The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

         Let R be a commutative ring , the pseudo – von neuman  regular graph of the ring R is define as a graph whose vertex set consists of all elements of R and any two distinct vertices a and b are adjacent if and only if   , this graph denoted by P-VG(R) ,  in this work we got some new results a bout chromatic number of  P-VG(R).

          The experiment was conducted in two stages: first stage: determination of the most effective dose of Cyperus rotundus tubers aquatic extract in male rats for 5 days, which was concentrated as (200 mg/kg body weight). The second stage was designed to observe and test the protective effects of C. rotundus tubers aquatic extract in the liver and kidney functions of male rats exposed to cadmium chloride poisoning (5 mg/kg bw) for 30 days. The animals were divided into (4) groups within each group (5) animals weighted (200-220g). The results of oral dose of cadmium chloride showed a significant increase of (P˂0.05) in the activity of both enzymes Alanine aminotransferas

Most real-life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subgraphs without coding or using assumption. The aim of this paper is to apply near concepts in the -closure approximation spaces. The basic notions of near approximations are introduced and sufficiently illustrated. Near approximations are considered as mathematical tools to modify the approximations of graphs. Moreover, proved results, examples, and counterexamples are provided.

 Lighting is a very important element of treatment if the color contains many imaging system (digital cameras) and the unit of light and the light within these units are not strong , but usefel when the light is low , in different lighting intensities conditions image quality will not persist good enough and image may become dark or slightly exposed to light which leads to lower the details in image where we can not modify contrast or light ness to compensate thr decrease without losing the light and dark deatials . So we went in this research to study the variation colored texts written on the painting and lighting cases of non –regular ( a few) and different distances . As the diversity of these texts written on the board a

This paper is concerned with introducing and studying the M-space by using the mixed degree systems which are the core concept in this paper. The necessary and sufficient condition for the equivalence of two reflexive M-spaces is super imposed. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are introduced. From an M-space, a unique supratopological space is introduced. Furthermore, the m-continuous (m-open and m-closed) functions are defined and the fundamental theorem of the m-continuity is provided. Finally, the m-homeomorphism is defined and some of its properties are investigated.

In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

Practically, torsion is normally combined with flexure and shear actions. Even though, the behavior of reinforced concrete continuous beams under pure torsion is investigated in this study. It was performed on four RC continuous beams under pure torsion. In order to produce torsional moment on the external supports, an eccentric load was applied at various distances from the longitudinal axis of the RC beams until failure.

Variables considered in this study are absolute vertical displacement of the external supports, torsional moment’s capacity, angle of twist and first cracks occurrences. According to experimental results; when load eccentricity increased from 30cm to 60cm, the absolute vertical displacement i

The research aims to identify the theoretical foundations for measuring and analyzing quality costs and continuous improvement, as well as measuring and analyzing quality costs for the Directorate of Electricity Supply / Middle Euphrates and continuous improvement of the distribution of electrical energy,The problem was represented by the high costs of failure and waste in electrical energy result to the excesses on the network and the missing (lost) energy,Thus, measuring and analyzing quality costs for the distribution of electrical energy and identifying continuous improvement leads to a reduction in missing and an increase in sales, as the research reached many conclusions, the most important of which is the high percentage o