xp Xoo„(x")P(x"')dx"dx"'. (10} If we compare these equations with the corresponding equations (19) of Mfffler and Kristensen' in the theory of nonlocal interaction between a local scalar (or pseudoscalar) field and a local spinor field, we notice that the internal eigenfunction x„(r) plays the role of a convergence factor. There is, however, an essential difference between their equations and o...

A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigen...

A system of equations for averaged velocity of turbulent motion of ideal fluid is derived from the assumption that this motion is ergodic. Several fluid flows are considered. A remarkable feature of the averaged equations is that in some cases they have a form of an eigenvalue problem similar to that for Schrődinger’s equation. The equations derived suggest that there are no universal equations...

We propose a method for the solution of non-Hermitian ill-conditioned nonlinear eigenvalue problems T (λ)x = 0, which is based on singularity theory of nonlinear equations. The singularity of T (λ) is characterized by a scalar condition μ(λ) = 0 where the singularity function μ is implicitly defined by a nonsingular linear system with the appropriately bordered matrix T (λ). One Newton step for...

The eigenvalue problem in difference equations, (--1)n-kAny(t) A l:,=o p()’,(), with y(0) 0, 0 < < k, Ak+iy(T + 1) 0, 0 _< < n k, is examined. Under suitable conditions on the coefficients Pi, it is shown that the smallest positive eigenvalue is a decreasing function of T. As a consequence, results concerning the first focal point for the boundary value problem with A are obtained.

In the positive definite case, the extreme generalized eigenvalues can be obtained by solving a suitable nonlinear system of equations. In this work, we adapt and study the use of recently developed low-cost derivative-free residual schemes for nonlinear systems, to solve large-scale generalized eigenvalue problems. We demonstrate the effectiveness of our approach on some standard test problems...

in this study, the vibration of cracked plates is investigated using the differential quadrature method and experimental modal analysis. the crack, which is assumed to be open, is modeled by the extended rotational spring. with its finite length, the crack divides the plate into six segments. then, the differential quadrature is applied to the governing differential equations of motion and the ...

This paper is concerned with the eigenvalue decay of the solution to operator Lya-punov equations with right-hand sides of finite rank. We show that the kth eigenvalue decays exponentially in √ k, provided that the involved operator A generates an exponentially stable continuous semigroup, and A is either self-adjoint or diagonalizable. Numerical experiments with discretizations of 1D and 2D PD...