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The uniform convergence of a double sequence of functions at a point and Korovkin-type approximation theorems
2020
Abstract In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in the last section, we compute the rate of convergence.
Voronovskaya type results and operators fixing two functions
2021
The present paper deals with positive linear operators which fix two functions. The transfer of a given sequence (Ln) of positive linear operators to a new sequence (Kn) is investigated. A general procedure to construct sequences of positive linear operators fixing two functions which form an Extended Complete Chebyshev system is described. The Voronovskaya type formula corresponding to the new sequence which is strongly influenced by the nature of the fixed functions is obtained. In the last section our results are compared with other results existing in literature.
Constant sign and nodal solutions for nonlinear robin equations with locally defined source term
2020
We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).
Generalised bisection method for optimum ultrasonic ray tracing and focusing in multi-layered structures
2021
Ultrasonic testing has been used for many decades, proving itself very efficient for detecting defects in many industrial sectors. The desire to apply ultrasonic testing to geometrically complex structures, and to anisotropic, inhomogeneous materials, together with the advent of more powerful electronics and software, is constantly pushing the applicability of ultrasonic waves to their limits. General ray tracing models, suitable for calculating the proper incident angle of single element probes and the proper time delay of phased array, are currently required. They can support the development of new imaging techniques, as Full Matrix Capture and Total Focusing Method, and the execution of …
Partial discharges behavior under different rectified waveforms
2017
In this work, a previous software used to simulate partial discharges (PDs) under Alternating Current (AC) stress has been modified in order to evaluate the PDs behavior under a voltage stress close to the Direct Current (DC) waveform. By using a full-wave and a half-wave rectifier, the specimen with an air void defects has been subjected to a gradual constant stress. Finally, a capacitive filter has been inserted in order to produce a steadier voltage supply. Simulation results show that under an almost DC waveform, the PDs activity become less compared to AC stress.
An exact method for the determination of differential leakage factors in electrical machines with non-symmetrical windings
2016
An exact and simple method for the determination of differential leakage factors in polyphase ac electrical machines with non-symmetrical windings is presented in this paper. The method relies on the properties of Gorges polygons that are used to transform an infinite series expressing the differential leakage factor into a finite sum in order to significantly simplify the calculations. Some examples are shown and discussed in order to practically demonstrate the effectiveness of the proposed method.
A Magnetohydrodynamic Auxiliary Propulsion system for docking assistance of autonomous vehicle
2016
In this article we present an approach to the description of Magnetohydrodynamic Auxiliary Propulsion system for docking assistance of autonomous vehicle. Preliminarily, an analytical model which includes an electromagnetic model and a thermal model is presented. Successively, in order to move beyond the analytical model, a 3-D MHD modeling tool and a Runge Kutta method based solver are presented and they are used to investigate an alternative MHD solutions. Some numerical analysis are given
Resistive communications based on neuristors
2017
Memristors are passive elements that allow us to store information using a single element per bit. However, this is not the only utility of the memristor. Considering the physical chemical structure of the element used, the memristor can function at the same time as memory and as a communication unit. This paper presents a new approach to the use of the memristor and develops the concept of resistive communication.
Stability of melt flow during magnetic sonication in a floating zone configuration
2018
Combined static and alternating magnetic fields are shown to create an oscillating pressure that can cause cavitation in molten metals. A time-averaged flow is also excited, consisting of two tori squeezed to thin boundary layers. Flow instability develops as a standing wave between these tori.
Preface for MMM 2016 focus issue
2017
International audience