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

Rock engineers widely use the uniaxial compressive strength (UCS) of rocks in designing
surface and underground structures. The procedure for measuring this rock strength has been
standardized by both the International Society for Rock Mechanics (ISRM) and American Society
for Testing and Materials (ASTM), Akram and Bakar(2007).
In this paper, an experimental study was performed to correlate of Point Load Index ( Is(50))
and Pulse Wave Velocity (Vp) to the Unconfined Compressive Strength (UCS) of Rocks. The effect
of several parameters was studied. Point load test, Unconfined Compressive Strength (UCS) and
Pulse Wave Velocity (Vp) were used for testing several rock samples with different diameters.
The predicted e

This research aims to clarify the advantages of using the regression method as analytical procedure in the tax audit to reducing the examination cost , time, effort, human and material resources, and represents an applied study in the General Commission of taxes. In order to achieve its objectives the research has used in the theoretical side the descriptive approach (analytical), and in the practical side regression method has been applied to the research sample represented by the soft drinks company that is subject to the tax settlement for the year 2014, where the value of sales has been verified by using the regression method without conductinga comprehensive examination. The most important results of the research indicate that the r

        The modern business environment has witnesses tremendous developments as a result of the globalization of markets and economic openness and technological as well as the acquisition of the issue of corporate governance of great importance regarding it as one of the global innovations trends of control provisions on the management of companies as result of these developments ,increasing on competition between economic unit ,thus a decrease in market share because they do not take into account the response to the requirements of customers ,which kept her to search a modern management accounting methods to help them keep up with the changes and the availability of information for the various adminis

This paper deals with the F-compact operator defined on probabilistic Hilbert space and gives some of its main properties.

Television white spaces (TVWSs) refer to the unused part of the spectrum under the very high frequency (VHF) and ultra-high frequency (UHF) bands. TVWS are frequencies under licenced primary users (PUs) that are not being used and are available for secondary users (SUs). There are several ways of implementing TVWS in communications, one of which is the use of TVWS database (TVWSDB). The primary purpose of TVWSDB is to protect PUs from interference with SUs. There are several geolocation databases available for this purpose. However, it is unclear if those databases have the prediction feature that gives TVWSDB the capability of decreasing the number of inquiries from SUs. With this in mind, the authors present a reinforcement learning-ba

  The role of the public sector- Investment customizations-  economic embargo -  The role of the private sector - Coexistence between the public and private sectors -   Ratio of growth

Space is considered as an important element in constructing artwork, it can be a dominant and fulfilled part that adds new existence to the content. Each artwork must have a space artistically or analytically. The internal and eternal space of artwork have associated with each other in order to be ann important connected unit that establishes the work epressions and helps the audience to understand it. Such kind of works can be represented by the works of the potter (Sheinyor Abdu Allah) which have uarious expressions of space which this study is based on.The study aims at finding out the treatment of apace in the ceramic sculpture works of the potter (Sheinyar Abdu Allah).The second chapter has many sections. T

This research aims to study the mechanism of application of international specification requirements (ISO 9001: 2015) at the Iraqi Center- Korean Vocational Training return to vocational training department at the Ministry of Labour and Social Affairs for the purpose of preparing and creating the center to get a certificate of conformity with the requirements of the standard (ISO 9001: 2015) that would elevate the level of performance and services provided in the respondent Center after it is identified and the study of the reality of the quality management system by identifying strengths and weaknesses in the system to diagnose the gap and find ways to address that gap, and adopted the researchers the case study method to conduc