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,

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

Prodigiosin, is a natural red pigment produced by various bacteria that firstly
characterized from Serratia marcescens. It is an alkaloid secondary metabolite with
a unique tripyrrol structure.This pigment is a promising drug owing to its reported
characteristics of having antifungal, immunosuppressive and anti-cancer activity. In
this study prodigiosin was produced by Serratia marcescens., which was isolated
from soil identified and characterized by morphology, Gram’s staining, biochemical
and carbohydrate fermentation tested and confirmed by the API 20E test.
From these samples, six isolates of Serratia marcescens( 24) % were obtained out
of 25 soil samples. Ability of these isolates in prodigiosin production

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

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

The nonlinear refractive (NLR) index and third order susceptibility (X3) of carbon quantum dots (CQDs) have been studied using two laser wavelengths (473 and 532 nm). The z-scan technique was used to examine the nonlinearity. Results showed that all concentrations have negative NLR indices in the order of 10−10 cm2/W at two laser wavelengths. Moreover, the nonlinearity of CQDs was improved by increasing the concentration of CQDs. The highest value of third order susceptibility was found to be 3.32*10−8 (esu) for CQDs with a concentration of 70 mA at 473 nm wavelength.