In this paper, we present a computational method for solving boundary INTEGRAL equations with LOGARITHMIC singular kernels which occur as reformulations of a boundary value problem for Laplace's equation. The method is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis. This approach utilizes the non- uniform Gauss-Legendre quadrature rule for approximating logarithm-like singular INTEGRALs and so reduces the solution of boundary INTEGRAL equations to the solution of linear systems of algebraic equations. The properties of CAS wavelets are used to make the wavelet coefficient matrices sparse, which eventually leads to the sparsity of the coefficient matrix of the obtained system. Finally, the validity and efficiency of the new technique are demonstrated through a numerical example.

In this article, we use an effective coupled technique to solve singular INTEGRAL equations with LOGARITHMIC kernel which it occurs in different branches of sciences such as mathematical physics, mechanics, isotropic elastic, etc. At first, we approximate the singular kernel by choosing suitable mesh points and multi-wavelet bases then, Galerkin method is used for solving INTEGRAL equations. In addition, for simplification and to achieve to a more accuracy, we convert INTEGRAL equation with LOGARITHMIC kernel to integro-differential equation with weakly singular kernel which is solvable with the proposed method. The numerical results show the high accuracy of the solution.

Let j be a holomorphic self-map and g a fixed holomorphic function on the unit ball B. The boundedness and compactness of the Volterra composition operatorTg, j ¦ (z)=ò10 ¦ (j (tz) Rg(tz) dt/ton the LOGARITHMIC Bloch space and little LOGARITHMIC Bloch space are studied in this paper.

In this paper, we introduce a new five-parameter distribution with increas-ing, decreasing, bathtub-shaped failure rate called the Beta-Weibull-LOGARITHMIC (BWL) distribution. Using the Sterling Polynomials, various properties of the new distribu-tion such as its probability density function, its reliability and failure rate functions, quantiles and moments, Renyi and Shannon entropies, moments of order statistics, Bonferroni and Lorenz curves were derived. then the maximum likelihood estimation of BWL distribution for the parameters of BWL distribution are found. Finally the usefulness of this distribution for real data are presented.