Richards in 1996 introduced the idea of leftly e ─ core transference by using many conditions, including that the difference between the colums (k) is greater than of weight. In this paper, we generalized this idea without the condition of Richards depending on the mathematical and computational solution.

     . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper,we introduce the generalized Cayley graph denoted by  which is a graph with a vertex set consisting of all column matrices  in which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of the similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and  and m . We aim to provide some basic properties of the new graph and determine the structure of  when  is a complete graph  for every , and n, m  .

In this paper, we define the concept of soft -connected sets and soft -connected spaces by using the notion of soft -open sets in soft topological spaces. Several properties of these concepts are investigated.

Background: Reports denote that changes in day length enhance or suppress components of immune function in several mammalian species. The aim of present experimental study is
directed to test the hypothesis deals with the effect of photoperiods on some immune limbs responsiveness.
Materials and Methods: Twenty six male and female BALB/C mice, 5-7 weeks old, 14- 18gm weight divided into two groups, test groups (n.=8 mice for each sex) and control
groups (n.=5 for each sex). Test groups were kept in a dark room for a month, while control groups were kept in a room where the photoperiod was day light: darkness 12:12hr. All
studied groups immunized with o.2ml (10% sheep red blood cells) on day 4 and 8 of the l

Let R be a 2-torision free prime ring and ?, ?? Aut(R). Furthermore, G: R×R?R is a symmetric generalized (?, ?)-Biderivation associated with a nonzero (?, ?)-Biderivation D. In this paper some certain identities are presented satisfying by the traces of G and D on an ideal of R which forces R to be commutative

We presented in this paper a new class containing analytic univalent functions defined on unit disk. We obtained many geometric properties , like , coefficient inequality , distortion and growth theorems, convolution property, convex set, arithmetic mean and radius of starlikness and convexity by using Gaussian hypergeometric function for the class

       Th  goal of the pr s nt p p r is to obt in some differ tial sub rdin tion an  sup r dination the rems for univalent functions related b  differential operator  Also, we discussed some sandwich-type results.

The main goal of this paper is to study applications of the fractional calculus techniques for a certain subclass of multivalent analytic functions on Hilbert Space. Also, we obtain the coefficient estimates, extreme points, convex combination and hadamard product.

In this paper a Г-ring M is presented. We will study the concept of orthogonal generalized symmetric higher bi-derivations on Г-ring. We prove that if M is a 2-torsion free semiprime    Г-ring ,  and  are orthogonal generalized symmetric higher bi-derivations  associated with symmetric higher bi-derivations   respectively for all n ϵN.