Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.

This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor

In this paper, some commonly used hierarchical cluster techniques have been compared. A comparison was made between the agglomerative hierarchical clustering technique and the k-means technique, which includes the k-mean technique, the variant K-means technique, and the bisecting K-means, although the hierarchical cluster technique is considered to be one of the best clustering methods. It has a limited usage due to the time complexity. The results, which are calculated based on the analysis of the characteristics of the cluster algorithms and the nature of the data, showed that the bisecting K-means technique is the best compared to the rest of the other methods used.

In this research, a new application has been developed for games by using the generalization of the separation axioms in topology, in particular regular, Sg-regular and SSg- regular spaces. The games under study consist of two players and the victory of the second player depends on the strategy and choice of the first player. Many regularity, Sg, SSg regularity theorems have been proven using this type of game, and many results and illustrative examples have been presented

Background: Diabetes mellitus is one of the commonest chronic disorders worldwide with a rapid rise in prevalence. In Iraq its prevalence is high especially in elderly age group. Patients with type 2 diabetes mellitus have higher vulnerability for complications, whether microvascular or macrovascular. Ocular complications are common in diabetes mellitus, and comprise diabetic retinopathy, diabetic papillopathy, cataract, glaucoma, dry eye disease and diabetic keratopathy. Diabetic keratopathy involves endothelial and epithelial tissues of the cornea, leading to persistent epithelial defect, corneal erosion, or corneal ulcers.

Aim of the Study: To compare the mean corneal endothelial cell count between patients wi

Background: Diabetes mellitus is a well
known metabolic and vascular illness associated
with high incidence of bacterial urinary tract
infections especially in diabetic complications
including both micro and macro-vascular types.
Objective: To study the incidence of bacterial
urinary tract infections in type 2 diabetic
patients, the type of micro-organism responsible
in relation to age, sex of patients, duration of the
disease & related micro & macrovascular
diabetic complications.
Methods: A prospective study of the diabetic
patients including 40 males with mean age of
54(±9) years and 50 females, mean age of 51(±7)
years and duration of the and sex matched
controls (27 males and 33