Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three dimensional scattering integral equations satisfying constraints of relativistic unitarity and covariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of va...

In this study, using a one-dimensionl MRA we constructed two-dimensional wavelet as well four masks which are not related to the MRA. Finally, provide some examples prove applicability of our construction in case finding numerical solution first kind Fredholm integral equations.

in this work, we present a computational method for solving second kindnonlinear fredholm volterra integral equations which is based on the use ofhaar wavelets. these functions together with the collocation method are thenutilized to reduce the fredholm volterra integral equations to the solution ofalgebraic equations. finally, we also give some numerical examples that showsvalidity and applica...

Questions of solution of three-dimensional diffraction problems are considered. Each problem is formulated as a single weakly-singular integral equation of the 1st kind for a single unknown function. Discretization of these equations is realized by means of special smoothing method of integral operators kernels. Numerical solutions of systems of linear algebraic equations, approximating integra...

One hundred years ago, Nekrasov published the widely cited paper (Nekrasov in Izvestia Ivanovo-Voznesensk Politekhn Inst 3:52–65, 1921), which he derived first of his two integral equations describing steady periodic waves on free surface water. We examine how arrived at these and approach to investigating their solutions. In connection with this, Nekrasov’s life after 1917 is briefly outlined,...