Browsing by Author "Guseinov, Gusein Sh"
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Article Citation Count: 3Description of the structure of arbitrary functions of the Laplace-Beltrami operator in hyperbolic space(Taylor & Francis Ltd, 2013) Hüseyin, Hüseyin Şirin; MathematicsWe 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.Article Citation Count: 16Dynamical systems and Poisson structures(Amer inst Physics, 2009) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh; Zheltukhin, Kostyantyn; MathematicsWe 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 Count: 17An expansion result for a Sturm-Liouville eigenvalue problem with impulse(Tubitak Scientific & Technological Research Council Turkey, 2010) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh; MathematicsThe 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 Count: 9Further properties of the Laplace transform on time scales with arbitrary graininess(Taylor & Francis Ltd, 2013) Hüseyin, Hüseyin Şirin; Guseinov, Gusein Sh; Karpuz, Basak; MathematicsIn 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.Article Citation Count: 1On a Quadratic Eigenvalue Problem and its Applications(Springer Basel Ag, 2013) Atalan, Ferihe; Guseinov, Gusein Sh; Hüseyin, Hüseyin Şirin; MathematicsWe 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.Article Citation Count: 61On the concept of spectral singularities(indian Acad Sciences, 2009) Hüseyin, Hüseyin Şirin; MathematicsIn 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.Article Citation Count: 0ON THE FUNCTIONS OF TWO COMMUTING LAPLACE-BELTRAMI OPERATORS IN HYPERBOLIC SPACE(Pergamon-elsevier Science Ltd, 2014) Hüseyin, Hüseyin Şirin; MathematicsWe 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.