We have studied some types of ideals in a KU-semigroup by using the concept of a bipolar fuzzy set. Bipolar fuzzy S-ideals and bipolar fuzzy k-ideals are introduced, and some properties are investigated. Also, some relations between a bipolar fuzzy k-ideal and k-ideal are discussed. Moreover, a bipolar fuzzy k-ideal under homomorphism and the product of two bipolar fuzzy k-ideals are studied.

Sports skills in some individual games require physical and motor qualities to facilitate the process of skill performance and also require the instructor or trainer to use more than one strategy, method and way to bring the performance to the level of mastery and avoid injury. The aim of the research is to know the effect of using special exercises using tools and their effect on teaching the skill of a front shoulder circle. The research hypothesis is that using special exercises with tools has a positive effect on teaching the skill of a front shoulder circle on the rings apparatus. Research method: - The researchers used the experimental method by designing two equal groups, the control and the experimental, to suit the research

The aim of this paper is to present a weak form of -light functions by using -open set which is -light function, and to offer new concepts of disconnected spaces and totally disconnected spaces. The relation between them have been studied. Also, a new form of -totally disconnected and inversely -totally disconnected function have been defined, some examples and facts was submitted.

The cross section evaluation for (α,n) reaction was calculated according to the available International Atomic Energy Agency (IAEA) and other experimental published data . These cross section are the most recent data , while the well known international libraries like ENDF , JENDL , JEFF , etc. We considered an energy range from threshold to 25 M eV in interval (1 MeV). The average weighted cross sections for all available experimental and theoretical(JENDL) data and for all the considered isotopes was calculated . The cross section of the element is then calculated according to the cross sections of the isotopes of that element taking into account their abundance . A mathematical representative equation for each of the element

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.

Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.

In this paper we investigated some new properties of π-Armendariz rings and studied the relationships between π-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, α-compatible rings and others. We proved that if R is a central Armendariz, then R is π-Armendariz ring. Also we explained how skew Armendariz rings can be ?-Armendariz, for that we proved that if R is a skew Armendariz π-compatible ring, then R is π-Armendariz. Examples are given to illustrate the relations between concepts.

The biggest problem of structural materials for fusion reactor is the damage caused by the fusion product neutrons to the structural material. If this problem is overcomed, an important milestone will be left behind in fusion energy. One of the important problems of the structural material is that nuclei forming the structural material interacting with fusion neutrons are transmuted to stable or radioactive nuclei via (n, x) (x; alpha, proton, gamma etc.) reactions. In particular, the concentration of helium gas in the structural material increases through deuteron- tritium (D-T) and (n, α) reactions, and this increase significantly changes the microstructure and the properties of the structural materials. T