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

This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving nonli

In the current study, two sites were selected from the city of Adhamiya, central Baghdad. The first site is the Adhamiya Corniche, which includes a sample of river water and the second includes domestic sewage in the same area. The total density of benthic invertebrates was 775 ind/m2, which is divided into 15 taxa. Biological indices were found, such as the stability index, the abundance index, the biodiversity index (Shannon’s index), the homogeneity index, and the invader’s guide. The result showed an increase in the density of benthic invertebrates, as well as an increase in the diversity of these organisms.

In this paper the effect of engagement length, number of teeth, amount of applied load, wave propagation time, number of cycles, and initial crack length on the principal stress distribution, velocity of crack propagation, and cyclic crack growth rate in a spline coupling subjected to cyclic torsional impact have been investigated analytically and experimentally. It was found that the stresses induced due to cyclic impact loading are higher than the stresses induced due to impact loading with high percentage depends on the number of cycles and total loading time. Also increasing the engagement length and the number of teeth reduces the principal stresses (40%) and
(25%) respectively for increasing the engagement length from (0.15 to 0

Exposure assays to magnetized water have so far revealed striking results. The present study was conducted to determine the effects of magnetized water treatment with in different intensities 500 , 1000 and 1500 Gauss on some biological aspects for species of freshwater Gastropod Lymnaea lagotis (Schrank, 1803) which important species in faun of aquatic habitats of Iraq. This species are considered a component of the food chain. The obtained results compared with these species which lived in the river(control). Result of these experiments showed increased significance the shell size (shell high, shell aperture length, shell aperture width and shell width) for L. lagotis with increased intensity magnetized water such as treated water with 1

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