In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise Lindelöf and locally Lindelöf topological spaces, which are generalizations of will-known concepts: Lindelöf topological space (1) "A topological space X is called a Lindelöf space if for every open cover of X has a countable subcover" and locally Lindelöf topological space (1) "A topological space X is called a locally Lindelöf space if for every point x in X, there exist a nbd U of x such that the closure of U in X is Lindelöf space". Either the new concepts are: "A fibrewise topological space X over B is called a fibrewise Lindelöf if the projection function p : X→B is Lindelöf" and "The fibrewise topological space X over B

The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

The study of fixed points on the  maps fulfilling certain contraction requirements has several applications and has been the focus of numerous research endeavors. On the other hand, as an extension of the idea of the best approximation, the best proximity point (ƁƤƤ) emerges. The best approximation theorem ensures the existence of an approximate solution; the best proximity point theorem is considered for addressing the problem in order to arrive at an optimum approximate solution. This paper introduces a new kind of proximal contraction mapping and establishes the best proximity point theorem for such mapping in fuzzy normed space ( space). In the beginning, the concept of the best proximity point was introduced. The concept of prox

We introduce and discus recent type of fibrewise topological spaces, namely fibrewise bitopological spaces, Also, we introduce the concepts of fibrewise closed bitopological spaces, fibrewise open bitopological spaces, fibrewise locally sliceable bitopological spaces and fibrewise locally sectionable bitopological spaces. Furthermore, we state and prove several propositions concerning with these concepts.

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

      Sequences spaces  , m  ,  p  have called quasi-Sobolev spaces were  introduced   by Jawad . K. Al-Delfi in 2013  [1]. In this  paper , we deal with notion of  quasi-inner product  space  by using concept of  quasi-normed  space which is generalized  to normed space and given a  relationship  between  pre-Hilbert space and a  quasi-inner product space with important  results   and   examples.  Completeness properties in quasi-inner   product space gives  us  concept of  quasi-Hilbert space .  We show  that ,  not  all  quasi-Sobolev spa

This study investigates the surgical and thermal effects on oral soft tissues produced by CO2 laser emitting at 10.6 micrometers with three different fluences 490.79, 1226.99 and 1840.4 J/cm2. These effects are specifically; incision depth, incision width and the tissue damage width and depth. The results showed that increasing the fluence and /or the number of beam passes increase the average depths of ablation. Moreover, increasing the fluence and the number of beam passes increase the adjacent tissue damage in width and depth. Surgeons using CO2 laser should avoid multiple pulses of the laser beam over the same area, to avoid unintentional tissue damage.

Ration power plants, to generate power, have become common worldwide. One such one is the steam power plant. In such plants, various moving parts of heavy machines generate a lot of noise. Operators are subjected to high levels of noise. High noise level exposure leads to psychological as well physiological problems; different kinds of ill effects. It results in deteriorated work efficiency, although the exact nature of work performance is still unknown. To predict work efficiency deterioration, neuro-fuzzy tools are being used in research. It has been established that a neuro-fuzzy computing system helps in identification and analysis of fuzzy models. The last decade has seen substantial growth in development of various neuro-fuzzy systems