Suppose that A be an abelain ring with identity, B be a unitary (left) A-module, in this paper ,we introduce a type of modules ,namely Quasi-semiprime A-module, whenever   is a Prime Ideal For proper submodule N of  B,then B is called Quasi-semiprime module ,which is a Generalization of Quasi-Prime A-module,whenever  ann_AN is a prime ideal for proper submodule N of B,then B is Quasi-prime module .A comprchensive study of these modules is given,and we study the Relationship between quasi-semiprime module and quasi-prime .We put the codition coprime over cosemiprime ring for the two cocept quasi-prime module and quasi-semiprime module are equavelant.and the cocept of  prime module and quasi

  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 R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.

 This paper devoted to the analysis of regular singular boundary value problems for ordinary differential equations with a singularity of the different kind , we propose semi - analytic technique using two point osculatory interpolation to construct polynomial solution, and discussion behavior of the solution in the neighborhood of the regular singular points and its numerical approximation. Many examples are presented to demonstrate the applicability and efficiency of the methods. Finally , we discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems.

In this article, we study some properties of anti-fuzzy sub-semigroup, anti fuzzy left (right, two sided) ideal, anti fuzzy ideal, anti fuzzy generalized bi-ideal, anti fuzzy interior ideals and anti fuzzy two sided ideal of regular semigroup. Also, we characterized regular LA-semigroup in terms of their anti fuzzy ideal.

This research deals with Salinger's concerns about predicaments of youth like Franny and her brother Zooey. Their predicaments are related to identity, family, religion, beliefs, life and death, education, source of power, and society. It illustrates adults struggle to adapt themselves to live a normal social American life. It proves necessary to balance their coexistence in a materialistic milieu to achieve spiritual peace, tranquility, and stability.

Let R be a ring with 1 and W is a left Module over R. A Submodule D of an R-Module W is small in W(D ≪ W) if whenever a Submodule V of W s.t W = D + V then V = W. A proper Submodule Y of an R-Module W is semismall in W(Y ≪_S W) if Y = 0 or Y/F ≪ W/F ∀ nonzero Submodules F of Y. A Submodule U of an R-Module E is essentially semismall(U ≪es E), if for every non zero semismall Submodule V of E, V∩U ≠ 0. An R-Module E is essentially semismall quasi-Dedekind(ESSQD) if Hom(E/W, E) = 0 ∀ W ≪es E. A ring R is ESSQD if R is an ESSQD R-Module. An R-Module E is a scalar R-Module if, ∀ , ∃ s.t V(e) = ze ∀ . In this paper, we study the relationship between ESSQD Modules with scalar and multiplication Modules. We show that

Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered.

In this paper, the concept of semi-?-open set will be used to define a new kind of strongly connectedness on a topological subspace namely "semi-?-connectedness". Moreover, we prove that semi-?-connectedness property is a topological property and give an example to show that semi-?-connectedness property is not a hereditary property. Also, we prove thate semi-?-irresolute image of a semi-?-connected space is a semi-?-connected space.

The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex