In this thesis, we study the topological structure in graph theory and various related results. Chapter one, contains fundamental concept of topology and basic definitions about near open sets and give an account of uncertainty rough sets theories also, we introduce the concepts of graph theory. Chapter two, deals with main concepts concerning topological structures using mixed degree systems in graph theory, which is M-space by using the mixed degree systems. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are defined and studied. In chapter three we study supra-approximation spaces using mixed degree systems and primary object in this chapter are two topological

     This article is devoted to presenting results on invariant approximations over a non-star-shsped weakly compact subset of a complete modular space by introduced a new notion called S-star-shaped with center f:  if   be a mapping and , . Then the existence of common invariant best approximation is proved for Banach operator pair of mappings by combined the hypotheses with Opial’s condition or demi-closeness condition

     In this paper, the bi-criteria machine scheduling problems (BMSP) are solved, where the discussed problem is represented by the sum of completion and the sum of late work times  simultaneously. In order to solve the suggested BMSP, some metaheurisitc methods are suggested which produce good results. The suggested local search methods are simulated annulling and bees algorithm. The results of the new metaheurisitc methods are compared with the complete enumeration method, which is considered an exact method, then compared results of the heuristics with each other to obtain the most efficient method.

In this research, beam expander, BEX, is explained and designed for illuminating the
remote flying target. The BEX is optically designed to be suited for Nd:YAG laser of given
specifications. The BEX is modified to be zoom one to meet the conditions of preventing the
receiving unit; i.e the photodetector, from getting saturated at near and far laser tracking.
Decollimation could be achieved by automatic motor, which controls zoom lens of the BEX
according to the required expansion ratio of beam expander

The aim of the current  study is to determine the elastic properties  of carbonate rocks using ultrasonic method.  Forty rock samples of  Anah formation  were collected at  different depths from  four wells drilled at the study area . The relationship between wave velocities and elastic properties of rocks was defined. Regression analyses to define these relations were applied. The results indicate that the elastic properties of the rocks show a linear relationship with both P- and S-wave velocities. The best relationship was obtained between both Young's modulus and Shear modulus with Vs in the determination of the coefficient ( R²  ), with values of 0.91 and 0.94,  respectively.&n

In this work, a series of new Nucleoside analogues (D-galactopyranose linked to oxepanebenzimidazole moiety) was synthesized via multisteps synthesis. The first step involved preparation of two benzimidazoles 2-styrylbenzimidazole and 2-(phenyl ethynyl) benzimidazole via reaction of phenylenediamine with cinnamic acid or ?-phenyl propiolic acid. Electrophilic addition of the prepared benzimidazoles by three anhydrides in the second step afforded (4-6) and (14-16) which in turn were treated with 1,2,3,4-di-O-isopropylidene galactopyranose in the third step to afford a series of the desirable protected nucleoside analogues (7-9) ,(17-19)which after hydrolysis in methanolic sodium methoxidein the fourth step afforded the free nucleoside analog

The primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent o

        This paper is concerned with the solution of the nanoscale structures consisting of the   with an effective mass envelope function theory, the electronic states of the  quantum ring are studied.  In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of  quantum rings are studied by the one electronic band Hamiltonian effective mass approximati

The steady state performance of the counter rotating floating ring Journal bearing is analyzed with isothermal finite bearing theory. The effect of different parameters affecting the performance of the bearing (namely speed ratio, clearance ratio and radii ratio), have been investigated. The load carrying capacity of the bearing increasing with decreasing the radii ratio (R₂/R₁) of the ring and clearance ratio (c₁/c₂), in the other hand, the coefficient of friction increases with increasing the clearance and radii ratios, while decreases with incre4asing the bearing to journal speed ratio (γ). It is shown during this work that different operating conditions are greatly enhanced the performance