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 concept of Assemblage appeared obviously in Postdramatic works, where a character or a text may stand as an assemblage of potentialities in the sense that it signifies unidentified subjectivity. Assemblages are constituted essentially of heterogeneous elements yet fused without specific demarcations. In order to enjoy the desired productivity at a "smooth pace," the regularities of political and societal institutionalization are disseminated. To achieve this dissemination, Deleuze-Guattari suggest an unsatiated platform of a "Body without Organs' (BwO), where desire escapes identification. Martin Crimp (b. 1956) defines his off-stage characters in Attempts on Her Life (1997), Anne, or whatever the name is, as a 'BwO', upon which

With the recent developments of technology and the advances in artificial intelligent and machine learning techniques, it becomes possible for the robot to acquire and show the emotions as a part of Human-Robot Interaction (HRI). An emotional robot can recognize the emotional states of humans so that it will be able to interact more naturally with its human counterpart in different environments. In this article, a survey on emotion recognition for HRI systems has been presented. The survey aims to achieve two objectives. Firstly, it aims to discuss the main challenges that face researchers when building emotional HRI systems. Secondly, it seeks to identify sensing channels that can be used to detect emotions and provides a literature review

The efforts in designing and developing lightweight cryptography (LWC) started a decade ago. Many scholarly studies in literature report the enhancement of conventional cryptographic algorithms and the development of new algorithms. This significant number of studies resulted in the rise of many review studies on LWC in IoT. Due to the vast number of review studies on LWC in IoT, it is not known what the studies cover and how extensive the review studies are. Therefore, this article aimed to bridge the gap in the review studies by conducting a systematic scoping study. It analyzed the existing review articles on LWC in IoT to discover the extensiveness of the reviews and the topics covered. The results of the study suggested that many re

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

The world is currently challenging the serious effects of the pandemic of the Coronavirus disease (COVID-19) caused by severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2). Data on pediatric COVID are rare and scattered in the literature. In this article, we presented the updated knowledge on the pediatric COVID-19 from different aspects. We hope it will increase the awareness of the pediatricians and health care professionals on this pandemic.