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

  The aim of the research is to identify the extent of the ability to ensure the integrated reports by the auditor in verifying the credibility of these reports, and their implications for the benefit of all parties dealing with the economic unit, as well as measuring the impact of the assurance procedures followed by the auditors and their role in confirming these reports.

  The research methodology was designed after studying the previous literature related to the research variables, and then the relationship between these variables was tested, through the use of a questionnaire list. A questionnaire targeting the community of auditors in the local environment, and the results of the study wer

This research reviews the aesthetic variables that were founded according to (theatrical rehearsal) as one of the most important pillars on which the theatrical process is based, because of its necessity in developing theatrical art on several levels that helped the theatrical director in organizing his work, and this became clear through the research chapters represented in the first chapter (methodological framework) and the second chapter, which consisted of the first topic (the duality of watching / rehearsal) and the second topic (the applications of theatrical rehearsal in theatrical experiences), all the way to the third chapter (research procedures), which included the analysis of theatrical rehearsals (sharing on life), and the

The paper is concerned with, the behavior of the hydrostatic thrust bearings lubricated with liquid-solid lubricants using Einstein viscosity formula, and taking into account the centrifugal force resulting from high speed.  Also studied is the effect of the bearing dimensions on the pressure, flow rate, load capacity, shear stress, power consumption and stiffness.

The theoretical results show an increase in load capacity by (8.3%) in the presence of solid graphite particles with concentration of (16%) by weight as compared with pure oil, with increasing shear stress.  .

In general the performance of hydrostatic thrust bearings improve for load carrying capacity, volume flow rate,

As regional development, as a matter of course, poses a number of systemic, scientific and political problems. While the issue of development is primarily at the national level to the limits of World War II in the industrialized world and to the 1960s borders in most Third World countries, the increasing awareness of regional disparities has led to the regional issue Were taken into consideration in the early 1960s and 1970s in most industrialized and developing countries alike. The local issue was only introduced in the early 1980s. The awareness of regional disparities and the fact that the regions do not have the same potential and that some regions have the resources to enable them to develop, grow and develop, unlike other r

The flow in a manifolds considered as an advanced problem in hydraulic engineering applications. The objectives of this study are to determine; the uniformity qn/q1 (ratio of the discharge at last outlet, qn to the discharge at first outlet, q₁) and total head losses of the flow along straight and rectangular loop manifolds with different flow conditions. The straight pipes were with 18 m and 19 m long and with of 25.4 mm (1.0 in) in diameter each. While, the rectangular close loop configuration was with length of 19 m and with diameter of 25.4 mm (1.0 in) also. Constant head in the supply tank was used and the head is 2.10 m. It is found that outlets spacing and manifold configuration are the main factors aff

This study aims to clarify areas of using information technology in accounting and its impact on the profession of auditors by reviewing the concept, types, areas and the importance of information technology and its implications on the audit profession as well as to clarify the extent of contribution of information technology in  developing of procedures of the audit profession and what its requirement, also this study aims to enhance the theoretical side by identifying the views of a sample of auditors in  Arab countries selected (Iraq, Syria, Jordan), for the extent of using of information technology in their work and level of their perception for the importance of that