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 futuristic age requires progress in handwork or even sub-machine dependency and Brain-Computer Interface (BCI) provides the necessary BCI procession. As the article suggests, it is a pathway between the signals created by a human brain thinking and the computer, which can translate the signal transmitted into action. BCI-processed brain activity is typically measured using EEG. Throughout this article, further intend to provide an available and up-to-date review of EEG-based BCI, concentrating on its technical aspects. In specific, we present several essential neuroscience backgrounds that describe well how to build an EEG-based BCI, including evaluating which signal processing, software, and hardware techniques to use. Individu

This research aims at analysing epitaphs written by Thomas Moore for the memory of Rupert Southey, the epitaph is analysed linguistically and stylistically on four levels graphology, phonology, morphology, and lexico-syntax level to explore the elements that the writer uses the most at each level. Bearing in mind Nowottny approach (1962) (to text analysis) who believes that the linguistic analysis of a literary text is not just a marginal but a necessity” (Bakuuro etal., 2018:34). The researcher has selected and analysed a written epitaph of famous individual associated with English, literature. The study involves both literary and linguistic analysis, with much more concentration through the analysis on the aspect of linguistics. In fact

     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 this paper two ranking functions are employed to treat the fuzzy multiple objective (FMO) programming model, then using two kinds of membership function, the first one is trapezoidal fuzzy (TF) ordinary membership function, the second one is trapezoidal fuzzy weighted membership function. When the objective function is fuzzy, then should transform and shrinkage the fuzzy model to traditional model, finally solving these models to know which one is better

<p>Photovoltaic (PV) systems are becoming increasingly popular; however, arc faults on the direct current (DC) side are becoming more widespread as a result of the effects of aging as well as the trend toward higher DC voltage levels, posing severe risk to human safety and system stability. The parallel arc faults present higher level of current as compared with the series arc faults, making it more difficult to spot the series arc. In this paper and for the aim of condition monitoring, the features of a DC series arc fault are analyzed by analysing the arc features, performing model’s simulation in PSCAD, and carrying out experimental studies. Various arc models are simulated and investigated; for low current arcs, the heur