This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

The research tagged (functional enhancement and its reflection on industrial product systems) focused on the possibility of enhancing industrial products in terms of form and functionality in a way that they are able to meet the needs of the user through the impact of technology and modern technologies on the functional enhancement of industrial products and their effectiveness in achieving formal and functional design variables, and producing products Industrial products are highly efficient and durable in order to improve them in order to meet the needs of the user, the transfer of technology between life forms and industrial products is desirable because the functional enhancement processes that occurred in general on industrial produ

The research aims to release the concept of auditing reporting and its role in the rationalization of economic decisions in the companies listed in the Iraq Stock Exchange from the viewpoint of academics, professionals, investors and lenders. Auditor reporting witnessed the great progress in many areas addressed many of the previous studies compare with Iraqi auditors reporting because there are some defects in these aria .The research problem focused whether the auditor report in Iraq is contains useful information to rationalize investment decisions & lending decisions in the shareholding companies listed on the Iraq Stock Exchange , and under that premise , " There is statistically significant relationship between the reporting au

Islam was keen to get every man and woman a share of those benefits and wanted to marry and urged him. In order to unite efforts and articulates the arrow and clarifies the goal and I have a share in building a sober Islamic society, for all this and other research title is ((modern or planting and its impact on marital happiness)).

The topic of supra.topological.spaces considered one of the important topics because it is a generalization to topological.spaces. Many researchers have presented generalizations to supra open sets such as supra semi.open and supra pre.open sets and others. In this paper, the concept of δ∼open sets was employed and introduced in to the concept of supra topology and a new type of open set was extracted, which was named S∼δ∼open. Our research entails the utilization of this category of sets to form a new concepts in these spaces, namely S∼δ∼limit points and S∼δ∼derive points, and examining its relationship with S∼open and S∼reg∼open. Based on this class of sets, we have introduced other new concepts such as S∼isolate

The Internet makes the world like a small village. It has the ability to make groups of the same ideas, thoughts, and identity close to each other by gathering them in one place. It is a way to communicate and share information and opinion; shaping and sharing of comprising individuals with common interests and the participation of individuals in a fruitful dialogue results in achieving a set of goals promote ideas and mobilizing people about issues and events of common interests.

To address the relationship of the internet via interactive communication and its ability to achieve social capital and discuss issues and various social events, the study sees that the problem of the study could be formulated as follows:

Consid

Abstract Globalization dominated in the last decade of the twentieth century and the eve of the third millennium over economic,politics,psychology,culture,communications and information sciences,it's a historical phenomenon refer to many important transitions in humanitarian life.It foxes on that state has illusion its historical role in the psychologist,economic and political buldings. Globalization issue and its influence in North Korea put a spotlight on political,economic and cultural situations,the political system resists any change with many limitations on political freedoms,human rights and political multiplicity.Libralism trends and free market are so weaken when it comparing within the bad economic situation of the coun

Abstract : This research is a field study of international cities that hosted various events of which (Sports, Exhibitions, Scientific, Cultural) and other events, these positive impacts on the city driven by such hosts were identified. The research goal was to support hosting events to improve the hostess city and to draw future plans for further developments and to invest event’s hosting to strengthen the city’s value according to a strategic vision that looks for the future the most important conclusions are Entering events hosting is a part of urban development strategies and The most important recommendations are coordination between hosting event activities and its facilities with the infrastructure structure of the host city, its