The distribution of the roots of a second order transcendental polynomial is analyzed, and it is used for solving the purely imaginary eigenvalue of a transcendental characteristic equation with two transcendental terms. The results are applied to the stability and associated Hopf bifurcation of a constant equilibrium of a general reaction–diffusion system or a system of ordinary differential e...

A technique is presented for determining the roots of a polynomial p(x) that is expressed in terms of an expansion in orthogonal polynomials. The roots are expressed as the eigenvalues of a nonstandard companion matrix Bn whose coefficients depend on the recurrence formula for the orthogonal polynomials, and on the coefficients of the orthogonal expansion. Some questions on the numerical stabil...

This paper addresses the classical and discrete Euler-Lagrange equations for systems of n particles interacting quadratically in R. By highlighting the role played by the center of mass of the particles, we solve the previous systems via the classical quadratic eigenvalue problem (QEP) and its discrete transcendental generalization. The roots of classical and discrete QEP being given, we state ...

n |sn−sn+1|, is presented. This Ising-like model is an interesting example of a graduate-level statistical mechanics problem where the eigenfunctions and eigenvalues of an integral operator, the transfer integral, can be determined exactly. This can be contrasted with the determination of eigenfunctions and eigenvalues of differential operators, such as the quantum mechanical finite-depth squar...

Abstract The nonlinear eigenvalue problem of a class second order semi-transcendental differential equations is studied. A defined as the initial condition which gives rise separatrix solution. equation can be integrated once to first equation, e.g., Ricatti equation. It shown that problems these are equivalent linear problems. They share exactly same eigenvalues. eigensolutions in two closely ...

time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. the stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. it is well-known that the stabi...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...