In this paper, the first and second order approximations of Taylor expansion are used for calculating the change of each natural frequency by modifying an arbitrary parameter of a system with a known amount and based on this approximation, the inverse eigenvalue problem is transformed to a solvable algebraic equation. The finite element formulation, based on the classical laminated plate theory...

We first develop an efficient spectral-Galerkin method and an rigorous error analysis for the generalized eigenvalue problems associated to a transmission eigenvalue problem. Then, we present an iterative scheme, based on computation of the first transmission eigenvalue, to estimate the index of refraction of an inhomogeneous medium. We present ample numerical results to demonstrate the effecti...

We consider the first Dirichlet eigenvalue of diffusion operators on the half line. A criterion for the equivalence of the first Dirichlet eigenvalue with respect to the maximum domain and that to the minimum domain is presented. We also describle the relationships between the first Dirichlet eigenvalue of transient diffusion operators and the standard Muckenhoupt’s conditions for the dual weig...

A method for solving the descriptor discrete-time linear system is focused. For easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...