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.

In this work, seven soil samples were brought brought to study and analyses the element concentrations from different southern regions of Iraq using laser-induced breakdown spectroscopy (LIBS) technique. It has been documented as an atomic emission spectroscopy (AES) technique. Laser-induced plasma utilized to analyze elements in materials (gases, liquids, and solids). In order to analyze elements in materials (gases, liquids, and solid). The Nd: YAG laser excitation source at 1064 nm with pulse width 9 ns is used to generate power density of 5.5 x 1012 MW/mm2, with optical spectrum in the range 320-740 nm. From this investigation, the soil sample analysis of the southern cities of Iraqi, it is concluded that the rich soil element of P, Si,

This study aims to develop a recommendation engine methodology to enhance the model’s effectiveness and efficiency. The proposed model is commonly used to assign or propose a limited number of developers with the required skills and expertise to address and resolve a bug report. Managing collections within bug repositories is the responsibility of software engineers in addressing specific defects. Identifying the optimal allocation of personnel to activities is challenging when dealing with software defects, which necessitates a substantial workforce of developers. Analyzing new scientific methodologies to enhance comprehension of the results is the purpose of this analysis. Additionally, developer priorities were discussed, especially th

Field trial was conducted during the growing season of 2011-2012 at the Research
Field, Department of Biology, College of Science, Baghdad University to test the
performance of wheat cv Rabyaa, Latifiya, Al-Iraq, Tummose 2, Abu-Graib 3, IPA
99 and Sham 6 grown under different soil water deficit stresses. Several agronomic
and physiological traits and yield and yield components of the test cultivars were
determined. The experiment was conducted in split plot design with five replications
for each treatment. The cultivars were kept in the sub plot while water stress
treatment was assigned as main plot. Water stress was applied by irrigated the plots
to the soil field capacity (FC) then withheld next irrigation until

The subject of social capital is of great importance, as it provides an analytical framework for researchers interested in understanding the impact of the Internet on many dimensions of human and social life. And because social networking sites have infiltrated societies and produced new variables at the level of human and social communication, this study came to examine the relationship between the use of the social networking site Facebook and the accumulation of social capital among a sample of University of Algeria 3 students, by researching the variables of intensity of use and patterns of use as independent variables and their relationship to social capital. The results of the field study revealed a strong relationship between the

Refractive indices (nD), viscosities (η) and densities (r) were deliberated for the binary mixtures created by dipropyl amine with 1-octanol, 1-heptanol, 1-hexanol, 1-pentanol and tert-pentyl alcohol at temperature 298.15 K over the perfect installation extent. The function of Redlich-Kister were used to calculate and renovated of the refractive index deviations (∆nD), viscosity deviations (ηE), excess molar Gibbs free energy (∆G*E) and excess molar volumes(Vm E). The standard errors and coefficients were respected by this function. The values of ∆nD, ηE, Vm E and ∆G*E were plotted against mole fraction of dipropyl amine. In all cases the obtained ηE, ∆G*E, Vm E and ∆nD values were negative at 298.15K. Effect of carbon atoms

Recently, Social Sustainability has gained significant value as it was considered by the late studies as a principal dimension along with the environmental and economic sustainability. And because of, on the other hand, the significant social role of the school for forming the student’s personality, this research is an appeal for rehabilitating and promoting Iraqi Schools according the issue of social sustainability.As there is no evaluation for the Iraqi Schools, the research is dedicated to this problem, aiming to carry out the stated evaluation and define the design treatments needed for the rehabilitation process. To achieve this goal, a theoretical background for the concept of social sustainability, its criteria, the school and i

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.

Buckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g