The main goal of this paper is introducing and studying a new concept, which is named H-essential submodules, and we use it to construct another concept called Homessential modules. Several fundamental properties of these concepts are investigated, and other characterizations for each one of them is given. Moreover, many relationships of Homessential modules with other related concepts are studied such as Quasi-Dedekind, Uniform, Prime and Extending modules.

In this paper a mathematical model that describes the flow of infectious disease in a population is proposed and studied. It is assumed that the disease divided the population into four classes: susceptible individuals (S), vaccinated individuals (V), infected individuals (I) and recover individuals (R). The impact of immigrants, vaccine and external sources of disease, on the dynamics of SVIRS epidemic model is studied. The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of the model is studied. The occurrence of local bifurcation as well as Hopf bifurcation in the model is investigated. Finally the global dynamics of the proposed model is studied numerically.

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.

We dealt with the nature of the points under the influence of periodic function chaotic functions associated functions chaotic and sufficient conditions to be a very chaotic functions Palace

I attended some amides non grassy substitutes such as acrylic compounds Amaid Electron Amaid and Alsinamamaid interaction unsaturated acids such as acrylic acid or Ketronk ????????? with primary amines Malkhtlfah of acrylic monomers Alamayd

the Reception and the Creative Reaction

A new family of nematic liquid crystal dendrimers derived from 3,5-dihydroxybenzoic acid were synthesized. The synthesis of the dendrimers compounds shows the influence of the dendritic core on the mesomorphic properties. The liquid crystalline properties were studied by polarizing optical microscopy (POM) equipped with a hot stage, the structures of the synthesized compounds characterized using FTIR and 1HNMR spectroscopy.

     In this work, we present new types of compact and Lindelöf spaces and  some facts and results related to them. There are also types of compact and Lindelöf functions and the relationship between them has been investigated. Further, we have present some properties and results related to them.

solid state reaction technique (SSR) was used to prepare high-Tc phase in superconductors the effect of additional Pb to was investigated it has been found