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

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

     Credit card fraud has become an increasing problem due to the growing reliance on electronic payment systems and technological advances that have improved fraud techniques. Numerous financial institutions are looking for the best ways to leverage technological advancements to provide better services to their end users, and researchers used various protection methods to provide security and privacy for credit cards. Therefore, it is necessary to identify the challenges and the proposed solutions to address them.  This review provides an overview of the most recent research on the detection of fraudulent credit card transactions to protect those transactions from tampering or improper use, which includes imbalance classes, c

                In the past years, the Algerian Economy has witnessed various monetary developments characterized by different monetary and banking reforms aimed by monetary authorities to achieve monetary stability and driving overall growth. It should be noted that there is evidence to initiate fundamental changes on the basis of which new monetary, financing and banking policy mechanisms must be formulated in Algeria by enhancing the pursuit of reforming the monetary system, in order to improve monetary and economic indicators.

                The study a

The present study dealt with the morphological, anatomical,trichomespollen grains,and ecological characteristics of Caroxylon jordanicola (EigAkhani & Roalson (Amaranthaceae) in Al-Tar Caves, Karbala, Iraq which belongs to the Amaranthaceae family. The results of the present study demonstrated that There are distinctive characteristics of the studied species distinguish it from other species and facilitate its diagnosis. The sample was diagnosed using the taxonomic keys of the Iraqi flora and the flora of neighboring countriesIn addition to some available research. The results of the morphological and anatomical features investigation provide really significant taxonomical value to distinguish the species. The results that showe