Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc

The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica^®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4^th order Runge-Kutta meth

The effect of number of pulses of pulsed laser on materials is studied analytically, different pulses has been used with the same delay time.  The depth of possible damage to the surface of copper and titanium as well as depth of the crater to both materials were considered in this study.  The study revealed that linear model is only possible when estimating depth of possible damage for copper material, this means that the depth of possible damage increases with the increment of number of laser pulses .As for titanium material, it is found  the relationship is nonlinear.  The depth of possible damage of titanium and copper is not the same, and copper seems to be more predictable than titanium.  
 

    This article aims to explore the importance of estimating the a semiparametric regression function ,where we suggest a new estimator beside the other combined estimators and then we make a comparison among them by using simulation technique . Through the simulation results we find  that the suggest estimator is the best with the first and second models ,wherealse for the third model we find Burman and Chaudhuri (B&C) is best.

The aim of the research is to identify the cognitive method (rigidity flexibility) of third-stage students in the collage of Physical Education and Sports Sciences at The University of Baghdad, as well as to recognize the impact of using the McCarthy model in learning some of skills in gymnastics, as well as to identify the best groups in learning skills, the experimental curriculum was used to design equal groups with pre test and post test and the research community was identified by third-stage students in academic year (2020-2021), the subject was randomly selected two divisions after which the measure of cognitive method was distributed to the sample, so the subject (32) students were distributed in four groups, and which the pre te

The determination of river pollution impact on the performance of water treatment plants is achieved by two main objectives. The first is to study raw and treated water qualities and comparing them with standards and the second is to evaluate the treatment plants efficiency. The analyzed data were those water quality parameters in relation to physical, chemical and bacteriological characteristics for river water and produced water by seven water treatment plants located on Tigris River passing through Baghdad City.
The results of this study indicated that all raw water characteristic are within the surface water standards established by Iraqi and USA criteria except Bacterial Counts.
Tigris River water is of good quality to be trea

This study is considered to be the first on this sector of Tigris River after 2003, to evaluate the effect of Tharthar Arm on the composition and diversity of Copepoda in Tigris River. Six sampling sites were selected; two on the Tharthar Arm and four sites along the Tigris River, one before the confluence as a control site and the others downstream the confluence; thirty-five copepod taxa were recorded, 34 taxa in the Tigris River and 25 taxa in the Tharthar Arm.
The highest density of Copepoda was in site 2 at Tharthar Arm was 265584.2 Ind./m3 lead to an increasing in Copepoda density in Tigris River from 63878.2 Ind./m3 in site 1 before the confluence to 127198.3 Ind./m3 in site 4 immediately downstream the confluence. Also, the me