Discriminant analysis is a technique used to distinguish and classification an individual to a group among a number of  groups based on a linear combination of a set of relevant variables know discriminant function. In this research  discriminant analysis used to analysis data from repeated measurements design. We  will  deal  with the problem of  discrimination  and  classification in the case of  two  groups by assuming the Compound Symmetry covariance structure  under  the  assumption  of  normality for  univariate  repeated measures data.

Let R be a commutative ring with unity 1 6= 0, and let M be a unitary left module over R. In this paper we introduce the notion of epiform∗ modules. Various properties of this class of modules are given and some relationships between these modules and other related modules are introduced.

Throughout this paper we introduce the notion of coextending module as a dual of the class of extending modules. Various properties of this class of modules are given, and some relationships between these modules and other related modules are introduced.

Let R be a commutative ring with identity, and let M be a unitary (left) R- modul e. The ideal annRM  = {r E R;rm  = 0 V  mE M} plays a central

role  in  our  work.  In  fact,  we  shall  be  concemed   with  the  case  where annR1i1 = annR(x) for   some   x EM such  modules  will  be  called bounded  modules.[t  htrns out that there are many classes of modules properly contained in the class of bounded modules such as cyclic modules, torsion -G·ee modulcs,faithful  multiplicat

            This paper is interested in certain  subclasses of univalent and bi-univalent functions concerning  to shell- like curves connected with k-Fibonacci numbers involving modified Sigmoid activation function θ(t)=2/(1+e^(-t) ) ,t ≥0 in unit disk |z|<1 . For estimating of the initial coefficients |c_2 | , |c_3 |, Fekete-Szego ̈ inequality and the  second Hankel determinant have been investigated for the functions in our classes. 

  Let M be an R-module, where R is commutative ring with unity. In this paper we study the behavior of strongly hollow and quasi hollow submodule in the class of strongly comultiplication modules. Beside this we give the relationships between strongly hollow and quasi hollow submodules with V-coprime, coprime, bi-hollow submodules.

Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of

 The current specialized research tagged (intellectual and artistic concepts of the cultural context and their impact on contemporary ceramic sculpture) paves the way for the emergence of the context in ceramics active in life, so that this relationship will indicate the development and presence of ceramics or not and the volume of its circulation in the joints of the culture of the Arab recipient. As a result, the researcher collected scientific materials to serve the subject of the research in four chapters: Chapter One (General Methodological Framework) To clarify the problem of the research, the importance of the research to achieve benefit in higher education and education for scholars and teachers, while the research aims to revea

“Child of today is a man of the future" this slogan is one of the most popular logos of international organizations and institutions that dealing with human beings needs in general and children needs in particular, whether these needs are educational, health, social, or economic. Children require special care and extra legal protection, since the child-raising is not the Child’s own issue, but it's the issue of the society in which he/she would integrate.

As the education and language skillsacquisition primarily associated with hearing, because human being receives most of the skills and knowledge through the hearing; that imitate sounds and learn how to speak isacquired only by hearing, so therefore the hearing - impairedchi