R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

<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 present investigation aims to study the effect of heat treatment by quenching in different quenching media (salt water, water and oil) following by tempering on wear resistance of EN25 steel. EN25 steel is an alloy of medium carbon low alloy steel which is used for many applications requiring high tensile strength and wear resistance such as connecting rods, adapters and in power sectors extensively. The specimens are machined to 20 mm in length and 10 mm in diameter. This study is done by two stages: The first stage is done by austenitizing EN25 steel to 850  for 1 hr by quenching the specimens in three different quenching media and then tempered at 300   in air. While the second stage is performed by wear

This work presents a novel technique for the detection of oil aging in electrical transformers using a single mode optical fiber sensor based on surface plasmon resonance (SPR). The aging of insulating oil is a critical issue in the maintenance and performance of electrical transformers, as it can lead to reduce insulation properties, increase risk of electrical breakdown, and decrease operational lifespan. Many parameters are calculated in this study in order to examine the efficiency of this sensor like sensitivity (S), signal to noise ratio (SNR), resolution (refractive index unit) and figure of merit (FOM) and the values are for figure of merit is 11.05, the signal to noise ratio is 20.3, the sensitivity is 6.63, and the resolution is 3

In this paper, a computational method for solving optimal problem is presented, using indirect method (spectral methodtechnique) which is based on Boubaker polynomial. By this method the state and the adjoint variables are approximated by Boubaker polynomial with unknown coefficients, thus an optimal control problem is transformed to algebraic equations which can be solved easily, and then the numerical value of the performance index is obtained. Also the operational matrices of differentiation and integration have been deduced for the same polynomial to help solving the problems easier. A numerical example was given to show the applicability and efficiency of the method. Some characteristics of this polynomial which can be used for solvin

In this paper the variable structure control theory is utilized to derive a discontinuous controller to the magnetic levitation system. The magnetic levitation system model is considered uncertain, which subjected to the uncertainty in system parameters, also it is open-loop unstable and strongly nonlinear. The proposed variable structure control to magnetic levitation system is proved, and the area of attraction is determined. Additionally, the chattering, which induced due to the discontinuity in control law, is attenuated by using a non-smooth approximate. With this approximation the resulted controller is a continuous variable structure controller with a determined steady state error according to the selected control

The research aims to explain the role of the flexible budget in assessing the feedback resulting from deviations by comparing the actual results with the planned performance in light of the economic crisis that the world witnessed during the spread of Corona disease. As most companies, including the Electronic Industries Company, face the problem of controlling production costs and are trying hard to reduce these costs to the lowest level starting from measuring these costs and allocating them and distributing them to products. This helps in controlling deviations and thus the flexible budget becomes a tool that helps in controlling elements Costs