The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓM-modules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c M and α,βΓ, is Jordan generalized triple higher derivation of M into X.

In this paper we introduced many new concepts all of these concepts completely
depended on the concept of feebly open set. The main concepts which introduced in
this paper are minimal f-open and maximal f-open sets. Also new types of
topological spaces introduced which called Tf min and Tf max spaces. Besides,
we present a package of maps called: minimal f-continuous, maximal f-continuous,
f-irresolute minimal, f-irresolute maximal, minimal f-irresolute and maximal firresolute.
Additionally we investigated some fundamental properties of the concepts
which presented in this paper.

     In this paper, we introduce the concept of generalized strong commutativity (Cocommutativity) preserving right centralizers on a subset of a Γ-ring. And we generalize some results of a classical ring to a gamma ring.

   The purpose of this paper is to study   new  types of open sets in bitopological spaces.    We shall introduce the concepts of  L- pre-open and L-semi-p-open sets

  5-(mercapto-1,3,4-thiadiazole-2yl)α,α-(diphenyl)methanol have been synthesized by ring closer of potassium xanthate[which  have been prepared by reaction of benzilic acid hydrazide with carbon disulphide in potassium hydroxide] using conc.sulphuric acid at (0-5)°C scheme(I).       Their characterization was carried out from T.L.C, M.P, FT.IR and 1H-NMR.

Background & Objective: Breast cancer (BC) is the most prevalent disease among women around the world, considered the world's leading cause of death (15% of the total cancer deaths) in women in 2018. β-catenin is a multifunctional protein located in the cytoplasm and/or nucleus of the cell. Several studies suggested that β-catenin expression plays a critical role in cancer invasion and metastasis. This research sought to examine β-catenin expression in breast cancer and its associations with clinico-pathological features (such as histopathological types, grade, and invasion depth of tumor as well as lymph node involvement) and breast cancer patient survival. Methods:

In this paper, we provide some types of - -spaces, namely, - ( )- (respectively, - ( )- , - ( )- and - ( )-) spaces for minimal structure spaces which are denoted by ( -spaces). Some properties and examples are given.
The relationships between a number of types of - -spaces and the other existing types of weaker and stronger forms of -spaces are investigated. Finally, new types of open (respectively, closed) functions of -spaces are introduced and some of their properties are studied.

  In this paper, we introduce a new class of sets, namely , s*g--open sets and we show that the family of all s*g--open subsets of a topological space ) ,X(  from a topology on X which is finer than  . Also , we study the characterizations and basic properties of s*g-open sets and s*g--closed sets . Moreover, we use these sets to define and study a new class of functions, namely , s*g-  -continuous functions and s*g-  -irresolute functions in topological spaces . Some properties of these functions have been studied .

In order to investigate the levels of reduced glutathione GSH and  α1-antitrypsine in the sera of 20 type 2 diabetic patients and 10 healthy subjects, were enrolled in this study. A significant reduction in GSH level was found in the patient group compared with control.  On the other hand a significant elevation in α1-antitrypsine in patient compared with control was observed.  Correlation between α1-antitrypsine and reduced glutathion was found to be positive (+Ve) for diabetes mellitus type2 patients and negative (-Ve) for healthy control with r values 0.257 and – 0.339 respectively.  In conclusion the depletion of GSH as antioxidant defense insured higher free radical generation in diabetic patients

This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations  like Mann, Ishikawa, oor, D- iterations, and *-  iteration for new contraction mappings called  quasi contraction mappings. And we  proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *-  iteration) equivalent to approximate fixed points of  quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type  by employing zenali iteration also discussed.