The design of reinforced concrete spread foundations mainly depends on soil bearing capacity, loading value, and column size. So for each design case, tiresome calculations and time consumption are needed. In this paper, generalized design charts are presented and plotted according to derivations based on the ACI 318 M-2019 Code. These charts could be used directly by the structural designers to estimate the column size, foundation thickness, and dimensions as well as the foundation reinforcement under a certain given concentric load assuming a uniformly distributed contact pressure underneath the foundation. Of noteworthy, these charts are oriented to deal with square isolated footings with a square concentric column, covering reasonable r

The numerical resolve nonlinear system of Volterra integral equation of the second kind (NLSVIEK2) has been considered. The exponential function is used as the base function of the collocation method to approximate the resolve of the problem. Arithmetic epitome are performed which have already been solved by weighted residual manner,  Taylor manner and block- by- block(2, 3, 5).

         The optimum balance values for different coefficient of spherical aberration (third and fifth degree also focal shift) were studied, the optical system includes different apertures (circle, ellipse, square and triangle) using point spread function (PSF).       By using (Marechal) method; the minimum value of mean square of variance in wave front was founded, so we can get the maximum of central intensity according to (Strehl) criterion.

In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using   is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.