Journal of Mahani Mathematical Research
Volume:4 Issue: 1, Winter and Spring 2015

Let X1;X2;...;Xn have a jointly multivariate exchangeable normal distribution. In this work we investigate another proof of the independence of X and S2 using order statistics. We also assume that (Xi ; Yi); i =1; 2;...; n; jointly distributed in bivariate normal and establish the independence of the mean and the variance of concomitants of order statistics.

‎This article develops a direct method for solving numerically‎ ‎multi delay-fractional differential and integro-differential equations‎. ‎A Galerkin method based on Legendre polynomials is implemented for solving‎ ‎linear and nonlinear of equations‎. ‎The main characteristic behind this approach is that it reduces such problems to those of‎‎solving a system of algebraic equations‎. ‎A convergence analysis and an error estimation are also given‎. Numerical results with comparisons are given to confirm the reliability of the proposed method‎.

‎In this paper‎, ‎two iterative methods are constructed to solve the operator equation $ Lu=f $ where $L:Hrightarrow H $ is a bounded‎, ‎invertible and self-adjoint linear operator on a separable Hilbert space $ H $‎. ‎ By using the concept of frames of subspaces‎, ‎which is a generalization of frame theory‎, ‎we design some  algorithms based on Galerkin and Richardson methods‎, ‎and then we investigate the convergence and optimality of them‎.

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