In this work, we introduce  a new convergence formula. We also define cluster point , δ-Cauchy sequence, δ-convergent, δ-completeness , and define sequentially contraction  in approach space. In addition, we prove the contraction condition is necessary and sufficient to get the  function is sequentially contraction  as well as we put a new structure for the norm in the approach space which is called approach –Banach space, we discuss the normed approach space with uniform condition is a Hausdorff space. Also, we prove a normed approach space is complete if and only if the metric generated from approach space is complete as well as prove every finite –dimensional approach normed space is δ-complete. We prove several r

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 introduce and study the notion of the maximal ideal graph of a commutative ring with identity. Let R be a commutative ring with identity. The maximal ideal graph of R, denoted by MG(R), is the undirected graph with vertex set, the set of non-trivial ideals of R, where two vertices I₁ and I₂ are adjacent if I₁ I₂ and I₁+I₂ is a maximal ideal of R. We explore some of the properties and characterizations of the graph.

Fabrication of solar cell prepared by thermal spray and vacuum thermal evaporation method on silicon wafer(n-type) and studying its efficiency. The film have been deposited on three layers(ZnO then CdS and CdTe) on Si and glass respectively.Direct energy gap was calculated and equal to (4.3,3.4,3)eV and indirect energy gap equal to (3.5,2.5,1.5)eV respectively . Efficiency was calculated for the cell of area 2cm2 it was equal to 0.14%.

Background: Dietary supplementation is a common strategy to achieve a specific health status or performance benefit. The aim of this study was to describe the use of dietary supplement in Iraqi genders.

Patients and Methods:  several questions on dietary supplement use were asked as a part of single performed on 112 female and 247 women aged 35–74 years in 2021 .n = 359) ,reported the frequency and prevalence of supplement use by sex and type of supplement .

Results: the mean percentage of dietary supplement use varied among female and men. Use was higher in women than in men. Vitamins, minerals were the predominant types of supplements reported, but the

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 acidity of spent lubricant was treated using sodium hydroxide solution. The effect of three variables on the treatment have been studied . These are mixing time rangingfrom 5-35 minutes, NaOH to lubricant weight ratio ranging from  0.25-1.25 and weight percentage  of NaOH ranging from  2-6 % .

The experimental design of Box-Wilson method is adopted to find a useful relationship between the three controllable variables and the lowering in the acidity of the spent lubricant. Then the effective variables and interactions are identified using the statistical analysis(F-test) of  three variable fractional design. The mathematical model is well represented  by a second order polynomial.

By

Encouraging children towards the cognitive motivation through the discovery and knowledge of the environment around them is essential. Thus, during the two researchers’ supervision of the practical lessons that involved the female students’ application of their experience in the Applied Kindergarten Laboratory, it has been noticed that there was a difference in the cognitive motivation of kindergarten children. In order to reinforce the research problem, the two researchers sent an open questionnaire to a sample of randomly selected kindergarten teachers from Al-Karkh and Al-Rasafa sides. The responses collected accentuated the researchers’ sense of the existing problem. To achieve the aim of the study represented by examining the