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 topic of supra.topological.spaces considered one of the important topics because it is a generalization to topological.spaces. Many researchers have presented generalizations to supra open sets such as supra semi.open and supra pre.open sets and others. In this paper, the concept of δ∼open sets was employed and introduced in to the concept of supra topology and a new type of open set was extracted, which was named S∼δ∼open. Our research entails the utilization of this category of sets to form a new concepts in these spaces, namely S∼δ∼limit points and S∼δ∼derive points, and examining its relationship with S∼open and S∼reg∼open. Based on this class of sets, we have introduced other new concepts such as S∼isolate

The research tagged (functional enhancement and its reflection on industrial product systems) focused on the possibility of enhancing industrial products in terms of form and functionality in a way that they are able to meet the needs of the user through the impact of technology and modern technologies on the functional enhancement of industrial products and their effectiveness in achieving formal and functional design variables, and producing products Industrial products are highly efficient and durable in order to improve them in order to meet the needs of the user, the transfer of technology between life forms and industrial products is desirable because the functional enhancement processes that occurred in general on industrial produ

In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

The Internet makes the world like a small village. It has the ability to make groups of the same ideas, thoughts, and identity close to each other by gathering them in one place. It is a way to communicate and share information and opinion; shaping and sharing of comprising individuals with common interests and the participation of individuals in a fruitful dialogue results in achieving a set of goals promote ideas and mobilizing people about issues and events of common interests.

To address the relationship of the internet via interactive communication and its ability to achieve social capital and discuss issues and various social events, the study sees that the problem of the study could be formulated as follows:

Consid

Abstract Globalization dominated in the last decade of the twentieth century and the eve of the third millennium over economic,politics,psychology,culture,communications and information sciences,it's a historical phenomenon refer to many important transitions in humanitarian life.It foxes on that state has illusion its historical role in the psychologist,economic and political buldings. Globalization issue and its influence in North Korea put a spotlight on political,economic and cultural situations,the political system resists any change with many limitations on political freedoms,human rights and political multiplicity.Libralism trends and free market are so weaken when it comparing within the bad economic situation of the coun

Image pattern classification is considered a significant step for image and video processing. Although various image pattern algorithms have been proposed so far that achieved adequate classification, achieving higher accuracy while reducing the computation time remains challenging to date. A robust image pattern classification method is essential to obtain the desired accuracy. This method can be accurately classify image blocks into plain, edge, and texture (PET) using an efficient feature extraction mechanism. Moreover, to date, most of the existing studies are focused on evaluating their methods based on specific orthogonal moments, which limits the understanding of their potential application to various Discrete Orthogonal Moments (DOM

A field experiment was conducted in Al-Yusufiya district - Al-Mahmoudiya district, Baghdad province during the winter season 2021, to study improving the efficiency and management of water use and the productivity of lettuce under different irrigation systems. The Nested-Factorial Experiments design was used, where the main plots include the first factor, irrigation levels (I1) 50%, (I2) 75%, (I3) 100, (I4) 125%, (I5) 150% ETpan. After depleting 35% of the available water and in terms of climatic data from the American Evaporative Basin, Class A. Then the main factor is divided into three replicates, and the coefficients of the second factor are distributed randomly within each replicate, which includes the irrigation system: surface drip i

Background: The ideal maxillofacial prosthesis should have fine and thin boundaries that bindwith the surrounding facial structures and possess high tear strength.This study aims to determinethe best percentages of nanofiller (TiO2) and intrinsic pigment (silicone functional intrinsic) thatcould be mixed in as additives to improve the tear strength of Cosmesil M511 andVST50F siliconeelastomers with the least effect on their hardness.Materials and Methods: In this in vitro experimental study, a total of 80 samples, 40 for eachelastomer, were fabricated. Each elastomer sample was split into two equal groups to test for tearstrength and Shore A hardness. Each group consisted of 20 samples, including 10 control sampleswithout additives and 10 e