞) and the Normalized Counting Measure of eigenvalues of BJB, where J is defined below in (2.6), converges weakly, then the Normalized Counting Measure of eigenvalues of Mn converges weakly in probability to a non-random limit, and its Stieltjes transform can be found from a certain functional equation.

2017-01-01T00:00:00Z Serbenyuk, S.O. http://dspace.nbuv.gov.ua:80/handle/123456789/140565 2018-07-10T22:23:20Z 2017-01-01T00:00:00Z

Continuous Functions with Complicated Local Structure Defined in Terms of Alternating Cantor Series Representation of Numbers Serbenyuk, S.O. The paper is devoted to one infinite parametric class of continuous functions with complicated local structure such that these functions are defined in terms of alternating Cantor series representation of numbers. The main attention is given to differential, integral and other properties of these functions. Conditions of monotony and nonmonotony are found. The functional equations system such that the function from the given class of functions is a solution of the system is indicated.

2017-01-01T00:00:00Z Korobov, V.I. Revina, T.V. http://dspace.nbuv.gov.ua:80/handle/123456789/140564 2018-07-10T22:23:19Z 2017-01-01T00:00:00Z

On Robust Feedback for Systems with Multidimensional Control Korobov, V.I.; Revina, T.V. The paper deals with local robust feedback synthesis problem for systems with multidimensional control and unknown bounded perturbations. Using V.I. Korobov's controllability function method, a bounded control which steers an arbitrary initial point to the origin at some finite time is constructed; an estimate from above for the time of motion is given. The range of a segment where the perturbations can vary is found. As an example, the problem of stopping the oscillations of the system of two coupled pendulums is considered.

2017-01-01T00:00:00Z Hatamleh, R. Zolotarev, V.A. http://dspace.nbuv.gov.ua:80/handle/123456789/140563 2018-07-10T22:23:18Z 2017-01-01T00:00:00Z

On the Abstract Inverse Scattering Problem for Trace Class Perturbations Hatamleh, R.; Zolotarev, V.A. The scattering problem for a pair of selfadjoint operators {L₀, L}, where L - L₀ is of trace-class, is studied. The explicit form of the scattering matrix and its properties are defined. The equation for the inverse problem is obtained.

2017-01-01T00:00:00Z