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. 

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

The effect of substitution of Ni on Cu in (Bi0.8Pb0.2)2(Sr0.9Ba0.1)2 Ca2Cu3-x Nix O10+? for (x=0,0.1….1,2,3) superconductor system and sintering time has been investigated .The samples were prepared by solid-state reaction methods. The results show that the optimum sintering temperature is equal to 850 ºC, and the sintering time is equal to 140 h. The highest transition temperature (Tc) obtained for (Bi0.8Pb0.2)2(Sr0.9Ba0.1)2 Ca2Cu3-x NixO10+? composition was 113 with x=0.8 Phase analyses of the samples by X-ray diffraction (XRD) analysis showed an orthorhombic structure with a high Tc phases (2223) as a dominant phase and low Tc phase (2212) in addition to some impurity phases.

Four electrodes were synthesized based on molecularly imprinted polymers (MIPs). Two MIPs were prepared by using the diclofenac sodium (DFS) as the template, 2-hydroxy ethyl metha acrylate(2-HEMA) and 2-vinyl pyridine(2-VP) as monomers as well as divinyl benzene and benzoyl peroxide as cross linker and initiator respectively. The same composition used for prepared non-imprinted polymers (NIPs) but without the template (diclofenac sodium). To prepared the membranes electrodes used different plasticizers in PVC matrix such as: tris(2-ethyl hexyl) phosphate (TEHP), tri butyl phosphate (TBP), bis(2-ethyl hexyl) adipate (BEHA) and tritolyl phosphate (TTP). The characteristics studied the slop, detection limit, life time and linearity range of DF

In modern hydraulic control systems, the trend in hydraulic power applications is to improve efficiency and performance. “Proportional valve” is generally applied to pressure, flow and directional-control valves which continuously convert a variable input signal into a smooth and proportional hydraulic output signal. It creates a variable resistance (orifice) upstream and downstream of a hydraulic actuator, and is meter in/meter out circuit and hence pressure drop, and power losses are inevitable. If velocity (position) feedback is used, flow pattern control is possible. Without aforementioned flow pattern, control is very “loose” and relies on “visual” feed back by the operator. At this point, we should examine how this valv

Background: Toll-like receptor -2 (TLR-2)play important roles in tumor biology; by activation and promotion of tumor cell proliferation, resistance to apoptosis andalso, enhancement of tumor cell invasion and metastasis by regulating metalloproteinase and integrin’s.As toll-like receptors are widely expressed on tumor cells and participatein the initiation and progression of cancer, they may thus serve an important target and have an effective perspective on breast cancer treatment.
Objectives:The aims of the present study was to determine the levels of TLR-2 in the sera of healthy people and patients with benign and malignant breast tumors and also to investigate the validity of using TLR-2 as specific diagnostic markers of breast

      Let R be a commutative ring with unity. And let E be a unitary R-module. This paper introduces the notion of 2-prime submodules as a generalized concept of 2-prime ideal, where proper submodule H of module F over a ring R is said to be 2-prime if , for r R and x F implies that  or . we prove many properties for this kind of submodules, Let H is a submodule of module F over a ring R then H is a 2-prime submodule if and only if [N ] is a 2-prime submodule of E, where r R. Also, we prove that if F is a non-zero multiplication module, then [K: F] [H: F] for every submodule k of F such that H K. Furthermore, we will study the basic properties of this kind of submodules.

     We introduce in this paper, the notion of a 2-quasì-prime module as a generalization of quasi-prime module, we know that a module E over a ring R is called quasi-prime module, if (0) is quasi-prime submodule. Now, we say that a module E over ring R is a 2-quasi-prime module if (0) is 2-quasi-prime submodule, a proper submodule K of E is 2-quasi-prime submodule if whenever ,  and , then either  or .

Many results about these kinds of modules are obtained and proved, also, we will give a characterization of these kinds of modules.