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

This research shows the issues of Ibn Hisham's illusion in its leadership of the grammarians; As Ibn Hisham attributed - during his presentation of grammatical issues - grammatical opinions to a number of grammarians claiming them in them, and after referring to the main concepts that pertain to those grammarians, we found that Ibn Hisham had delusional in those allegations, in addition to that clarifying the terms illusion and claim in the two circles of language And the terminology, and perhaps the most prominent result in this research is that he worked to investigate these issues by referring to their original sources, with an explanation of the illusions of Ibn Hisham in his attribution to these issues.

Given the growing interest in digital marketing operations and the technology imposed by the reality in which both companies and their customers are affected, the researchers attempted to shed light on the reality and challenges of digital marketing from the faculty members viewpoint at Jouf university, the problem is that technology has imposed a new reality that has resulted in a major change in behavioral patterns of customers with a number of obstacles and challenges confronted customers in digital marketing, it is expected that the outcomes of this study help companies in overcoming the obstacles that prevent the desire and ability of the customer to change his behavioral style to deal with electronic shopping operations and

In order to get advanced results, we must stand at the pointsthat have been observed by the trainers that are of significance inthe sport of fencing and concern for capacity optical (traceoptical and precision visual animation), so we must learn some ofthese types of capacity, whichever is more influential in the gamefencing so that they add a new axis to the player to pick andchoose in order to achieve the desired goal and raise the level ofthe game.The study aimed to identify the relationship between the visualtracking and accuracy of visual animated face and the results ofcompetitions Sabre of the other.Used a much more descriptive approach to study relational on asample of players clubs Sabre and the way intentional, whoqualified to the

Magneto-rheological (MR) valve is one of the devices generally used to control the speed of Hydraulic actuator of MR fluid. The performance of valve depends on the magnetic circuit design. Present study deals with a new design of MR valve. A mathematical model for the MR valve is developed and the simulation is carried out to evaluate the newly developed MR valve. The design of the magnetic circuit is accomplished by magnetic finite element software such as Finite Element Method Magnetic (FEMMR). The model dimensions of MR valve, material properties are taken into account. The results of analysis are presented in terms of magnetic strength H and magnetic flux density B. The simulation results based on the proposed model indicate that the ef

major goal of the next-generation wireless communication systems is the development of a reliable high-speed wireless communication system that supports high user mobility. They must focus on increasing the link throughput and the network capacity. In this paper a novel, spectral efficient system is proposed for generating and transmitting twodimensional (2-D) orthogonal frequency division multiplexing (OFDM) symbols through 2- D inter-symbol interference (ISI) channel. Instead of conventional data mapping techniques, discrete finite Radon transform (FRAT) is used as a data mapping technique due to the increased orthogonality offered. As a result, the proposed structure gives a significant improvement in bit error rate (BER) performance. Th

There is a continuous and massive need for newer cephalosporins that should have resistance against β-lactamases and can be used orally. An approach of using cephalexin, as a well-studied and potent antibacterial compound is considered to prepare new designed derivatives.  These derivatives include the incorporation of amino acid moiety linked through an amide bond with the α-amino group of cephalexin. Certain aliphatic amino acids were used, such as glycine, alanine, valine and proline. The chemical structures of these derivatives were confirmed by IR spectroscopy and elemental analyses. All the synthesized compounds were subjected for preliminary evaluation of antimicrobial activity using well diffusion method, against certa

Sliding Mode Controller (SMC) is a simple method and powerful technique to design a robust controller for nonlinear systems. It is an effective tool with acceptable performance. The major drawback is a classical Sliding Mode controller suffers from the chattering phenomenon which causes undesirable zigzag motion along the sliding surface. To overcome the snag of this classical approach, many methods were proposed and implemented. In this work, a Fuzzy controller was added to classical Sliding Mode controller in order to reduce the impact chattering problem. The new structure is called Sliding Mode Fuzzy controller (SMFC) which will also improve the properties and performance of the classical Sliding Mode control

<p><span>Medium access control (MAC) protocol design plays a crucial role to increase the performance of wireless communications and networks. The channel access mechanism is provided by MAC layer to share the medium by multiple stations. Different types of wireless networks have different design requirements such as throughput, delay, power consumption, fairness, reliability, and network density, therefore, MAC protocol for these networks must satisfy their requirements. In this work, we proposed two multiplexing methods for modern wireless networks: Massive multiple-input-multiple-output (MIMO) and power domain non-orthogonal multiple access (PD-NOMA). The first research method namely Massive MIMO uses a massive numbe