A new definition of a graph called Pure graph of a ring denote Pur(R) was presented , where the vertices of the graph represent the elements of R such that there is an edge between the two vertices ???? and ???? if and only if ????=???????? ???????? ????=????????, denoted by pur(R) . In this work we studied some new properties of pur(R) finally we defined the complement of pur(R) and studied some of it is properties

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

A new human-based heuristic optimization method, named the Snooker-Based Optimization Algorithm (SBOA), is introduced in this study. The inspiration for this method is drawn from the traits of sales elites—those qualities every salesperson aspires to possess. Typically, salespersons strive to enhance their skills through autonomous learning or by seeking guidance from others. Furthermore, they engage in regular communication with customers to gain approval for their products or services. Building upon this concept, SBOA aims to find the optimal solution within a given search space, traversing all positions to obtain all possible values. To assesses the feasibility and effectiveness of SBOA in comparison to other algorithms, we conducte

In this paper, various aspects of smart grids are described. These aspects include the components of smart grids, the detailed functions of the smart energy meters within the smart grids and their effects on increasing the awareness, the advantages and disadvantages of smart grids, and the requirements of utilizing smart grids. To put some light on the difference between smart grids and traditional utility grids, some aspects of the traditional utility grids are covered in this paper as well.

The No Mobile Phone Phobia or Nomophobia notion is referred to the psychological condition once humans have a fear of being disconnected from mobile phone connectivity. Hence, it is considered as a recent age phobia that emerged nowadays as a consequence of high engagement between people, mobile data, and communication inventions, especially the smart phones. This review is based on earlier observations and current debate such as commonly used techniques that modeling and analyzing this phenomenon like statistical studies. All that in order to possess preferable comprehension concerning human reactions to the speedy technological ubiquitous. Accordingly, humans ought to restrict their utilization of mobile phones instead of prohibit

Labor movement is considered important in Britain because it is an international phenomenon of the feudal system and one of the flowerings of the era of the capitalist machine. At the beginning of the 18th century, the world witnessed a change and progress in many aspects of the industrial fields such as the different means of production .this era is called the industrial revolution which especially appeared in Britain and extended to other areas of the world .it leads to many changes in Europe and participated in different economic, political and cultural and social fields. and it has a very important role in progress and development but its disadvantage is that it is exploited by the capitalists to achieve their special rights .in othe

Endoscopy is a rapidly growing field of Neurosurgery, it is defined as the applying of endoscope to treat different conditions of brain pathology within cerebral ventricular system and beyond it, endoscopic procedures performed by using different equipment and recording system to make a better visualization enhancing the surgeon's view by increasing illumination and magnification to look around corner and to capture image on video or digital format for later studies.

This research which is entitled (Devine Beauty), aims at studying the philosophical and literary extensive visions of Andalusian poets in search of pleasure in the beauty of divine self and its impact on the formation of a philosophical frame of mind. It also attempts to investigate the aesthetic aspects that highlight the prestige and greatness and majesty of that absolute beauty.
The most important conclusion of the reach is the Bany Ahmar poets use the beauty of women and the pleasure of wine as cods to reach divine beauty and get the happiness desired with the reflection of absolute beauty in a clear philosophy and thinking of the kingdom of God Almighty.