For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptio

The aim of this article is to study the dynamical behavior of an eco-epidemiological model. A prey-predator model comprising infectious disease in prey species and stage structure in predator species is suggested and studied. Presumed that the prey species growing logistically in the absence of predator and the ferocity process happened by Lotka-Volterra functional response. The existence, uniqueness, and boundedness of the solution of the model are investigated. The stability constraints of all equilibrium points are determined. The constraints of persistence of the model are established. The local bifurcation near every equilibrium point is analyzed. The global dynamics of the model are investigated numerically and confronted with the obt

The prediction of the blood flow through an axisymmetric arterial stenosis is one of the most important aspects to be considered during the Atherosclrosis. Since the blood is specified as a non-Newtonian flow, therefore the effect of fluid types and effect of rheological properties of non-Newtonian fluid on the degree of stenosis have been studied. The motion equations are written in vorticity-stream function formulation and solved numerically. A comparison is made between a Newtonian and non-Newtonian fluid for blood flow at different velocities, viscosity and Reynolds number were solved also. It is found that the properties of blood must be at a certain range to preventing atheroscirasis

  In this work, the theoretical study for designing of dielectric mirrors of high reflectance in the visible region of electromagnetic spectrum between wavelength of 400-700 nm is presented, and searching on the performance properties of the design, like there reflectance as a function to the wavelength, as beam incident in a normal form, for the materials of neglected absorbance, and scattering, in the form of thin film deposition, which are deposited on glass substrate, and by using matrix system in the study, which are used as computer simulation in MATLAB code.      The materials which are used in this study are represented by ( AlAs ), (TiO2 ),( SiC ), and  (Si3N4 ), which used in the designing mirrors alter

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This research aims to know and the role of the marketing recovery dimensions in improving the organization's reputation through an exploratory study of private banks in the city of Baghdad. The aim of the research is to define the role of the marketing recovery through its dimensions (compensation, apology, speed of response, assistance and problem solving), in improving the organization's reputation, as the research will attempt to provide a theoretical framework for the dimensions studied through the most important of what researchers presented and then conduct the applied aspect of the research. Data were collected using a questionnaire-based survey consisting of 35 questions and distributed to 110 managers of private banks in

The Audit evedances represent the reconciliation tools between the Financial data shown on financial statements, and the level of satisfaction level of the Auditor about these statements. According that, the Auditor try to achieve the highest quantity of These evidances, and the most satisfactive of it…, but that will be so hard sometimes, when the internal controlling system is not good, and when the Auditor had some satisfied evidences, but not sharp… So, this research comes to inspect the relation between the quantity, and the level of satisfaction, and argument to prove that evidences gives. This research assumes that getting enough evidences leads to reduce faults, improves the auditing operation, and avoids risks. The research

This study aimed at revealing the degree of availability of standards of word problems in mathematics books for the first three grades of the basic stage in Palestine. For this purpose, the researcher prepared an analysis tool and a list of criteria consisting of two areas: linguistic formulation and mathematical content. Every area had seven items. The results of the study showed that the third-grade mathematics book has the highest degree of availability of the standards with 85.75%, and then came the second-grade mathematics book with 83.12%. Finally, the first-grade mathematics book came with 80.13%. In the light of the previous results, the researcher recommended to develop the language of word problems, to take into account their i