Let G be a finite group and X be a conjugacy class of order 3 in G. In this paper, we introduce a new type of graphs, namely A₄-graph of  G, as a simple graph denoted by A₄(G,X) which has X as a vertex set. Two vertices,  x and y, are adjacent if and only if  x≠y and  x y^-1=y x^-1. General properties  of the A₄-graph as well as the structure of A₄(G,X) when G@ ³D₄(2) will be studied.

    ان ظاهرة الالعاب المحرضة على العنف اصبحت منتشرة في الاسواق بشكل واسع الذي يعزو الى ضعف القوانين والانظمة والتعليمات المطبقة بحق المتاجرين وبالتالي انعدام التطبيقات القضائية ، ولخطورة التوجه الكبير لهذه الألعاب ، كما ان البحث في هذا الموضوع  وتحديد مسؤولية المتاجر بهذه الالعاب يجعل الدولة أكثر تحكما في هذه الظاهرة وتساعد على  الحد من انتشارها ومن ثم تخفيف حدة العنف السائد في المجتم

This paper deals with the F-compact operator defined on probabilistic Hilbert space and gives some of its main properties.

In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

The effect of smoking, age and exposure duration in pesticide risk groups were studied > Groups were all men and included farmers (25), pesticide sellers (25), pesticides manufacture workers (Al-Tark factory for agricultural pesticide production) (25), Control group (25) were from Baghdad university staff (living in Baghdad city) > The cytogenetic parameters studied were Chromosomal aberrations (CA), induction of micronuclei (Mn)formation .Results revealed that smoking synergized pesticides exposure in induction of structural CAs in all groups with significant differences (P<0.01) and the worst effect recorded in workers , the increment was more than folds the level of control group (0.68) for the non smokers and was 5.78 times (control gr

The primary objective of this paper is to present a new concept of fibrewise topological spaces over B is said to be fibrewise slightly topological spaces over B. Also, we introduce the concepts of fibrewise slightly perfect topological spaces, filter base, contact point, slightly convergent, slightly directed toward a set, slightly adherent point, slightly rigid, fibrewise slightly weakly closed, H.set, fibrewise almost slightly perfect, slightly∗ .continuous fibrewise slightly∗ topological spaces respectively, slightly Te, locally QHC, In addition, we state and prove several propositions related to these concepts.

The essential objective of this paper is to introduce new notions of fibrewise topological spaces on D that are named to be upper perfect topological spaces, lower perfect topological spaces, multi-perfect topological spaces, fibrewise upper perfect topological spaces, and fibrewise lower perfect topological spaces. fibrewise multi-perfect topological spaces, filter base, contact point, rigid, multi-rigid, multi-rigid, fibrewise upper weakly closed, fibrewise lower weakly closed, fibrewise multi-weakly closed, set, almost upper perfect, almost lower perfect, almost multi-perfect, fibrewise almost upper perfect, fibrewise almost lower perfect, fibrewise almost multi-perfect, upper^* continuous fibrewise upper^∗ topol

The purpose of this paper is to study a new types of compactness in the dual bitopological spaces. We shall introduce the concepts of L-pre- compactness and L-semi-P- compactness .

The proliferation of electronic games, video games and computers has caused children and teenagers to become attracted to these games and become their favorite entertainment. The widespread of these games has generated widespread debate about positive aspects and negative aspects. It is evident that there are two main trends in the impact of electronic games on the behavior of children and adolescents. The first trend is that e-games have positive effects on children and adolescents, especially in cognitive abilities and skills in learning. While the second view sees that electronic games have negative effects that appear in social isolation and lack of movement and aggression. Through the review of previous literature, the current resea

The aim of this research is to study some types of fibrewise fuzzy topological spaces. The six major goals are explored in this thesis. The very first goal, introduce and study the notions types of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j={δ,θ,α,p,s,b,β} The second goal is to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuz