The main purpose of this paper, is to introduce a topological space , which is induced by reflexive graph and tolerance graph , such that  may be infinite. Furthermore, we offered some properties of  such as connectedness, compactness, Lindelöf and separate properties. We also study the concept of approximation spaces and get the sufficient and necessary condition that topological space is approximation spaces.

This paper focuses on developing a strategy to represent the -connected ominoes using an abacus. We use the idea of -connected ominoes with respect to a frame in modelling nested chain abacus. Then, we formulate and prove the unique connected partition for any -connected ominoes. Next, the topological structure of nested chain abacus is presented.

Both traditional and novel techniques were employed in this work for magnetic shielding evaluation to shed new light on the magnetic and aromaticity properties of benzene and 12 [n]paracyclophanes with n = 3–14. Density functional theory (DFT) with the B3LYP functional and all-electron Jorge-ATZP and x2c-TZVPPall-s basis sets was utilized for geometry optimization and magnetic shielding calculations, respectively. Additionally, the 6-311+G(d,p) basis set was incorporated for the purpose of comparing the magnetic shielding results. In addition to traditional evaluations such as NICS/NICSzz-Scan, and 2D-3D σiso(r)/σzz(r) maps, two new techniques were implemented: bendable grids (BGs) and cylindrical grids (CGs) of ghost atoms (Bqs). BGs a

The aim of the research is to identify the percentage of success and failure of some compound offensive skills in joiner basketball. It was evident that development only occurred though the mastery of the basic single offence skills as well as the ability to perform compound skills accurately and consistently. Not paying enough attention to compound skills leads evidentially to weakness in the athlete's level that in turn leads to mistakes in performance. Six joiner games of the best four teams in Baghdad were filmed and analyzed. The results of analyzing the compound offence skills were as follows:  There was some weakness in the athletes' ability in using compound offence skills specially receiving, dribbling and following through that

The research work was conducted to investigate the effect of oral administration of aqueous extract of turmeric at doses of (5, 10) mg/kg body weight for two weeks daily by determining the genotoxic effect (mitotic index), evaluation of immunological effect (IgG, IgM, IgA, C3, C4) and measuring fertility hormones (follicles stimulation hormone/FSH, lutenising hormone/LH) levels with histological examinations of female albino swiss mice ovaries in comparison with control (normal saline). A clear effect in increasing mitotic activity was reveled for both doses in comparison with control. Results also showed a significant increase in the value of all immunological parameters at both doses, in comparison with control. Also, obvious rais