We dealt with the nature of the points under the influence of periodic function chaotic functions associated functions chaotic and sufficient conditions to be a very chaotic functions Palace

           Titanium dioxide nanoparticles (TiO₂ NPs) are generally used in different types of applications such as the industry of plastics, paper industry, paints, toothpaste, cosmetics, sunscreens, and in various lifestyles, because of the vast range of applications and our daily exposure to these nanoparticles and a lack of information on animal and human health this study was designed to reveal dose and time-dependent effects of TiO₂-NPs on the thyroid gland and kidney functions in male rats.

For this study 54, Sprague-Dawley albino adult male rats were classified into three main groups each of 18 rats treated for a particular duration (1,2, and 4) weeks respectively. Each group was subdivided i

In this work we explain and discuss new notion of fibrewise topological spaces, calledfibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.

In this paper, we define a new type of pairwise separation axioms called pairwise semi-p- separation axioms in bitopological spaces, also we study some properties of these spaces and relationships of each one with the ordinary separation axioms in the bitopological spaces.

By use the notions pre-g-closedness and pre-g-openness we have generalized a class of separation axioms in topological spaces. In particular, we presented in this paper new types of regulαrities, which we named ρg­regulαrity and Sρg­regulαrity. Many results and properties of both types have been investigated and have illustrated by examples.

  In this paper we introduce a new class of degree of best algebraic approximation polynomial Α,, for unbounded functions in weighted space Lp,α(X), 1 ∞ .We shall prove direct and converse theorems for best algebraic approximation in terms modulus of smoothness in weighted space

This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor

In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.