Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes

The problem of rapid population growth is one of the main problems effecting countries of the world the reason for this the growth in different environment areas of life commercial, industrial, social, food and educational. Therefore, this study was conducted on the amount of potable water consumed using two models of the two satellite and aerial images of the Kadhimiya District-block 427 and Al-Shu^,laa district-block 450 in Baghdad city for available years in the Secretariat of Baghdad (2005, 2011,2013,2015). Through the characteristics of geographic information systems, which revealed the spatial patterns of urban creep by determining the role and buildings to be created, which appear in the picture for the

In this paper by using δ-semi.open sets we introduced the concept of weakly δ-semi.normal and δ-semi.normal spaces . Many properties and results were investigated and studied. Also we present the notion of δ- semi.compact spaces and we were able to compare with it δ-semi.regular spaces

The importance of knowledge is represented in the use of various sources of information, the corresponding to the same level of importance is the use of modern means and technologies in the delivery and investment of these sources to the beneficiaries, among these means and technologies are the multimedia that deal with most of the human senses, but the most important of which is sight and hearing, if these are invested the means in the field of education will give many positive results, such as the speed of receiving information, its clarity, and its freedom from impurities and influences, as well as its stability in memory as it is based on nderstanding, not memorization. On this basis, the experience of supporting the education process

Abstract

Black paint laser peening (bPLP) technique is currently applied for many engineering materials , especially for aluminum alloys due to high improvement in fatigue life and strength . Constant and variable   bending fatigue tests have been performed at RT and stress ratio R= -1 . The results of the present  work observed that the significance of the surface work hardening which generated high negative residual stresses in bPLP specimens .The fatigue life  improvement factor (FLIF)  for bPLP constant fatigue behavior was from 2.543 to 3.3 compared to untreated  fatigue and the increase in fatigue strength at 10⁷ cycle was 21% . The bPLP cumulative fatigue life behav

Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.

The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.

The significance of the research lies in the fact that electronic technologies represent an important step in evaluating legal situations, and the research problem centered on the lack of attention to visual requirements and the absence of a clear image of legal situations that may be difficult for the referee to apply correctly in addition to the lack of focus on visual requirements and the unclear depiction of some legal cases which make it difficult for the referee to interpret them correctly This is because the referee's main tool is visual perception, which interprets live situations such as violations, fouls, and other cases that arise during a game Moreover, there are numerous responses and challenges in evaluating legal situ

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

        In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using  Mathcad 15.and graphic in Matlab R2015a.