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

At the beginning of the twentieth century distorting handling totalitarian phenomena of art, which can be called the stage of the test, transition from the theory of ideal theory and other realistic is not cushy, since it requires vision and reading and other concepts, and in light of this dialectic manifested research problem by asking the following Is affected by the design idealism and realism. Through the above mentioned questions, the researcher found rationale for addressing this problem, the study through his research, which is marked (idealism and realism in a comparative study design). And demonstrated the importance of research in the identification of the concept and the effectiveness of the two theories idealism and realism a

The present study attempts to give a detailed discussion and analysis of parenthetical constructions in English and Arabic, the aim being to pinpoint the points of similarity and difference between the two languages in this particular linguistic area.The study claims that various types of constructions in English and Arabic could be considered parenthetical; these include non-restrictive relative clauses, non-restrictive appositives, comment clauses, vocatives, interjections, among others. These are going to be identified, classified, and analyzed according to the Quirk grammar - the approach to grammatical description pioneered by Randolph Quirk and his associates, and published in a series of reference grammars during the 1970

When scheduling rules become incapable to tackle the presence of a variety of unexpected disruptions frequently occurred in manufacturing systems,  it is necessary to develop a reactive schedule which can absorb the effects of such disruptions. Such responding requires efficient strategies, policies, and methods to controlling production & maintaining high shop performance. This can be achieved through rescheduling task which defined as an essential operating function to efficiently tackle and response to uncertainties and unexpected events. The framework proposed in this study consists of rescheduling approaches, strategies, policies, and techniques, which represents a guideline for most manufacturing companies operatin

The objective of this study is to highlight the skills of office managers and it's impact on the effectiveness of time management in the institutes and faculties of middle technical university and a group of cognitive and practical aims. The managers skills forms mthe modern trend and the main source to provide organizations with highly skilled managers with distinctive performance and because of the sharp changes in the environment which today's organizations works in it , business organizations generally and managers especially realise the importance of time management and it's role in achieving competitive advantage . The problem of this study raised from this point which reflect the extent of departments managers realisation

 Polyaniline organic Semiconductor polymer was prepared by oxidation polymerization by adding hydrochloric acid concentration of 0.1M and potassium per sulfate concentration of 0.2M to 0.1M of aniline at room temperature, the polymer was deposited at glass substrate, the structural and optical properties were studies through UV-VIS, IR, XRD measurements, films have been operated as a sensor of vapor  H₂SO₄ and HCl  acids.

The research dealt with a topic that has been practiced and transmitted news in satellite channels in recent years a lot. That is to say the role of satellite channels in the culture of a protest. In general, this study aims to reach to know the extent of the impact of television, especially the impact of the programs that bear the contents of protest and remonstration on the public; and what can be resulted out of these programs as cognitive, emotional and behavioral effects as a result of the individual's exposure to these programs and their impact from the culture of pretense. In addition to that, the research was interested in explaining the role of Iraqi satellite channels in developing and cultivating such culture; and following up

Background: Hypothyroidism is the most prevalent thyroid disorders worldwide.  Hypothyroidism manifestations are wide spectrum, affecting various systems in human body including the nervous system. Hypothyroidism can cause neuropsychiatric symptoms such as anxiety, depression and diminishing in attention, memory and executive function. Aim: to investigate the level of anxiety and depression in patients with hypothyroidism receiving levothyroxine treatment. Method: a cross-sectional study was conducted at Baghdad Center for Nuclear Medicine and Radiation Therapy from March to June 2022. The study population included patients of both genders, aged 18-65 years, diagnosed with hypothyroidism, were receiving levothyroxine treatment and

Microfinance Institutions (MFIs) offers small loans with easy repayment system and till now these institutions have served millions of needy people around the globe. This study highlights the hurdles influence the smooth working and growth of Microfinance institution in Egypt. The structured interviews were conducted from the top and mid-level managers of MFI's. This study revealed that interest rate, political and economic conditions, corruption, customer outreach, competition and technology are the important elements for MFI's success. It is evident that lack of use of technology and less importance drawn on customer outreach programs are the main challenges of MFI's in Egypt. This study provides a roadmap for practitioners and strategic