In this article, we introduce a new type of soft spaces namely, soft  spaces as   a generalization of soft paces. Also, we study the weak forms of soft  spaces, namely, soft  spaces, soft  spaces, soft  space, and soft  spaces. The characterizations and fundamental properties related to these types of soft spaces and the relationships among them are also discussed.

     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.

Background: celiac disease, is an autoimmune inflammatory disease of the small intestine that is precipitated by the ingestion of gluten, a component of wheat protein, in genetically susceptible persons. Serologic tests for antibodies against Endomysium, Reticulin, and Gliadin identify most patients with the disease. Early diagnosis and management are important to forestall serious consequences of malabsorption, such as osteoporosis and anemia
Aims of the study: This study compared the sensitivity, specificity, and predictive value of, anti-reticulin and anti-gliadin antibodies according to anti endomysium antibodies , in consecutive patients investigated for celiac disease antibodies.
Patient& Methods: Total 509 patients (236

Background: To elucidate distinctive CT imaging features that allows a diagnosis of hepatic hydatidosis.
Patients and methods : The computed tomographic (CT) findings of 58 patients with sonographically detected cystic liver lesions were prospectively analyzed. These patients were
followed up until a final diagnosis was reached.
Results : By CT scanning we correctly localized and diagnosed 81 hepatic hydatid cysts in 50 patients. These were all proved by surgery or endoscopic retrograde cholangio-pancreatography (ERCP). Stage III and II hydatid cysts were the commonest types (29 % and 25 % respectively ). 52 % of the cysts were 5-10 cm at presentation. At CT, we identified some ancillary imaging fea

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