Simple derivation of the dual conservation integrals in small strain elasticity is presented, without the aid of Noether’s theorem on invariant variational principles. The derived integrals are related to the release rates of the potential and complementary potential energy associated with the defect motion. The analysis corrects the errors in earlier derivation of the relationship between the ...

purpose: the purpose of this study was to investigate the structure of the discipline categorization and its overlap with isi subject categories. this will help detect the systematic errors arising from the scientometrics studies. methodology: the scientometrics methodology was used. all articles which were indexed in the web of science database (2007) and also the articles citing them during 2...

Keywords: Hyperelliptic integrals Elliptic integrals Epstein–Hubbell integral Bessel functions Lauricella function a b s t r a c t The elliptic integrals and its generalizations are applied to solve problems in various areas of science. This study aims to demonstrate a new method for the calculation of integrals through Bessel functions. We present solutions for classes of elliptic integrals an...

We study the scalar and tensor integrals associated with the pentabox topology: the class of two-loop box integrals with seven propagators five in one loop and three in the other. We focus on the case where the external legs are light-like and use integration-by-parts identities to express the scalar integral in terms of two master integrals and present an explicit analytic expression for the p...

In a previous part I, we introduced a method for the evaluation of singular integrals arising in the discretization of integral equations based on the repeated subdivision of domains. The integrals defined on these subdomains are classified such that a class of integrals can be expressed as a sum of regular integrals and representatives of other classes. A system of equations describes the rela...

There are two basic types of improper integrals. Integrals with an infinite limit are defined as the limit of a series of proper integrals as one of the limits approaches infinity. Improper integrals with finite limits are needed when the integrand does not have a finite limiting value as the variable of integration approaches a particular “critical” value. In this case, the improper integral i...

We consider   bivariate  mean-value interpolationproblem, where the integrals over circles are interpolation data. In this case the problem  is described  over   circles of the same radius and with  centers are on astraight line and it is shown that in this case the interpolation is not correct.

‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

A collocation method for approximating integrals of rapidly oscillatory functions is analyzed. The method is efficient for integrals involving Bessel functions J,.(rx) with a large oscillation frequency parameter r, as well as for many other oneand multi-dimensional integrals of functions with rapid irregular oscillations. The analysis provides a convergence rate and it shows that the relative ...