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.

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

Background: Nickel-titanium (NiTi) archwires have become increasingly popular because of their ability to release constant light forces, which are especially useful during initial alignment and leveling phase. The aim of the present study was to investigate and compare the load–deflection characteristics of four commercially available NiTi archwires. Materials and methods: 200 NiTi 0.014, 0.016, 0.018, 0.016x0.022 and 0.019x0.025-inch nickel–titanium archwires from four different manufacturers (3M, Ortho Technology, Jiscop and Astar) were tested. The load-deflection properties of these archwires were evaluated by a full arch bending test in both palatal and gingival directionsat 37°C temperature using a universal material t

Background and Aim: The use of food dyes can cause certain diseases, such as anemia and indigestion, along with other disorders, tumors, and even cancer. Therefore, this study aimed to determine the chemical nature and toxicity of some commercial dyes locally used in processed foods compared with standard food dyes. Materials and Methods: Three types of standard and commercial food color additives (Sunset Yellow, Tartrazine, and Carmoisine) were extensively examined. The chemical structures and functional groups of the dyes were evaluated by Fourier-transform infrared (FTIR) spectroscopy. The melting temperatures of the dyes were also determined by chemical thermal analysis. The acute toxicity test to evaluate the standard and commercial

Background: Polymeric composites have been widely used as dental restorative materials. A fundamental knowledge and understanding of the behavior of these materials in the oral cavity is essential to improve their properties and performance. The goal of this study was to measure water sorption of four composite resins containing different filler and resin matrix contents. Materials and method: Resin composite specimens giomer (Beautifil II) Filtek™ P90, Filtek™ Z350 XT, and Tetric N Ceram were prepared in a cylindrical mould of 3mm thickness and 6mm diameter (n=10) and light cured . All specimens placed in silica-gel desiccators at 37˚C for seven days, a constant weight was obtained. All samples were immersed in deionized distill

 Investigating the heavy metals in soil is important to the life of humans and living organisms. Diyala River Lower Reaches was chosen due to the changes in environmental characteristics that took place in recent years. Twelve sediment samples were collected from four different sites. The physical, and chemical properties and the concentrations of nine heavy metals were indicated. The results showed that the average concentrations of arsenic, copper, chromium, cobalt, iron, manganese, nickel, lead, and zinc are 8.5, 45.7, 538.5, 12.2, 5.07, 991.7, 183.5, 16.07, 136.5 ppm, respectively. They reflect contamination with arsenic, chromium, and nickel, while they are free of lead, and zinc contamination, according to the Environmental P