https://elib.bsu.by:443/handle/123456789/147864 Mon, 20 Apr 2026 12:05:58 GMT 2026-04-20T12:05:58Z https://elib.bsu.by:443/handle/123456789/266250 Заглавие документа: Constructive methods for factorization of matrix-functions Авторы: Rogosin, S.; Mishuris, G. Аннотация: A survey of constructive methods for the factorization of n × n matrix-functions is presented. The importance of these methods for theoretical and practical applications is singled out. Several classes of matrices are considered which are factorized by the proper technique. The perspective of the constructive methods and procedures is discussed and open questions are formulated. Fri, 01 Jan 2016 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/266250 2016-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/265835 Заглавие документа: Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements Авторы: Rogosin, S.; Mishuris, G.; Koroleva, A.; Vinakurava, A. Аннотация: A three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in accounting not only for the normal (vertical), but also for tangential vertical (horizontal) displacements of the contacting surfaces. Exact general relationships have been established between the contact approach and some integral characteristics of the contact pressure, including the contact force. Asymptotic representations for the contact pressure integral characteristics are obtained in terms of the contact approach and some integral characteristics of the contact zone. The main result is represented by the first-order approximation problem. We supply the theoretical description of the asymptotic method by numerical analysis of the model. Our calculations demonstrate good convergence of the numerical scheme in determination of the parameters. In particular, it is shown that accounting for the tangential displacement is important in cases where the contact zone is non-circular. Fri, 01 Jan 2016 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/265835 2016-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/265816 Заглавие документа: Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles Авторы: Peck, D.; Rogosin, S.V.; Wrobel, M.; Mishuris, G. Аннотация: A generalization of the approach developed in the recent papers by the authors is presented. It aims to provide a description of the Hele-Shaw cell in the presence of multiple small obstacles/moving particles. We perform an asymptotic analysis of the dynamics of the moving boundary and the moving particles. For this, a modification of Maz’ya–Movchan–Nieves uniform asymptotic formula for the Green’s function of the mixed boundary value problem for the Laplace equation in a multiply connected domain is utilized. The paper contains extensive numerical analysis, accounting for various physical mechanisms of particle movement in the Hele-Shaw flow. Fri, 01 Jan 2016 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/265816 2016-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/265718 Заглавие документа: Factorization of a class of matrix-functions with stable partial indices Авторы: Mishuris, G.; Rogosin, S. Аннотация: A new effective method for factorization of a class of nonrational n × n matrix-functions with stable partial indices is proposed. The method is a generalization of one recently proposed by the authors, which was valid for the canonical factorization only. The class of matrices being considered is motivated by their applicability to various problems. The properties and steps of the asymptotic procedure are discussed in detail. The efficiency of the procedure is highlighted by numerical results. Copyright © 2016 John Wiley & Sons, Ltd. Copyright Fri, 01 Jan 2016 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/265718 2016-01-01T00:00:00Z