Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.

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

Abstract

There have been a number of positive developments in inclusive education in many different countries, recognizing that all students, including those with disabilities, have a right to education. Around the world, educators, professionals, and parents are concerned about including children with disabilities in mainstream schools along with their peers. As a result of this trend, a number of factors are contributing, including the increasing importance of education in achieving social justice for pupils with special education needs; the right of individuals with disabilities to attend mainstream schools together with their typically developing peers; the benefit of equal opportunities for everyone in achie

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

The present work investigates the effect of; superficial air velocities of: 1, 3, and 6 cm/s for two types of perforated distributor on hydrodynamic characteristic in a gas-liquid dispersion column of; air-water, and airaqueous-n-propanol solution. Bubble distribution, gas holdup, and power consumption are parameters take in consideration. Experimental work was carried out in perspex column of 8.5 cm inside diameter and 1.5 m height. Two types of bubble generator (perforated plate) were fixed at the bottom of the column; plate A (99 holes of 0.5 mm diameter and free area of 0.34%), plate B (20 holes of 1.5 mm diameter and free area of 0.62%). Photographic technique was used to measure the bubble parameters. The experimental results were

In the United States, the pharmaceutical industry is actively devising strategies to improve the diversity of clinical trial participants. These efforts stem from a plethora of evidence indicating that various ethnic groups respond differently to a given treatment. Thus, increasing the diversity of trial participants would not only provide more robust and representative trial data but also lead to safer and more effective therapies. Further diversifying trial participants appear straightforward, but it is a complex process requiring feedback from multiple stakeholders such as pharmaceutical sponsors, regulators, community leaders, and research sites. Therefore, the objective of this paper is to describe three viable strategies that can p

Multi-spectral satellite images of the Landsat satellite by the tow sensitive Thematic Mapper (TM) and Thematic Mapper Enhancement (ETM+), which covered the study area located south east of Iraq. In this research; used the sixth thermal spectral band (Thermal Band) for study the water cover in the Al-Razzaza Lake located within the province of Karbala. We intended to study the cover a case of the study area, used satellite images showing the status of region during the period from 1990 to 2001 and 2007. From this study we conclude that cover the water of the study area change in sequence case to decrease during these years.

This work is concerned with the design and performance evaluation of a shell and double concentric tubes heat exchanger using Solid Works and ANSY (Computational Fluid Dynamics).

Computational fluid dynamics technique which is a computer-based analysis is used to simulate the heat exchanger involving fluid flow, heat transfer. CFD resolve the entire heat exchanger in discrete elements to find: (1) the temperature gradients, (2) pressure distribution, and (3) velocity vectors.  The RNG k-ε model of turbulence is used to determining the accurate results from CFD.

The heat exchanger design for this work consisted of a shell and eight double concentric tubes. The number of inlets are three and that of o