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

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The subject of this research is an important topic, which is frequently repeated, and people need to know its wisdom, and has made it in front and the preface and three detectives, showed through discussion the meaning of the survey on the socks, its wisdom, its rules and conditions, and the duration of the survey on it, spoiled and reasoned and compared to the doctrinal doctrines, And the most correct statement of words I have concluded with a number of things, as follows:

1. The need to ensure that the slippers are clean, visible and inwa

The evaluation of subsurface formations as applied to oil well drilling started around 50 years ago. Generally, the curent review articule includes all methods for coring, logging, testing, and sampling. Also the methods for deciphering logs and laboratory tests that are relevant to assessing formations beneath the surface, including a look at the fluids they contain are discussed. Casing is occasionally set in order to more precisely evaluate the formations; as a result, this procedure is also taken into account while evaluating the formations. The petrophysics of reservoir rocks is the branch of science interested in studying chemical and physical properties of permeable media and the components of reservoir rocks which are associated

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 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

Microplastics in aquatic ecosystem has a cumulative effect on the environment, especially fish population, which is directly associated with human health. The impact on fish health differs among the neurological, digestive, and immune systems, as well as behavioral, circulatory, and antioxidant defense systems. This study aims to review previously published studies about the correlation between microplastics and physiological alteration in fish.

               The research aimed at designing a teaching aid for learning backswing into handstand as well as identifying its effect on learning skill performance. The researchers hypothesized statistical differences between pre and post-tests in favor of the research group. They used the experimental method on six (13 – 16) year–old Baghdad club gymnasts. The researchers used the one group design in which all players perform pretests followed by special tests on the teaching aid than are tested posttests. The researchers conclude that the teaching aid positively affected learning the skill as well as the teaching aid was very good and endured the performance of all gymnasts. The researcher recommended making simi

Artificial intelligence (AI) offers significant benefits to biomedical research and academic writing. Nevertheless, using AI-powered writing aid tools has prompted worries about excessive dependence on these tools and their possible influence on writing proficiency. The current study aimed to explore the academic staff’s perspectives on the impact of AI on academic writing. This qualitative study incorporated in-person interviews with academic faculty members. The interviews were conducted in a semi-structured manner, using a predetermined interview guide consisting of open-ended questions. The interviews were done in person with the participants from May to November 2023. The data was analyzed using thematic analysis. Ten academics aged