Throughout this paper R represents commutative ring with identity, and M is a unitary left R-module. The purpose of this paper is to study a new concept, (up to our knowledge), named a semi-extending modules, as generalization of extending modules, where an Rmodule M is called semi-extending if every sub module of M is a semi-essential in a direct summand of M. Various properties of semi-extending module are considered. Moreover, we investigate the relationships between semi-extending modules and other related concepts, such as CLS-modules and FI- extending modules.

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .

    In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

Ab – initio density function theory (DFT) calculations coupled with Large Unit Cell (LUC) method were carried out to evaluate the electronic structure properties of III-V zinc blend (GaAs). The nano – scale that have dimension (1.56-2.04)nm. The Gaussian 03 computational packages has been employed through out this study to compute the electronic properties include lattice constant, energy gap, valence and conduction band width, total energy, cohesive energy and density of state etc. Results show that the total energy and energy gap are decreasing with increase the size of nano crystal . Results revealed that electronic properties converge to some limit as the size of LUC increase .

In this research PbS and PbS:Cu films were prepered with thicknesses (0.85±0.05)?m and (0.55±0.5)?m deposit on glass and silicon substrate respectively using chemical spray pyrolysis technique with a substrate temperature 573K, from lead nitrate salt, thiourea and copper chloride. Using XRD we study the structure properties for the undoped and doped films with copper .The analysis reveals that the structure of films were cubic polycrystalline FCC with a preferred orientation along (200) plane for the undoped films and 1% doping with copper but the orientation of (111) plane is preferred with 5% doping with the rest new peaks of films and appeared because of doping. Surface topography using optical microscope were be checked, it was found

      This paper offers a monthly prediction method for planning production, inventory, workforce, sales and prices until N years. Each monthly decision will depend on last month, decisions and take in consideration the future forecasted demand. The manager can run the program in any month within a year. This method is executed by computer programming technique to maximize profits.

 Lighting is a very important element of treatment if the color contains many imaging system (digital cameras) and the unit of light and the light within these units are not strong , but usefel when the light is low , in different lighting intensities conditions image quality will not persist good enough and image may become dark or slightly exposed to light which leads to lower the details in image where we can not modify contrast or light ness to compensate thr decrease without losing the light and dark deatials . So we went in this research to study the variation colored texts written on the painting and lighting cases of non –regular ( a few) and different distances . As the diversity of these texts written on the board a

Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.

The effect of heat treatment using different annealing temperatures on optical properties of bulk heterojunction blend (BHJ) Alq3: C60 thin films which are fabricated by the spin coating technique were investigated in this study. The films have been coated on a glass substrate with speed of 2000 rpm for one min and treated with different annealing temperature (373, 423 and 473) K under vacuum. The optical properties and the chemical bonds structure of blends as-deposited and heat treated have been studied by UV-Vis spectroscopic and Fourier Transform-Infra Red (FTIR) measurements respectively. The results of UV visible show that the optical energy gap decreasing with increasing the annealing temperature for the ratio (100:1) while decrea