Let R be a commutative ring with unity and let M be a left R-module. We define a proper submodule N of M to be a weakly prime if whenever  r  R,  x  M, 0  r x  N implies  x  N  or  r  (N:M). In fact this concept is a generalization of the concept weakly  prime ideal, where a proper ideal P of R is called a weakly prime, if for all a, b  R, 0  a b  P implies a  P or b  P. Various properties of weakly prime submodules are considered. 

      Let R be a commutative ring with identity and M be 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 -prime if for each r  R and x  M, if rx  P, then either x  P + (P) or r M  P + (P) . Some of the properties of this concept will be investigated. Some characterizations of -prime submodules will be given, and we show that under some assumptions prime submodules and -prime submodules are coincide. 

     Let  be a commutative ring with identity, and a fixed ideal of  and  be an unitary -module. In this paper we  introduce and study the concept of -nearly prime submodules as genrealizations of nearly prime and we investigate some properties of this class of submodules. Also, some characterizations of -nearly prime submodules will be given.

    In this paper, the concepts of -sequence prime ideal and -sequence quasi prime ideal are introduced. Some properties of such ideals are investigated. The relations between -sequence prime ideal and each of primary ideal, -prime ideal, quasi prime ideal, strongly irreducible ideal, and closed ideal, are studied. Also, the ideals of a principal ideal domain are classified into quasi prime ideals and -sequence quasi prime ideals.

In this study, pebble bed as an absorber and storage material was placed in a south facing, flat plate air-type solar collector at fixed tilt angle of (45°). The effect of this material and differ- ent parameters on collector efficiency has been investigated experimentally and
theoretically. Two operation modes were employed to study the performance of the solar air heater. An inte- grated mode of continuous operation of the system during the period of (11:00 am – 3:00 pm) and non-integrated mode in which the system stored the solar energy through the day then used the stored energy during the period of (3:00 pm – 8:00 pm). The results of parametric study in case of continuous operating showed that the maximum average temperatur

Background: The denture base inaccuracies during processing negatively influence the retention and stability of finished complete denture. The aims of this study were to evaluate teeth movement and palatal adaptation of autoclave cured denture bases and their relationship with palatal depths and investments. Materials and methods: A nightly maxillary complete dentures prepared, processed and organized to be tested as follows: 1. Processing methods: water bath and autoclave with both fast and slow cycles. 2. Palatal depth: shallow, medium and deep. 3. Investing medium: stone and silicone. For every finished denture, two measurements were done: first: teeth movement by attaching metallic reference screws on the right and left centrals, first

Complex-valued regular functions that are normalized in the open unit disk are vastly studied. The current study introduces a new fractional integrodifferential (non-linear) operator. Based on the pre-Schwarzian derivative, certain appropriate stipulations on the parameters included in this con-structed operator to be univalent and bounded are investigated and determined.

In this paper,  we introduce the concepts of  higher reverse left (resp.right)   centralizer, Jordan higher reverse left (resp. right) centralizer, and Jordan triple higher reverse left (resp. right) centralizer of  G-rings. We prove that every Jordan higher reverse left (resp. right) centralizer of a 2-torsion free prime G-ring M is a higher reverse left (resp. right) centralizer of  M.