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

This paper deals with an analytical study of the flow of an incompressible generalized Burgers’ fluid (GBF) in an annular pipe. We discussed in this problem the flow induced by an impulsive pressure gradient and compare the results with flow due to a constant pressure gradient. Analytic solutions for velocity is earned by using discrete Laplace transform (DLT) of the sequential fractional derivatives (FD) and finite Hankel transform (FHT). The influences of different parameters are analyzed on a velocity distribution characteristics and a comparison between two cases is also presented, and discussed in details. Eventually, the figures are plotted to exhibit these effects.

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

   The inhibitive action of a blend of sodium nitrite/sodium hexametaphosphate (SN+SHMP) on corrosion of carbon steel in simulated cooling water systems (CWS) has been investigated by weight loss and electrochemical polarization technique. The effect of temperature, velocity, and salts concentrations on corrosion of carbon steel were studied in the absence and presence of mixed inhibiting blend. Also the effect of inhibitors blend concentrations (SN+SHMP), temperatures, and rotational velocity, i.e., Reynolds number (Re) on corrosion rate of carbon steel were investigated using Second-order Rotatable Design (Box-Wilson Design) in performing weight loss and corrosion potential approach. Electrochemical polarization measurements

In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

Expansion the engineering consultancy offices in the universities of Iraq, about (14) offices, leading to increas the competition between them, especially after the great trends of Iraqi government agencies to use the academic experiences and their efficiencies in general, due to non-existence of the engineering qualification in the government institutions to do the engineering designs ,supervision of projects and other engineering works which are practicing by the engineering consultancy offices in order to get the best performance of the work.Within this serious competition, needing a specific approach to enable government agencies to choose the optimal and alternative consultancy office to meet specific project and not rely on cronyis

The survival analysis is one of the modern methods of analysis that is based on the fact that the dependent variable represents time until the event concerned in the study. There are many survival models that deal with the impact of explanatory factors on the likelihood of survival, including the models proposed by the world, David Cox, one of the most important and common models of survival, where it consists of two functions, one of which is a parametric function that does not depend on the survival time and the other a nonparametric function that depends on times of survival, which the Cox model is defined as a semi parametric model, The set of parametric models that depend on the time-to-event distribution parameters such as

One of the most important challenges facing project management at present time is to ensure project accomplishment in spite of the specific restrictions like the specific time the financial resources specialized to do the project ; which require an accurate consideration for time and cost . the modern village project (residential building aspect) is one of the great project that ministry of agriculture is trying to do Wasit  governorate it is chosen as the work in this project is dilatory for that is being studied in term of some modern mathematical and scientific methods like critical path method (CPM)which is one of the project management and scheduling methods to know the time needed to accomplish residential building pro

A numerical study of the two-dimensional steady free convection flow in an inclined annulus between two concentric square cavities filled with a porous medium is presented in this paper for the case when the side outer walls are kept with differentially heated temperature while the horizontal outer walls and the inner walls are insulated. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value. The Darcy model is used and the fluid is assumed to be a standard Boussinesq fluid. For the Cartesian coordinate system, the governing equations which were used in stream function form are discretized by using the finite difference method with successive under – relaxation method (SUR) and are solv

One of the concerns of adopting an e-voting systems in the pooling place of any critical elections is the possibility of compromising the voting machine by a malicious piece of code, which could change the votes cast systematically. To address this issue, different techniques have been proposed such as the use of vote verification techniques and the anonymous ballot techniques, e.g., Code Voting. Verifiability may help to detect such attack, while the Code Voting assists to reduce the possibility of attack occurrence. In this paper, a new code voting technique is proposed, implemented and tested, with the aid of an open source voting. The anonymous ballot improved accordingly the paper audit trail used in this machine. The developed system,