In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

In the present paper, a simply* compact spaces was introduced it defined over simply*- open set previous knowledge and we study the relation between the simply* separation axioms and the compactness, in addition to introduce a new types of functions known as 𝛼𝑆 𝑀∗ _irresolte , 𝛼𝑆 𝑀∗ __𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 and 𝑅 𝑆 𝑀∗ _ continuous, which are defined between two topological spaces.

The chemical properties of chemical compounds and their molecular structures are intimately connected. Topological indices are numerical values associated with chemical molecular graphs that help in understanding the physicochemical properties, chemical reactivity and biological activity of a chemical compound. This study obtains some topological properties of second and third dominating David derived (DDD) networks and computes several K Banhatti polynomial of second and third type of DDD.

    The aim of our work is to develop a new type of games which are related to (D, WD, LD) compactness of topological groups. We used an infinite game that corresponds to our work. Also, we used an alternating game in which the response of the second player depends on the choice of the first one. Many results of winning and losing strategies have been studied, consistent with the nature of the topological groups. As well as, we presented some topological groups, which fail to have winning strategies and we give some illustrated examples. Finally, the effect of functions on the aforementioned compactness strategies was studied.  

   Let M is a Г-ring. In this paper the concept of orthogonal symmetric higher bi-derivations on semiprime Г-ring is presented and studied and the relations of two symmetric higher bi-derivations on Г-ring are introduced.

Optical Mark Recognition (OMR) is an important technology for applications that require speedy, high-accuracy processing of a huge volume of hand-filled forms. The aim of this technology is to reduce manual work, human effort, high accuracy in assessment, and minimize time for evaluation answer sheets. This paper proposed OMR by using Modify Bidirectional Associative Memory (MBAM), MBAM has two phases (learning and analysis phases), it will learn on the answer sheets that contain the correct answers by giving its own code that represents the number of correct answers, then detection marks from answer sheets by using analysis phase. This proposal will be able to detect no selection or select more than one choice, in addition, using M

Optical Mark Recognition (OMR) is an important technology for applications that require speedy, high-accuracy processing of a huge volume of hand-filled forms. The aim of this technology is to reduce manual work, human effort, high accuracy in assessment, and minimize time for evaluation answer sheets. This paper proposed OMR by using Modify Bidirectional Associative Memory (MBAM), MBAM has two phases (learning and analysis phases), it will learn on the answer sheets that contain the correct answers by giving its own code that represents the number of correct answers, then detection marks from answer sheets by using analysis phase. This proposal will be able to detect no selection or select more than one choice, in addition, using M

In this research, a new application has been developed for games by using the generalization of the separation axioms in topology, in particular regular, Sg-regular and SSg- regular spaces. The games under study consist of two players and the victory of the second player depends on the strategy and choice of the first player. Many regularity, Sg, SSg regularity theorems have been proven using this type of game, and many results and illustrative examples have been presented