In this paper we introduce generalized (α, β) derivation on Semirings and extend some results of Oznur Golbasi on prime Semiring. Also, we present some results of commutativity of prime Semiring with these derivation.
This paper introduces some properties of separation axioms called α -feeble regular and α -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our α -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.
The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.
In this work we define and study new concept of fibrewise topological spaces, namely fibrewise soft topological spaces, Also, we introduce the concepts of fibrewise closed soft topological spaces, fibrewise open soft topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces.
We introduce and discuss recent type of fibrewise topological spaces, namely fibrewise soft bitopological spaces. Also, we introduce the concepts of fibrewise closed soft bitopological spaces, fibrewise open soft bitopological spaces, fibrewise locally sliceable soft bitopological spaces and fibrewise locally sectionable soft bitopological spaces. Furthermore, we state and prove several propositions concerning these concepts.
Background. Alopecia areata (AA) is a common form of noncicatricial hair loss of unknown cause, affecting 0.1-0.2% of the general population. Most evidence supports the hypothesis that it is disease of the hair follicle of autoimmune nature mediated by T-cells, with important cytokine role. Objective of the Study. The objective of this study is to study the association and changes in serum levels of interleukin-15 (IL-15) and tumor necrosis factor-α (TNF-α) in patients with AA in relation to the type, activity, and disease duration. Patients and Methods. Thirty-eight patients with AA and 22 individuals without the disease as controls were enrolled in this case-controlled study conducted in the Department of Dermatology in the Al-K
... Show MoreIn this work we explain and discuss new notion of fibrewise topological spaces, calledfibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.