In this work, we introduced the Jacobson radical (shortly Rad (Ș)) of the endomorphism semiring Ș =  ( ), provided that  is principal P.Q.- injective semimodule and some related concepts, we studied some properties and added conditions that we needed. The most prominent result is obtained in section three

-If   is a principal self-generator semimodule, then (_ȘȘ) = W(Ș).

Subject Classification: 16y60

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.

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

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 work many amide polymers were prepared according to the modification reaction of polyacryloyl chloride or poluacrulic acid with different primary amines to mesuringninizing hormone were investgaited prior tq surgery in 10 postmenopaisal women with benign and 10 postmenopausal women with maliganant healthy

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

This paper analyzes a piled-raft foundation on non-homogeneous soils with variable layer depth percentages. The present work aims to perform a three-dimensional finite element analysis of a piled-raft foundation subjected to vertical load using the PLAXIS 3D software. Parametric analysis was carried out to determine the effect of soil type and initial layer thickness. The parametric study showed that increasing the relative density from 30 % to 80 % of the upper sand layer and the thickness of the first layer has led to an increase in the ultimate load and a decrease in the settlement of piled raft foundations for the cases of sand over weak soil.  In clay over weak soil, the ultimate load of the piled raft foundation w

Heart failure (HF) is characterized by family history and clinical examination combined with diagnostic tools such as electrocardiogram, chest x-ray and an assessment of left ventricular function by echocardiography. An early diagnosis of heart failure is still based on symptoms of dyspnea, fatigue and signs of fluid overload. Serum N-terminal pro-B-type natriuretic peptide (NT-pro BNP) is cardiac biomarker has emerged as potential predictor of heart failure. It is used as a sensitive biomarker in diagnosis and assessment severity of heart failure. This study assed the diagnostic value of (NT-pro BNP), in Iraqi children patients with heart failure and its correlation with LVEF% especially in emergency rooms of hospitals.Ninety (90) consecut

This study was aimed to monitor oral zinc sulfate role on local cervical proinflammatory cytokines in HPV-infected women comparing with these cytokines before treatment application. A cervical secretion got from 28 infected women before and after treatment with zinc sulfate, these samples assessed various markers of inflammation including interleukin-1β, IL-8, and IL-12. Results manifested that improve and clear the cervical HPV infections after three months of zinc treatment 46.43% and 21.43%, respectively. Viral infections with single and multiple HPV high-risk types are raising of studied cytokines after 3-month compared with single HPV low-risk type. Moreover, this increasing was statistically significant only in IL-12 and IL-1. Women