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D. Kh. Giniyatova

Bio: D. Kh. Giniyatova is an academic researcher from Kazan Federal University. The author has contributed to research in topics: Diffraction & Parallel algorithm. The author has an hindex of 1, co-authored 3 publications receiving 5 citations.

Papers
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TL;DR: The main result of as mentioned in this paper is analogues of the Schwarz lemma for the torsional rigidity and the conformal moment of inertia of simply connected domains, and they obtain Schwarz-Pick type inequalities for these quantities and consider some generalizations and applications.
Abstract: Themain result of this paper is analogues of the Schwarz lemma for the torsional rigidity and the conformal moment of inertia of simply connected domains. Moreover we obtain Schwarz-Pick type inequalities for these quantities and consider some generalizations and applications.

6 citations

Journal ArticleDOI
TL;DR: Numerical results are presented for the problem of diffraction by a rectangular screen, as well as by screen octagonal shape and the analysis shows that the method of moments implementation by GPU significantly improves the performance of the algorithm for solving theproblem of electromagnetic wave Diffraction by the flat metal screens.
Abstract: The problem of electromagnetic wave diffraction by a flat convex screen of arbitrary shape is considered. The numerical solution for the problem is obtained by the method of moments using the parallel programming technology CUDA. As basic and testing functions RWG functions are used. To construct the corresponding RWG elements on CUDA, a simple and fast algorithm of triangulation for a convex screen with an arbitrary boundary is developed. Numerical results are presented for the problem of diffraction by a rectangular screen, as well as by screen octagonal shape. The results obtained for the rectangle are in good correspondence with the results published in previous works. A comparative analysis of the running time of sequential and parallel algorithms is presented. The analysis shows that the method of moments implementation by GPU significantly improves the performance of the algorithm for solving the problem of electromagnetic wave diffraction by the flat metal screens.

2 citations

Journal ArticleDOI
TL;DR: In this article, the authors obtained analogs of Schwarz-Pick type inequalities in the class A(Ω, gH) = {f: Ω → Π} of functions locally holomorphic in Ω; for the domain Ω, they considered the exterior of the unit disk and the upper half-plane.
Abstract: Let Ω and Π be two domains in the extended complex plane equipped by the Poincare metric. In this paper we obtain analogs of Schwarz-Pick type inequalities in the class A(Ω, gH) = {f: Ω → Π} of functions locally holomorphic in Ω; for the domain Ω we consider the exterior of the unit disk and the upper half-plane. The obtained results generalize the well-known theorems of Szasz and Ruscheweyh about the exact estimates of derivatives of analytic functions defined on the disk |z| < 1.

1 citations


Cited by
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TL;DR: New integral Hardy-type inequalities for compactly supported functions in arbitrary plane domains of hyperbolic type are given in this article, and special cases for domains with uniformly perfect boundaries are studied and some applications are considered.
Abstract: New integral Hardy-type inequalities for compactly supported functions in arbitrary plane domains of hyperbolic type are given. Special cases for domains with uniformly perfect boundaries are studied and some applications are considered. The proofs depend substantially on fundamental equations and formulae for the hyperbolic metric, and use is also made of characteristics of domains in terms of moduli. These date back to Teichmuller. Bibliography: 20 titles.

27 citations

Journal ArticleDOI
TL;DR: The main result of as mentioned in this paper is analogues of the Schwarz lemma for the torsional rigidity and the conformal moment of inertia of simply connected domains, and they obtain Schwarz-Pick type inequalities for these quantities and consider some generalizations and applications.
Abstract: Themain result of this paper is analogues of the Schwarz lemma for the torsional rigidity and the conformal moment of inertia of simply connected domains. Moreover we obtain Schwarz-Pick type inequalities for these quantities and consider some generalizations and applications.

6 citations