In this paper, the concept of a neutrosophic KU-algebra is introduced and some related properties are investigated. Also, neutrosophic KU-ideals of a neutrosophic KU-algebra are studied and a few properties are obtained. Furthermore, a few results of neutrosophic KU-ideals of a neutrosophic KU-algebra under homomorphism are discussed

The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex

Background: Juvenile idiopathic arthritis (JIA) is a chronic disease of childhood. Increased prevalence of periodontal disease and dental caries in juvenile idiopathic arthritis is due to difficulties in executing good oral hygiene. This study was conducted to assess oral health status in patients with Juvenile idiopathic arthritis according to age and duration of illness. Materials and methods: A research was conducted among Juvenile idiopathic arthritis patients attending Baghdad Teaching Hospital with different age and both gender, underwent a clinical evaluation of their dental and oral condition. Diagnosis of dental caries was done according to the criteria of WHO (1997). Dental plaque, gingival condition, calculus were assessed by PI/

Most real-life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subgraphs without coding or using assumption. The aim of this paper is to apply near concepts in the -closure approximation spaces. The basic notions of near approximations are introduced and sufficiently illustrated. Near approximations are considered as mathematical tools to modify the approximations of graphs. Moreover, proved results, examples, and counterexamples are provided.

       Let R be a commutative ring with unity .M an R-Module. M is called coprime module     (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M   In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.

      Let R be a commutative ring with identity and M  an unitary R-module. Let (M)  be the set of all submodules of M, and : (M)  (M)  {} be a function. We say that a proper submodule P of M is end--prime if for each   EndR(M) and x  M, if (x)  P, then either x  P + (P) or (M)  P + (P). Some of the properties of this concept will be investigated. Some characterizations of end--prime submodules will be given, and we show that under some assumtions prime submodules and end--prime submodules are coincide.

Throughout this paper R represents commutative ring with identity, and M is a unitary left R-module. The purpose of this paper is to study a new concept, (up to our knowledge), named a semi-extending modules, as generalization of extending modules, where an Rmodule M is called semi-extending if every sub module of M is a semi-essential in a direct summand of M. Various properties of semi-extending module are considered. Moreover, we investigate the relationships between semi-extending modules and other related concepts, such as CLS-modules and FI- extending modules.