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 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.

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.

The research aims to recognize the impact of the training program based on integrating future thinking skills and classroom interaction patterns for mathematics teachers and providing their students with creative solution skills. To achieve the goal of the research, the following hypothesis was formulated: There is no statistically significant difference at the level (0.05) between the mean scores of students of mathematics teachers whose teachers trained according to the proposed training program (the experimental group) and whose teachers were not trained according to the proposed training program (the control group) in Pre-post creative solution skills test. Research sample is consisted of (31) teachers and schools were distribut

A total of 50 fertile human hydatid cases {33(66%) females and (34%) males}, obtained from Al-Ramadi public Hospital during the period from December 2003 to July 2004 were examined to study any bacterial infections. The specimens were obtained from hydatid fluid and then cultured on appropriate culture media to distinguish some species of bacteria which resulted in obtaining: Staphylococcus aureus (18%), Pseudomonas aeruginosa(12%), Escherichia coli(6%) and Streptococcus pneumonia (4%). These bacteria were confirmed by isolation from interacyst fluid and blood culture technique. The possible routs of infection may be through blood, biliary ducts and bronchioles .The selectivity permeable of the cyst wall may be absent and that may allow

The current problem is summarized in what is called the development failing experience
in comprehencing the studying materials , so the students will feel worry of repeating failure
in he future , so he would seek blind keeping on heart for the studying material bond this isbad due to the forgetting in the future , one side of thesis research problem is that there is
many contradictory researches result in relation to the learning styles which impose the
nessicity to find results lessen this contradiction . the importance of the research is
summarized in the importance of the subject under the study , in that the researcher ( as in
her knowledge ) did not find a thesrs tackling the subject of the distinguished students

Infertility represents a growing health problem in Mosul city and worldwide. Infertility defined as a failure to induce pregnancy after unprotected sexual intercourse for more than 12 months. Infertility in male is a multifactorial complex pathology that leads to different types of problems. This work try to explore the correlation between glycosylation gap and seminal fructosamine and another parameter in the young male patient in Mosul city. The study included 50 subjects with age range 19-29 year with BMI 18-26. The infertility group include 25 patients newly diagnosed with infertility before starting any treatment; have no infection and no structural abnormality. The control group included 25 healthy subjects. HbA1c, fructosamine, Se

God is the source of every grace in which man lives and enjoys, and there is no one in the world told himself that created and destined and ridiculed and found out of nothing God Almighty alone.
The grace is an affliction from God Almighty, when God Almighty blesses his servant with money or children and others, the slave thinks the acceptance of God Almighty, but may be a source of affliction and scrutiny.