Fibrewise topological spaces theory is a relatively new branch of mathematics, less than three decades old, arisen from algebraic topology. It is a highly useful tool and played a pivotal role in homotopy theory. Fibrewise topological spaces theory has a broad range of applications in many sorts of mathematical study such as Lie groups, differential geometry and dynamical systems theory. Moreover, one of the main objects, which is considered in fibrewise topological spaces theory is connectedness. In this regard, we of the present study introduce the concept of connected fibrewise topological spaces and study their main results.

<p>In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.</p>

The efficiency of internal combustion engines (ICE) is usually about thirty percent of the total energy of the fuel. The residual energy is lost in the exhaust gas, the lubrication, and the cooling water in the radiators. Recently much of the researcher’s efforts have focused on taking advantage of wasted energy of the exhaust gas. Using a thermoelectric generator (TEG) is one of the promising ways. However, TEG depends entirely on the temperature difference, which may be offered by the exhaust muffler. An experimental test has been conducted to study the thermal performance of a different muffler internal design. The researchers resort to the use of lost energy in an ICE using TEG, which is one of the ways to take adv

Based on the streamer growth model, the streamer discharge propagation was simulated in aid of finite element technique. That was done within two non- mixed dielectric liquids (Normal-Hexane and Acetone) located between two electrodes in pin - plane configuration. The output results show that, the path of the streamer was affected by the interface between the two liquids; the streamer path crosses this interface under some conditions such as the permittivity of the liquids and the distance between this interface and the tip of the pin. Under other conditions, the streamer path grows along the interface. The results were assisted by the development of the potential and the electric field distributions with the growth of the streamer propa

Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.

Abstract. Fibrewise micro-topological spaces be a useful tool in various branches of mathematics. These mathematical objects are constructed by assigning a micro-topology to each fibre from a fibre bundle. The fibrewise micro-topological space is then formed by taking the direct limit of these individual micro-topological spaces. It can be adapted to analyze various mathematical structures, from algebraic geometry to differential equations. In this study, we delve into the generalizations of fibrewise micro-topological spaces and explore the applications of these abstract structures in different branches of mathematics. This study aims to define the fibrewise micro topological space through the generalizations that we use in this paper, whi

The separation of fluid-fluid mixtures is a major issue in various sectors. The liquid-liquid hydro-cyclone has a wide range of applications in various sectors due to its great efficiency in separating fluid mixtures, ease of installation, and low cost. In crude oil production, high water is consumed following the degrading of production quality, high processing costs, costs, and environmental impacts. Axial hydro cyclone is a tool for Downhole Oil/Water Separation (DOWS) in the petroleum production industry, but it has limitations. The main purpose of this work is to simulate the effect of compacting the conventional inline hydro cyclone with a converging-diverging nozzle on the oil/water dynamic flow and the separation process to

Doppler broadening technique is suggested to monitor the development of tumours. It depends on the sensitivity of positronium (Ps) annihilation parameters to the sub- microstructural changes in biological tissues. This technique uses high resolution HpGe detector to measure the lineshape parameters (S and W) in normal mice's mammary tissues and adenocarcinoma mammary tissues as a function of tumour growth. The results demonstrate that the central parameter (S) decreases and the wing parameter (W) increases as the tumour grow. It is found that the S parameter changes considerably with the distribution of voids which are affected by the tumour development. Therefore the present technique can successfully be employed to monitor the developm