In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if  for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph K_n, Complete bipartite graph K_m,n and Complete tripartite graph K_l,m,n. It has also been studied how the lucky number changes whi

Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

The main goal of this paper is to dualize the two concepts St-closed submodule and semi-extending module which were given by Ahmed and Abbas in 2015. These dualizations are called CSt-closed submodule and cosemi-extending mod- ule. Many important properties of these dualizations are investigated, as well as some others useful results which mentioned by those authors are dualized. Furthermore, the relationships of cosemi-extending and other related modules are considered.

The main objective of this work is to introduce and investigate fixed point (F. p) theorems for maps that satisfy contractive conditions in weak partial metric spaces (W.P.M.S), and give some new generalization of the fixed point theorems of Mathews and Heckmann. Our results extend, and unify a multitude of (F. p) theorems and generalize some results in (W.P.M.S). An example is given as an illustration of our results.

This study was aimed to investigate the effect of essential oil extracted from the yellow peels of Citrus aurantium on the growth of four species of fungi: Penicillium expansum, Penicillium oxalicum, Fusarium oxysporum and Fusarium proliferatum and effect of one fungicide: Aliette (fosetyl-aluminum) against these fungi. The results showed that the essential oil of C. aurantium inhibited the radial growth of P. oxalicum at concentration 4.5% while P. expansum and F. oxysporum at concentrations 5% and F. proliferatum at concentrations 5.5% additionally the one fungicide tested showed inhibitory effect on radial growth of these fungi. So that there is a negative relationship between the increasing of concentration and radial growth of fungi.

This study examined the effect of essential oils extracted from peel of Citrus paradisi and Citrus sinensis on two species of fungi: Penicillium oxalicum and Fusarium oxysporum as well as effect of two fungicides: Carbendazim and Thiophanatemethyl against above fungi. Results showed that the essential oil of Citrus paradisi inhibited the radial growth of Penicillium oxalicum and Fusarium oxysporum at concentration 4%. Nevertheless, the essential oil of Citrus sinensis inhibited the radial growth at concentration 5 and 4%, respectively. Furthermore, the two studied fungicides inhibited radial growth of these fungi too. Therefore, there are a positive relationship between the evaluating of concentration and the percentage of inhibiting of rad

      This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.