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

Objectives: The demand for orthodontic treatment is nowadays increasing significantly for aesthetic improvement and to correct various kinds of malocclusion, yet the prolonged treatment time remains the main obstacle. This review aimed to demonstrate various orthodontic techniques and highlight the evidence-based successful approaches used for acceleration of orthodontic tooth movement. Materials and Methods: Data and sources of information pertaining to accelerated orthodontic tooth movement premised on English-written articles were searched using electronic databases including Google Scholar, Scopus, PubMed and MEDLINE. Results: This review demonstrated the availability of different surgical and non-surgical methods to enhance tooth movem

    Feature selection represents one of the critical processes in machine learning (ML). The fundamental aim of the problem of feature selection is to maintain performance accuracy while reducing the dimension of feature selection. Different approaches were created for classifying the datasets. In a range of optimization problems, swarming techniques produced better outcomes. At the same time, hybrid algorithms have gotten a lot of attention recently when it comes to solving optimization problems. As a result, this study provides a thorough assessment of the literature on feature selection problems using hybrid swarm algorithms that have been developed over time (2018-2021). Lastly, when compared with current feature selection procedu

     Social media and networks rely heavily on images. Those images should be distributed in a private manner. Image encryption is therefore one of the most crucial components of cyber security. In the present study, an effective image encryption technique is developed that combines the Rabbit Algorithm, a simple algorithm, with the Attractor of Aizawa, a chaotic map. The lightweight encryption algorithm (Rabbit Algorithm), which is a 3D dynamic system, is made more secure by the Attractor of Aizawa. The process separates color images into blocks by first dividing them into bands of red, green, and blue (RGB). The presented approach generates multiple keys, or sequences, based on the initial parameters and conditions, which are

In this work 27 events have been chosen for the period from (17 Feb 2000 to 10 Sep 2014) to analyze their intensity profile and find out what is the most effective reason behind the bulk of the accelerated SEPs as seen in the interval from the onset to the maximum intensity. It was found that the parameters of the associated eruptions (CME and solar flare) could play a major role in this acceleration. We considered some of these parameters such as: flare class related to soft X-ray flux, CME's speed and acceleration, site of the eruption (western, eastern) and particle transport in the IP medium. The shape of the profile showed a clear changing in ΔT1 (time from onset to maximum), as an inverse relation with the acceleration of coronal

Dyspepsia is a significant public health issue that affects the entire world population. In this work, we formulate and analyze a deterministic model for the population dynamics of Gut bacteria in the presence of antibiotics and Probiotic supplements. All the possible equilibria and their local stability are obtained. The global stability around the positive equilibrium point is established. Numerical simulations back up our analytical findings and show the temporal dynamics of gut microorganisms.

The continuous increases in the size of current telecommunication infrastructures have led to the many challenges that existing algorithms face in underlying optimization. The unrealistic assumptions and low efficiency of the traditional algorithms make them unable to solve large real-life problems at reasonable times.
The use of approximate optimization techniques, such as adaptive metaheuristic algorithms, has become more prevalent in a diverse research area. In this paper, we proposed the use of a self-adaptive differential evolution (jDE) algorithm to solve the radio network planning (RNP) problem in the context of the upcoming generation 5G. The experimental results prove the jDE with best vecto