The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then A is called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

A class of hyperrings known as divisible hyperrings will be studied in this paper. It will be presented as each element in this hyperring is a divisible element. Also shows the relationship between the Jacobsen Radical, and the set of invertible elements and gets some results, and linked these results with the divisible hyperring. After going through the concept of divisible hypermodule that presented 2017, later in 2022, the concept of the divisible hyperring will be related to the concept of division hyperring, where each division hyperring is divisible and the converse is achieved under conditions that will be explained in the theorem 3.14. At the end of this paper, it will be clear that the goal of this paper is to study the concept

Audio classification is the process to classify different audio types according to contents. It is implemented in a large variety of real world problems, all classification applications allowed the target subjects to be viewed as a specific type of audio and hence, there is a variety in the audio types and every type has to be treatedcarefully according to its significant properties.Feature extraction is an important process for audio classification. This workintroduces several sets of features according to the type, two types of audio (datasets) were studied. Two different features sets are proposed: (i) firstorder gradient feature vector, and (ii) Local roughness feature vector, the experimentsshowed that the results are competitive to

We dealt with the nature of the points under the influence of periodic function chaotic functions associated functions chaotic and sufficient conditions to be a very chaotic functions Palace

In this research we will present the signature as a key to the biometric authentication technique. I shall use moment invariants as a tool to make a decision about any signature which is belonging to the certain person or not. Eighteen voluntaries give 108 signatures as a sample to test the proposed system, six samples belong to each person were taken. Moment invariants are used to build a feature vector stored in this system. Euclidean distance measure used to compute the distance between the specific signatures of persons saved in this system and with new sample acquired to same persons for making decision about the new signature. Each signature is acquired by scanner in jpg format with 300DPI. Matlab used to implement this system.

     Ring theory is one of the influential branches of abstract algebra. In this field, many algebraic problems have been considered by mathematical researchers who are working in this field. However, some new concepts have been created and developed to present some algebraic structures with their properties. Rings with derivations have been studied fifty years ago, especially the relationships between the derivations and the structure of a ring. By using the notatin of derivation, many results have been obtained in the literature with different types of derivations. In this paper, the concept of the derivation theory of a ring has been considered. This study presented the definition of

     Ring theory is one of the influ

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

In this paper, we study the effect of group homomorphism on the chain of level subgroups of fuzzy groups. We prove a necessary and sufficient conditions under which the chains of level subgroups of homomorphic images of an a arbitrary fuzzy group can be obtained from that of the fuzzy groups . Also, we find the chains of level subgroups of homomorphic images and pre-images of arbitrary fuzzy groups