Profile URL: https://hdl.handle.net/20.500.14411/8081
Job Title:Profesör Doktor
Main Affiliation: Mathematics
Status: Former Staff
Name Variants:
H.,Hüseyin H.S.Huseyin H.,Huseyin Sirin Hüseyin, Hüseyin Şirin H., Huseyin Sirin H.,Hüseyin Şirin Huseyin, Huseyin Sirin Hüseyin,H.Ş. Hüseyin Şirin, Hüseyin H., Huseyin Huseyin,H.S. H.Ş.Hüseyin Huseyin Sirin, Huseyin Guseinov, Gusein Sh. Guseinov, GS Guseinov, Gusein Sh Guseinov, G. Sh. Guseinov, Gusein S. H. Guseinov, Gusein SH. Guseinov,G.S. Guseinov,G.Sh. Guseinov,G.S.
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Article Citation - WoS: 1Citation - Scopus: 1On an Inverse Problem for Two Spectra of Finite Jacobi Matrices(Elsevier Science inc, 2012-03) Guseinov, Gusein Sh.We solve a version of the inverse spectral problem for two spectra of finite order real Jacobi matrices. The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the last diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. (C) 2012 Elsevier Inc. All rights reserved.Conference Object On the Riemann Integration on Time Scales(Crc Press-taylor & Francis Group, 2004) Guseinov, GS; Kaymakçalan, BIn this paper we introduce and investigate the concepts of Riemann's delta and nabla integrals on time scales. Main theorems of the integral calculus on time scales are proved.Article Citation - WoS: 13Citation - Scopus: 17The Laplace Transform on Isolated Time Scales(Pergamon-elsevier Science Ltd, 2010-09) Bohner, Martin; Guseinov, Gusein Sh.Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classical theorem of Titchmarsh for the usual continuous convolution. (C) 2010 Elsevier Ltd. All rights reserved.Conference Object Inverse Spectral Problems for Complex Jacobi Matrices(Springer New York LLC, 2013) Guseinov,G.S.The paper deals with two versions of the inverse spectral problem for finite complex Jacobi matrices. The first is to reconstruct the matrix using the eigenvalues and normalizing numbers (spectral data) of the matrix. The second is to reconstruct the matrix using two sets of eigenvalues (two spectra), one for the original Jacobi matrix and one for the matrix obtained by deleting the last row and last column of the Jacobi matrix. Uuniqueness and existence results for solution of the inverse problems are established and an explicit procedure of reconstruction of the matrix from the spectral data is given. It is shown how the results can be used to solve finite Toda lattices subject to the complex-valued initial conditions. © Springer Science+Business Media New York 2013.Article Citation - WoS: 3On Construction of a Quadratic Sturm-Liouville Operator Pencil From Spectral Data(inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2014) Guseinov, Gusein S. H.Derivation of fundamental equations of the inverse spectral problem for a quadratic Sturm-Liouville operator pencil is presented. An algorithm for solving the inverse problem is offered.Article Citation - WoS: 16Citation - Scopus: 15Dynamical Systems and Poisson Structures(Amer inst Physics, 2009-11-01) Guerses, Metin; Guseinov, Gusein Sh; Zheltukhin, Kostyantyn; Gürses, MetinWe first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender et al. [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that all dynamical systems in R-n are locally (n-1)-Hamiltonian. We give also an algorithm, similar to the case in R-3, to construct a rank two Poisson structure of dynamical systems in R-n. We give a classification of the dynamical systems with respect to the invariant functions of the vector field (X) over right arrow and show that all autonomous dynamical systems in R-n are super-integrable. (C) 2009 American Institute of Physics. [doi:10.1063/1.3257919]Article Citation - WoS: 33Citation - Scopus: 47Higher-Order Self-Adjoint Boundary-Value Problems on Time Scales(Elsevier Science Bv, 2006-10) Anderson, Douglas R.; Guseinov, Gusein Sh.; Hoffacker, JoanIn this study, higher-order self-adjoint differential expressions on time scales and their associated self-adjoint boundary conditions are discussed. The symmetry property of the corresponding Green's functions is shown, together with specific formulas of Green's functions for select time scales. (c) 2005 Elsevier B.V. All rights reserved.Article Citation - WoS: 3Instability Intervals of a Hill's Equation With Piecewise Constant and Alternating Coefficient(Pergamon-elsevier Science Ltd, 2004-01) Guseinov, GS; Karaca, IYIn this paper, we obtain asymptotic formulas for eigenvalues of the periodic and the semiperiodic boundary value problems associated with a Hill's equation having piecewise constant and alternating coefficient. As a corollary, it is shown that the lengths of instability intervals of the considered Hill's equation tend to infinity. (C) 2004 Elsevier Ltd. All rights reserved.Conference Object Citation - WoS: 67Improper Integrals on Time Scales(Dynamic Publishers, inc, 2003) Bohner, M; Guseinov, GSIn this paper we study improper integrals on time scales. We also give some mean value theorems for integrals on time scales, which are used in the proof of an analogue of the classical Dirichlet-Abel test for improper integrals.Article Citation - WoS: 47Citation - Scopus: 66The Convolution on Time Scales(Hindawi Publishing Corporation, 2007) Bohner, Martin; Guseinov, Gusein Sh.The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. Via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. As an extensive example, we consider the q-difference equations case. Copyright (c) 2007 M. Bohner and G. Sh. Guseinov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.