Stiffness matrices of beams with stochastic distributed parameters modelled by random fields are considered. In finite element analysis, deterministic shape functions traditionally employed to derive stiffness using the variational principle. Such not exact because derived from solution governing partial differential equation relevant boundary conditions. This paper proposes an analytical metho...

We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient: In particular, we give a lower bound on the largest singular value of a matrix and generalize a result of Finck and Grohmann about the largest eigenvalue of a graph. Keywords: extreme eigenvalues, tight interlacing, graph Laplacian, singular values, nonnegative matrix 1 Introduction Our notation is st...

The exact quantum S-matrices and conserved charges are known for affine Toda field theories(ATFTs). In this note we report on a new type of bi-linear sum rules of conserved quantities derived from these exact S matrices. They exist when there is a multiplicative identity among S-matrices of a particular ATFT. Our results are valid for simply laced as well as non-simply laced ATFTs. We also pres...

This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error ana...

Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given an...

One may consider that the algebraic complexity of basic linear algebra over an abstract field K is well known. Indeed, if ω is the exponent of matrix multiplication over K, then for instance computing the determinant, the matrix inverse, the rank or the characteristic polynomial of an n×n matrix over K can be done in O (̃n) operations in K. Here the soft “O” notation indicates some missing logar...