It was conjectured by H. Zassenhaus that a torsion unit of an integral group ring of a finite group is conjugate to a group element within the rational group algebra. The object of this note is the computational aspect of a method developed by I. S. Luthar and I. B. S. Passi which sometimes permits an answer to this conjecture. We illustrate the method on certain explicit examples. We prove wit...

This note considers cooperative irreducible systems of ordinary differential equations admitting a C1 first integral with positive gradient. We prove that all forward or backward nonwandering points are equilibria. We obtain also some results on the global phase portrait of such systems. The main tool of proof is a canonically defined Finsler structure with respect to which the derivative skew-...

An iteration method is described to solve one-dimensional, first-kind integral equations with finite integration limits and difference kernel, K(x − x ′), that decays exponentially. The method relies on deriving via the Wiener–Hopf factorization and solving by suitable iterations in the Fourier complex plane a pair of integral relations, where each iteration accounts for all end point singulari...

E-Methnds for .,aflving linear Volterra integral equatitms of the first kind with smot~th kernels are considered. E-MethotL~ are a new type of numerical algorithms computing numerical approximations together with mathematically guaranteed do.~ error I~amds, The basic concepts from verifi~ttion thet~ry are sketched and such ~lf-validating numerics derived. O~mputati~mal experiments show the effi...

In this tutorial we will introduce the reader to how the direct integral forms for a partial differential equation can be derived. We will start from the well-known form for the integration by parts rule and then we will generalize it to demonstrate how Green’s second identity works. Therefore the main objectives of this tutorial are: 1. To review the philosophy behind the integration by part r...

We consider a linear Abel integral operator A : L 2 (0; 1) ?! L 2 (0; 1) deened by (A y)(t) = 1 ?() Z t 0 (t ? s) ?1 K(t; s)y(s)ds; 0 t 1; 0 < 1: We construct a scale fX g 2R of Hilbert spaces of functions in (0; 1) and relate it with a Hilbert scale of Sobolev spaces. Under suitable assumptions on K, we prove that kA uk L 2 (0;1) gives an equivalent norm in X ?. On the basis of this equivalenc...

Solitary wave solutions to the Broer-Kaup equations and approximate long water wave equations are considered challenging by using the rst integral method.The exact solutions obtained during the present investigation are new. This method can be applied to nonintegrable equations as well as to integrable ones.

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

An expression for the path integral of a single quantum panicle in a non-local pseudopotential is derived. This expression is then used to model the behavior of an electron in the potential field of a sodium ion. The amplitude of the 3s and the 3p ohitals of sodium are calculated with an open boundary molecular dynamics simulation. These amplitudes agree favorably with those obtained using the ...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...