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

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 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

Gelatin-grafted N- proflavine acryl amide was synthesized through two steps; firstly the Gelatin was grafted with acrylic acid free radically using Ammonium per-sulfate at 60℃, Then it was modified to its corresponding acyl chloride derivation, second step included the substitution with amino group of proflavine, in this research Gelatin was used as a natural nontoxic, water soluble polymer as a drug carrier. The prepared pro drug polymer was characterized by FTIR and 1H-NMR spectroscopies, Controlled drug release was studied in different pH values at 37℃. Many advantages were obtained comparing with other known methods.

ABSTRACT. The reaction between benzil and hexamethylenediamine formed a new ligand [L], [(1Z,3Z)-2,3-diphenyl-5,6,7,8,9,10-hexahydro-1,4-diazecine], of the type [N2], was synthesized by the condensation reaction through Schiff base reaction between benzil and hexamethylenediamine. The new Schiff base ligand reacts with Mnп, Niп and Coп metal ions to give the complexes with the general formula: [M(L)Cl2]. The elemental investigations have been used to analyze the ligand and its complexes by CHN, FT-IR, UV-Vis, TLC, mass spectrum, melting point with the study of biological activity to the formed compounds. From the data obtained, the proposed molecular structure adopts square planar structure about the metal ions. The study reveals

Complexes of Co(II),Ni(II),Cu(II) and Zn(II) with mixed ligands of phenylalanine (L) and tributylphosphine (TBPh) were prepared in aqueous ethanol with (2:1:1) (M:L:TBPh). The prepared complexes were characterized using flame atomic absorption,(C.H.N)Analysis, FT.IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements. In addition biological activity of the phenylalanine and complexes against two selected type of bacteria were also examined. Some of the complexes exhibit good bacterial activities. From the obtained data the octahedral structure was suggested for all prepared complexes.