In this paper we presented an extension of previous results given in the papers [15], [17],[19], main idea proofs is: write down difference trigonometric kernel general expansion considered, and have to estimate resulting infinite sums. For terms these sums used sharper different estimates than literature (the most exact where by V.A.Il’n, I. Joó V.Komornik).

We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius op...

We propose a simple level set method for the Dirichlet k-partition problem which aims to partition an open domain into K different subdomains as minimize sum of smallest eigenvalue Laplace operator in each subdomain. first formulate nested minimization functional function and eigenfunction defined As approximation, we simply replace by so that can then be converted single problem. apply standar...

Abstract The paper suggests a new technique for solution of the inverse problem for Maxwell’s equations in a dissipating medium. Being non-self-adjoint, the problem generally requires computing an adjoint operator on each step of gradient descent minimization procedure. The suggested approach introduces a conjugation operator and develops a representation of the system of Maxwell’s equations ba...

We propose and analyze a new spectral collocation method to solve eigenvalue problems of compact integral operators, particularly, piecewise smooth operator kernels and weakly singular operator kernels of the form 1 |t−s|μ , 0 < μ < 1. We prove that the convergence rate of eigenvalue approximation depends upon the smoothness of the corresponding eigenfunctions for piecewise smooth kernels. On t...