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

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

In this work, we focused on studying 1,4-naphthoquinones and their derivatives, and knowing the methods of preparing them using different auxiliary agents and forming derivatives containing heterocyclic rings, active groups and saturated rings containing heterogeneous elements . In addition, due to their strong antibacterial, antifungal and anticancer activity, 1,4-naphthoquinone compounds biological importance and are considered a source of various pharmaceutical compounds.

      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

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