Browsing by Author "Guseinov, Gusein Sh"

Now showing 1 - 12 of 12

Citation - WoS: 4
Citation - Scopus: 5
Construction of a Complex Jacobi Matrix From Two-Spectra
(Hacettepe Univ, Fac Sci, 2011) Guseinov, Gusein Sh; Mathematics; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper we study the inverse spectral problem for two-spectra of finite order complex Jacobi matrices (tri-diagonal 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 deleting the first column and the first row of the Jacobi matrix. An explicit procedure of reconstruction of the matrix from the two-spectra is given.
Citation - WoS: 3
Citation - Scopus: 3
Description of the Structure of Arbitrary Functions of the Laplace-Beltrami Operator in Hyperbolic Space
(Taylor & Francis Ltd, 2013) Guseinov, Gusein Sh; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We describe the structure of an arbitrary rapidly decreasing function of the Laplace-Beltrami operator in n-dimensional hyperbolic space showing that the function of the Laplace-Beltrami operator is an integral operator and giving an explicit formula for its kernel.
Citation - WoS: 16
Citation - Scopus: 15
Dynamical Systems and Poisson Structures
(Amer inst Physics, 2009) Guerses, Metin; Guseinov, Gusein Sh; Zheltukhin, Kostyantyn; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We 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]
Citation - WoS: 16
Citation - Scopus: 18
An Expansion Result for a Sturm-Liouville Eigenvalue Problem With Impulse
(Tubitak Scientific & Technological Research Council Turkey, 2010) Faydaoglu, Serife; Guseinov, Gusein Sh; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The 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.
Citation - WoS: 9
Citation - Scopus: 11
Further Properties of the Laplace Transform on Time Scales With Arbitrary Graininess
(Taylor & Francis Ltd, 2013) Bohner, Martin; Guseinov, Gusein Sh; Karpuz, Basak; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this work, we generalize several properties of the usual Laplace transform to the Laplace transform on arbitrary time scales. Among them are translation theorems, transforms of periodic functions, integration of transforms, transforms of derivatives and integrals, and asymptotic values.
Citation - WoS: 1
Citation - Scopus: 1
On a Quadratic Eigenvalue Problem and Its Applications
(Springer Basel Ag, 2013) Atalan, Ferihe; Guseinov, Gusein Sh; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We investigate the eigenvalues and eigenvectors of a special quadratic matrix polynomial and use the results obtained to solve the initial value problem for the corresponding linear system of differential equations.
Citation - WoS: 1
Citation - Scopus: 1
On Determination of a Finite Jacobi Matrix From Two Spectra
(Tech Science Press, 2012) Guseinov, Gusein Sh; Mathematics; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal 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 first 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.
Citation - WoS: 64
Citation - Scopus: 68
On the Concept of Spectral Singularities
(indian Acad Sciences, 2009) Guseinov, Gusein Sh; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we discuss the concept of spectral singularities for non-Hermitian Hamiltonians. We exihibit spectral singularities of some well-known concrete Hamiltonians with complex-valued coefficients.
Citation - WoS: 1
Citation - Scopus: 1
On the Determination of a Complex Finite Jacobi Matrix From Spectral Data
(Univ Politehnica Bucharest, Sci Bull, 2015) Guseinov, Gusein Sh; Mathematics; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we study the necessary and sufficient conditions for solvability of an inverse spectral problem for finite order complex Jacobi matrices (tri-diagonal symmetric matrices with complex entries). The problem is to reconstruct the complex Jacobi matrix from the spectral data consisting of eigenvalues and normalizing numbers of this matrix. An explicit procedure of reconstruction of the matrix from the spectral data is given.
On the Functions of Two Commuting Laplace-Beltrami Operators in Hyperbolic Space
(Pergamon-elsevier Science Ltd, 2014) Guseinov, Gusein Sh; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We describe the structure of arbitrary rapidly decreasing two-variable function of two commuting Laplace-Beltrami operators in the product of two many-dimensional hyperbolic spaces showing that the function of the commuting Laplace-Beltrami operators is an integral operator and giving an explicit formula for its kernel.
Citation - WoS: 1
RECONSTRUCTION OF COMPLEX JACOBI MATRICES FROM SPECTRAL DATA
(Hacettepe Univ, Fac Sci, 2009) Guseinov, Gusein Sh; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce spectral data for finite order complex Jacobi matrices and investigate the inverse problem of determining the matrix from its spectral data. Necessary and sufficient conditions for the solvability of the inverse problem are established. An explicit procedure of reconstruction of the matrix from the spectral data is given.
Citation - WoS: 6
Citation - Scopus: 7
Surface Areas and Surface Integrals on Time Scales
(Dynamic Publishers, inc, 2010) Bohner, Martin; Guseinov, Gusein Sh; Mathematics; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We study surfaces parametrized by time scale parameters, obtain an integral fomula for computing the area of time scale surfaces, introduce delta integrals over time scale surfaces, and give sufficient conditions that ensure existence of these integrals