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

When industrial and  constructional renaissance started in the world, the great interest was going on towards the equipment’s,  which was the first mean for production. After industry was settled the interest was going on towards the men ship which manpower on which the production depends. It was approved that it represents the basic part in all of the processes and the protection of those individuals against dangers of these equipment’s, industry and its accidents was the basic things which was studied in many researches until it crystallized in general principles for all industries and other take care in each industry.

     The professional safety is concerned as restrict which

Abstract: Residual ridge resorption is chronic, progressive, irreversible and cumulative condition associated with teeth loss. Management of a residual ridge with severe resorption to fulfill the patient’s esthetic and functional requirements is quite difficult for the practitioner and also in the construction of an acceptable appliance. As the height of the edentulous ridge reduces the mandibular denture will be improperly function. Severe resorption of the mandibular alveolar ridge may cause instability and discomfort of the convention acrylic resin denture. Dealing with this condition requires clinical skills and knowledge. Treating the severely resorbed mandibular ridge is a challenging effort for prosthodontics. This research present

Honeywords are fake passwords that serve as an accompaniment to the real password, which is called a “sugarword.” The honeyword system is an effective password cracking detection system designed to easily detect password cracking in order to improve the security of hashed passwords. For every user, the password file of the honeyword system will have one real hashed password accompanied by numerous fake hashed passwords. If an intruder steals the password file from the system and successfully cracks the passwords while attempting to log in to users’ accounts, the honeyword system will detect this attempt through the honeychecker. A honeychecker is an auxiliary server that distinguishes the real password from the fake passwords and t

Abstract The avulsion of the flexor digitorum profundus, also known as the jersey finger, is a well-known injury that can be treated surgically. It has been classified into four types, among them type IV which involves tendon avulsion from an associated bony fragment with subsequent retraction to the palm or proximal interphalangeal joint is very rare. We present a case of type IV injury in a 45-year-old man with a pulling-on injury. The repair followed a pull-out technique (reinserting the tendon into the avulsed fragment); the entire reduction was tied over a button on the dorsal aspect of the nail and was augmented with a volar plate. The case was reported due to its rarity. We found that early surgical management of this problem greatly