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 current study investigates the impact of virtual reality technology on industrial product design. The focus of this study is on the development of industrial products that utilize virtual reality technology, specifically examining the effects of this technology on the visual and design aspects of these products. The aim is to continuously improve the functionality of industrial products and enhance the user experience through virtual reality integration.
The first chapter of the study addresses the research problem, which centers around exploring the technological influence of virtual reality used in industrial products and understanding the functionalities it brings to the design process. Virtual reality technology facilitates th

Image fusion is one of the most important techniques in digital image processing, includes the development of software to make the integration of multiple sets of data for the same location; It is one of the new fields adopted in solve the problems of the digital image, and produce high-quality images contains on more information for the purposes of interpretation, classification, segmentation and compression, etc. In this research, there is a solution of problems faced by different digital images such as multi focus images through a simulation process using the camera to the work of the fuse of various digital images based on previously adopted fusion techniques such as arithmetic techniques (BT, CNT and MLT), statistical techniques (LMM,

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

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

   In this paper, we introduce new classes of sets called g *sD -sets , g *sD −α -sets , g *spreD − sets , g *sbD − -sets and g *sD −β -sets . Also, we study some of their properties and relations among them . Moreover, we use these sets to define and study some associative separation axioms .
 

International Journal on Technical and Physical Problems of Engineering

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.

Singapore has invested its human resources for the development of the country since earlier times, so it has directed attention to the education sector. Education and development complement each other, as investment in education has contributed over several years to the development of Singapore economy and has made it one of the strongest economies in Asia and the world. Despite the obstacles that faced educational policies in Singapore, the presence of a wise leadership capable of overcoming difficulties and solving them, and providing the appropriate atmosphere for the development of education has contributed significantly to making it one of the most advanced educational systems in the world, and making this system the main pillar for