In this paper, as generalization of second modules we introduce type of modules namely (essentially second modules). A comprehensive study of this class of modules is given, also many results concerned with this type and other related modules presented.

        Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of  weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an

Often phenomena suffer from disturbances in their data as well as the difficulty of formulation, especially with a lack of clarity in the response, or the large number of essential differences plaguing the experimental units that have been taking this data from them. Thus emerged the need to include an estimation method implicit rating of these experimental units using the method of discrimination or create blocks for each item of these experimental units in the hope of controlling their responses and make it more homogeneous. Because of the development in the field of computers and taking the principle of the integration of sciences it has been found that modern algorithms used in the field of Computer Science genetic algorithm or ant colo

In thisipaper, we introduce the concepts of the modified tupledicoincidence points and the  mixed finiteimonotone property. Also the existenceiand uniquenessiof modified tupled coincidenceipoint is discusses without continuous condition for mappings having imixed finite monotoneiproperty in generalizedimetric spaces.

The major target of this paper is to study a confirmed class of meromorphic univalent functions . We procure several results, such as those related to coefficient estimates, distortion and growth theorem, radii of starlikeness, and convexity for this class, n additionto hadamard product, convex combination, closure theorem, integral operators, and  neighborhoods.

         Saccharomyces cerevisiae filtrate showed inhibitory effect against Fusarium spp. when grow in a liquid medium (Sabouraud) with different concentrations (1, 3, 5) %. The higher inhibitory effect against fungus growth was (24.5) mm at (5%) in PDA medium compared with control (36.5) mm during the seventh day propagation. The filtrate of Lactobacillus plantarum isolate was mixed with the PDA medium ,which showed inhibitory effect against Fusarium spp. The concentrated filtrate( one fold) appcarcd a  higher effect against the same fungus compared with un concentrated filtrate one. Saceharomyces cerevisiae and Lactobacillus plantarum

Background: Infection with Hepatitis C virus (HCV) is a major cause of chronic liver disease, WHO estimated that about 170 million people are infected with Hepatitic C virus, Silymarin (Legalon) have been recently shown to be effective in treatment of Hepatitic C virus infection.
Objectives: The effectiveness of Legalon (Silymarin) on viral load in patients with Hepatitic C virus infection.
Patients and methods: A prospective case – control study included 400 patients with Hepatitis C virus infection. 200 patients (group A) were treated with (peg-interferon, ribavirin, silymarin) the other 200 patients (group B) were treated with (peg-interferon, ribavirin) . only G1 & G4 genotypes were included , viral load were assessed ini

  In this paper we introduce the notion of semiprime fuzzy module as a generalization of semiprime module. We investigate several characterizations and properties of this concept.

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed