In this paper, we introduce the notion of a 2-prime module as a generalization of prime module E over a ring R, where E is said to be prime module if (0) is a prime submodule. We introduced the concept of the 2-prime R-module. Module E is said to be 2-prime if (0) is 2-prime submodule of E. where a proper submodule K of module E is 2-prime submodule if, whenever rR, xE, E, Thus xK or [K: E].

This book includes four main chapters: 1. Indefinite Integral. 2. Methods of Integration. 3. Definite Integral. 4. Multiple Integral. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.

  In this paper we introduced the concept of 2-pure submodules as a generalization of pure submodules, we study some of its basic properties and by using this concept we define the class of 2-regular modules, where an R-module M is called 2-regular module if every submodule is 2-pure submodule. Many results about this concept are given. 

The effect of the annealing on the optical transmission , absorp tion coefficient,
dielectric constants (ε
r
),( ε
i
) ,Skin depth and the optical ener gy gap of (ZnO)x(CdO)1-x thin
films with (x=0.05) deposited on preheated glass substrates at a temperature of (450 C°) by
chemical pyrolysis technique were performed . These f ilms show direct allowed inter band
transition that influenced by annealing at ( 450 C°) for two hours . And it also found that the
optical ener gy gap has been increased fro m about (2.50 eV) before annealing to about (2.65
eV) after annealing , fro m the analysis of the absorp tion and transmission sp ectra in the
wavelength range (380-900nm) . The results show t

Ferrite with general formula Ni1-x Cox Fe2O4(where x=0.0.1,0.3,0.5,0.7, and 0.9), were prepared by standard ceramic technique. The main cubic spinel structure phase for all samples was confirmed by x-ray diffraction patterns. The lattice parameter results were (8.256-8.299 ^°A). Generally, x -ray density increased with the addition of Cobalt and showed value between (5.452-5.538gm/cm³). Atomic Force Microscopy (AFM) showed that the average grain size and surface roughness was decreasing with the increasing cobalt concentration. Scanning Electron Microscopy images show that grains had an irregular distribution and irregular shape. The A.C conductivity was found to increase with the frequency and the addition of Cobal

Bulk polycrystalline samples have been prepared by the two-step solid state reaction process. It has been observed that as grown Tl2-xHgxSr2Ca2Cu3O10+δ (with x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1) corresponds to the 2223 phase. It has been found that Tc varies with Hg content .The optimum Tc is about 120K for the composition Tl1.6Hg0.4Sr2Ca2Cu3O10+δ.The microstructure for Tl1.6Hg0.4Sr2Ca2Cu3O10+δ observed to be most dense and this phase exhibits the highest stability.

Synthesis And Studies Of Complexes Of Some Elements With 2-Mercaptohiazole (2-HMBT)

     In this research, the Boiti–Leon–Pempinelli (BLP) system was used to understand the physical meaning of exact and solitary traveling wave solutions. To establish modern exact results, considered. In addition, the results obtained were compared with those obtained by using other existing methods, such as the standard hyperbolic tanh function method, and the stability analysis for the results was discussed.

     In this study, the electron energy distribution function (EEDF), the electron swarm parameters , the effective ionization coefficients, and the critical field strength (dielectric strength) in binary He-H₂ gas mixture which is used as cryogenic for high-temperature superconducting power applications,  are evaluated using two-term solution  of the Boltzmann equation over the range of E/N ( the electric field to gas density) from 1 to 100 Td ( 1 Td=10^-17 Vcm²) at temperature 77 K and pressure 2MPa, taking into account elastic ( momentum transfer) and inelastic cross-sections. Using the electron energy distribution function (EEDF) electron swarm parameters (electron drift velocity, mean electron e