The restriction concept is a basic feature in the field of measure theory and has many important properties. This article introduces the notion of restriction of a non-empty class of subset of the power set on a nonempty subset of a universal set. Characterization and examples of the proposed concept are given, and several properties of restriction are investigated. Furthermore, the relation between the P*–field and the restriction of the P*–field is studied, explaining that the restriction of the P*–field is a P*–field too. In addition, it has been shown that the restriction of the P*–field is not necessarily contained in the P*–field, and the converse is true. We provide a necessary condition for the P*–field to obtain th

    Let R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.   

    The present study was performed to evaluate the anti-fungal effect of alcoholic extract of Solanum nigrum (AESn) on the growth of Microsporum canis, the causes agent of ring worm. The results of this work referred to the inhibitory effect of the studied extract on the growth of tested fungi. The percentages of inhibition were (7.88 %, 19.88%, 23.41%, 57.65%), in comparison to the control, when (2%, 4%, 6%,8% ) of tested extract were used, respectively. The data illustrated that the higher concentrations of the extract are applied, the more inhibition of fungal growth is produced. 

In this paper we introduce the notions of bi-ideal with respect to an element r
denoted by (r-bi- ideal ) of a near ring , and the notion fuzzy bi- ideal with respect
to an element of a near ring and the relation between F-r-bi-ideal and r-bi-ideal of
the near ring, we studied the image and inverse image of r-bi- ideal under
epimomorphism ,the intersection of r-bi- ideals and the relation between this ideal
and the quasi ideal of a near ring, also we studied the notion intuitionistic fuzzy biideal
with respect to an element r of the near ring N, and give some theorem about
this ideal .

     Segmentation is one of the most computer vision processes importance, it aims to understand the image contents by partitioning it into segments that are more meaningful and easier to analyze. However, this process comes with a set of challenges including image skew, noise, and object clipping. In this paper, a solution is proposed to address the challenges encountered when using Optical Character Recognition to recognize mathematical expressions. The proposed method involves three stages: pre-processing, segmentation, and post-processing. During pre-processing, the mathematical expression image is transformed into a binary image, noise reduction techniques are applied, image component discontinuities are resolved, and skew corre

Abstract The Synthesis in good yields of some new 1,8-Naphthyridine derivatives (1-9) and characterized on the basis of IR and 1H NMR spectra data. The compounds (1) and (6) were utilized as a starting material for the preparing of these compounds.

The purpose of this study is to determine the useful of Schiff bases derivatives containing (oxazepine, tetrazole) rings with biological activity which can be used as drug and antimicrobial, the present work is started from [Binary (2,5(4,'4-diaminophenyl) – 1,3,4 – oxadiazole]. A variety of Schiff bases and heterocyclic (oxazepine, tetrazole) have been synthesis, and confirm that structures by physical properties , FTIR , 1H-NMR, 13C-NMR, elemental analysis, [Microbial study against three type of bacteria (staphylococcus aurea and klebsiella pneumonia) and (Canadida albncans) fungi].All analyzation performed in center of consulatation University of Jordan.

      Let S be a commutative ring with identity, and A is an S-module. This paper introduced an important concept, namely strongly maximal submodule. Some properties and many results were proved as well as the behavior of that concept with its localization was studied and shown.

     In this paper we tend to describe the notions of intuitionistic fuzzy asly ideal of ring indicated by (I. F.ASLY) ideal and, we will explore some properties and connections about this concept.