In this paper, a new approach was suggested to the method of Gauss Seidel through the controlling of equations installation before the beginning of the method in the traditional way. New structure of equations occur after the diagnosis of the variable that causes the fluctuation and the slow extract of the results, then eradicating this variable. This procedure leads to a higher accuracy and less number of steps than the old method. By using the this proposed method, there will be a possibility of solving many of divergent values equations which cannot be solved by the old style.

Surfaces quality is one of the most specified customer requirements for machine parts. The major indication of surfaces quality on machined parts is surface roughness. The research aim is to study the cutting conditions and their effects on the surface roughness. This paper utilizes regression models to predict surface roughness over the machining time for variety of cutting conditions in turning. In the experimental part for turning, different types of materials (Aluminum alloy, Copper alloy, and Gray cast iron) were considered with different cutting speed ( ) and feed rate ( ). A mathematical Model depending on statistical-mathematical method between surface roughness (Rz ) and cutting condition ( , ) were derived, for the three materials

Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

A numerical model for Polypropylene 575 polymer melts flow along the solid conveying screw of a single screw extruder under constant heat flux using ANSYS-FLUENT 17.2 software has been conducted. The model uses the thermophysical properties such as Viscosity, thermal conductivity, Specific heat and density of polypropylene 575 that measured as a function of temperature, and residence time data for process simulation. The numerical simulation using CFD models for single screw extruder and the polymer extrusion was analysed for parameters such as (thermal conductivity, specific heat, density and viscosity) reveals a high degree of similarity to experimental data measured. The most important outcome of this study is that geometrical, parame

This research aims to solve the nonlinear model formulated in a system of differential equations with an initial value problem (IVP) represented in COVID-19 mathematical epidemiology model as an application using new approach: Approximate Shrunken are proposed to solve such model under investigation, which combines classic numerical method and numerical simulation techniques in an effective statistical form which is shrunken estimation formula. Two numerical simulation methods are used firstly to solve this model: Mean Monte Carlo Runge-Kutta and Mean Latin Hypercube Runge-Kutta Methods. Then two approximate simulation methods are proposed to solve the current study. The results of the proposed approximate shrunken methods and the numerical

The objective of the study was to identify the effect of the use of the Colb model for the students of the third stage in the College of Physical Education and Sports Sciences, University of Baghdad,As well as to identify the differences between the research groups in the remote tests in learning skills using the model Colb.The researcher used the experimental method and included the sample of the research on the students of the third stage in the College of Physical Education and Sports Science / University of Baghdad by drawing lots, the third division (j) was chosen to represent the experimental group,And the third division (c) to represent the control groupafter the distribution of the sample splitting measure according to the Colb mode

The research targets study of influence of additives on sand mold’s properties and, consequently, on
that of carbon steel CK45 casts produced by three molds. Three materials were selected for addition
to sand mix at weight percentages. These are sodium carbonates, glycerin and oat flour. Sand molds
of studied properties were produced to get casts from such molds. The required tests were made to
find the best additives with respect to properties of cast. ANSYS software is used to demonstrate
the stresses distribution of each produced materials. It is shown that the mechanical properties of
casts produced is improved highly with sodium carbonates and is less with oat flour and it is seem a
few with glycerin additives

This research aims to identify the impact of the selective model in acquiring the concepts of Kurdish grammar among female students in the eighth grade, and to achieve the goal of research, the researcher selected the experimental design with partial control  and dimensional testing; the sample includes basic schools in the Chim district of Chamal/ Sulaymaniyah and randomly selected the basic school (Maha Bad) to be the field of application of the experiment and the random drawing method was chosen: two out of three sections and the number of students of the two sections is (75) students; section (C) represents the experimental group that studied the rules according to the selective model and its number is (37) students, while secti

This research aims to find out the impact on the receptive style according to the specimen in the collection of material Brawner and retention as students at the Arabic Department at the Faculty of Education for Girls. For confirmation from the goal of the research, the researcher placed two hypotheses, one to two for collections and one for pods. - chosen as the College of Education for Girls / Department of Arabic language for the application of choice Intentionally search experience for reasons of researcher he is teaching them and thus ensures cooperation of teachers and students in them. - selected Division (b) of the fourth grade students of the Arabic language section at random to represent the experimental group, while the Division

The current research aims to find out ( the effectiveness of the structural model of learning in the acquisition of geographical concepts at the first grade average students ) , and achieving the goals of research has been formulating the null hypothesis of the following :

    " There is no difference statistically significant when Mistoi (0.5 ) between the mean scores of the collection of students in the experimental group that is studying the general geographical principles " Bonmozj constructivist learning " and the mean scores of the control group , which is considering the same article ," the traditional way " to acquire concepts.

The researcher adopted th