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 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

Background: Joubert syndrome (JS) is a very rare autosomal recessive disorder characterized by agenesis of cerebellar vermis, abnormal eye movements, respiratory irregularities, and delayed generalized motor development. Retinal dystrophy and cystic kidneys may also be associated with this clinical syndrome. The importance of recognizing JS is related to the outcome and its potential complications. This syndrome is difficult to diagnose clinically because of its variable phenotype. Its neuroimaging hallmarks include the characteristic molar tooth sign and bat wing-shaped fourth ventricle

A quadruped (four-legged) robot locomotion has the potential ability for using in different applications such as walking over soft and rough terrains and to grantee the mobility and flexibility. In general, quadruped robots have three main periodic gaits:  creeping gait, running gait and galloping gait. The main problem of the quadruped robot during walking is the needing to be statically stable for slow gaits such as creeping gait. The statically stable walking as a condition depends on the stability margins that calculated particularly for this gait. In this paper, the creeping gait sequence analysis of each leg step during the swing and fixed phases has been carried out. The calculation of the minimum stability margins depends up

      This piece of research deals with assimilation as one of the phonological processes in the language. It is a trial to give more attention to this important process in English language with deep explanation to its counterpart in Arabic. in addition, this study sheds light on the points of similarities and differences concerning this process in the two languages. Assimilation in English means two sounds are involved, and one becomes more like the other.

     The assimilating phoneme picks up one or more of the features of another nearby phoneme. The English phoneme /n/ has t

The aim of study is to shed light on an Islamic city which is unknown for a lot of people, it can have an old history in Parisian country and many events happen with it , This city is characterized with political, military, economic scientific ,and social features, This city is called Zanjan and it is one of the most important cities because it dates back to the period of post history and it has a good geographic location whereas it was, passage for trade caravans to pass through as well its land which was specialized in agriculture and industry. the study follows chronological order of historical events for the city, one of the most significant conclusions is to think that this city does belong to artifacts and it is an old city and it

يمثل الأخذ بالنظام الفيدرالي أطاراً تنظيمياً لشكل الدولة و مرحلة تحول مهمة في بنية الدولة العامة في مختلف مجالاتها، فالانتقال من المركزية في أدارة الشؤون العامة للدولة الى النمط الفيدرالي يمثل تحولا بنيوياً وسيكولوجياً ،حيث يكون هنالك توزيع مكاني - عمودي للسلطة والثروة بين الوحدات المكونة للدولة بشكل يختلف كليا عن الحالة المركزية، ونجد صور تنظيمية عديدة تتأسس ضمن اطار الفيدرالية العام ،

A new series polymers was synthesized from reaction starting material Bisacodyl A or [(2-Pyridinylmethylene) di-4, 1-phenylene di acetate] with hydrogen bromide, then the products were polymerized by addition polymerization from used adipoyl and glutaroyl chloride. The structure of these compounds was characterized by FT-IR, melting points, TLC, X-Ray, DSC and 1H-NMR for starting material. These compounds were also screened for their antibacterial activists?