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Article Citation - WoS: 1Citation - Scopus: 1On Construction of a Complex Finite Jacobi Matrix From Two Spectra(int Linear Algebra Soc, 2013) Guseinov, Gusein Sh.; MathematicsThis paper concerns with the inverse spectral problem for two spectra of finite order complex Jacobi matrices (tri-diagonal symmetric matrices with complex entries). 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 other 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.Article Citation - WoS: 16Citation - Scopus: 19An Expansion Result for a Sturm-Liouville Eigenvalue Problem With Impulse(Tubitak Scientific & Technological Research Council Turkey, 2010) Faydaoglu, Serife; Guseinov, Gusein ShThe paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.Article Citation - WoS: 2Citation - Scopus: 2On the eigenfunctions of the q-Bernstein operators(Springer Basel Ag, 2023) Ostrovska, Sofiya; Turan, MehmetThe eigenvalue problems for linear operators emerge in various practical applications in physics and engineering. This paper deals with the eigenvalue problems for the q-Bernstein operators, which play an important role in the q-boson theory of modern theoretical physics. The eigenstructure of the classical Bernstein operators was investigated in detail by S. Cooper and S. Waldron back in 2000. Some of their results were extended for other Bernstein-type operators, including the q-Bernstein and the limit q-Bernstein operators. The current study is a pursuit of this research. The aim of the present work is twofold. First, to derive for the q-Bernstein polynomials analogues of the Cooper-Waldron results on zeroes of the eigenfunctions. Next, to present in detail the proof concerning the existence of non-polynomial eigenfunctions for the limit q-Bernstein operator.Article Citation - WoS: 12Citation - Scopus: 12Boundary Value Problems for Nonlinear Impulsive Hamiltonian Systems(Elsevier Science Bv, 2014) Guseinov, Gusein Sh.We study two point boundary value problems for nonlinear impulsive Hamiltonian systems. Spectral analysis of the corresponding linear impulsive Hamiltonian system and a fixed point theorem are employed to obtain an existence and uniqueness result for solutions of the nonlinear problem. Two examples are given in which the main condition is made explicit. (C) 2013 Elsevier B.V. All rights reserved.Article Citation - Scopus: 3Instability Intervals of a Hill's Equation With Piecewise Constant and Alternating Coefficient(Elsevier Ltd, 2004) Guseinov,G.Sh.; Karaca,I.Y.In 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. © 2004 Elsevier Ltd. All rights reserved.
