Ill-posed problems arise as inverse problems in many areas of science and engineering. The  rst type Fredholm integral equation is a special kind of the inverse problem. A large number of inverse problems of mathematical physics have been translated into the  rst type Fredholm integral equation to solve the problem of computing. Fredholm integral equation of the  rst kind is one of the inverse problems that arise in many areas of science, physical models such as radiography, stereology, spectroscopy, cosmic radiation and engineering  elds such as image processing and electromagnetic. In this paper, we use the collocation method for to  nd an approximate solution of the problem by cubic B-spline basis. The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of proposed method.

In this paper, we propose a meshless Regularization technique for solving an optimal shape design problem (OSD) which consists of constructing the optimal con, gura-tion of a conducting body subject to given boundary conditions to minimize a certain objective function. This problem also can be seen as the problem of building a sup-port for a membrane such that its de ection is as close as possible to 1 in the subset D of the domain. We propose a numerical technique based on the combination of the method of fundamental solutions and application of the Tikhonov's Regulariza-tion method to obtain stable solution. Numerical experiments while solving several test examples are included to show the applicability of the proposed method for obtaining the satisfactory results.

Abstract: This work concerns the transient response in elastodynamic quarter plane problems with mixed boundary conditions. Two dimensional elastodynamic equations are solved analytically applying of integral transformations and Cagniard-de Hoop method and complex integration. The plots of stresses in response to step function are obtained by numerical integration.

Recently, it has been observed that a new method for generating continuous distributions, T 􀀀 X family, can be quite effectively used to analyze the data in one dimension. The aim of this study is to generalize this method to two dimensional space so that the marginals would have T 􀀀 X distributions. So, several examples and properties of this family have been presented. As an application, a special distribution of this family, called bivariate Weibull-Rayleigh-Rayleigh, is fitted to a data set and is shown to have a better fit.

The taxonomy, morphology and distribution of rust species on Arundineae (Poaceae) in Iran was studied. Five species of Puccinia viz. P. magnusiana Korn., P. phragmitis (Schumach.)Korn., P. isiacae G. Winter, P. trabutii Roum. & Sacc. and P. akiyoshidanensis Morim. are described and illustrated. Of these, Puccinia akiyoshidanensis is considered as a distinct species and newly recorded for Iranian rust flora. Moreover, on the basis of examination of type and authentic materials, P. isiacae, P. trabutii, P. moriokaensis S. Ito and P. okatamaensis S. Ito are considered as distinct species. A distribution map and key to the identified Puccinia species on Arundineae in Iran is also given.