Separate Fractional (p,q)-Integrodifference Equations via Nonlocal Fractional (p,q)-Integral Boundary Conditions

In this paper, we study a boundary value problem involving (p,q)-integrodifference equations, supplemented with nonlocal fractional (p,q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of (p,q)-integral that are used in our study.

Existence Results of a Nonlocal Fractional Symmetric Hahn Integrodifference Boundary Value Problem

The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of different orders. We first convert our nonlinear problem into a fixed point problem by considering a linear variant of the problem. When the fixed point operator is available, Banach and Schauder’s fixed point theorems are used to prove the existence results of our problem. Some properties of (q,ω)-integral are also presented in this paper as a tool for our calculations. Finally, an example is also constructed to illustrate the main results.

Business Model Quantification Framework for the Core Participants of the EV Charging Market

The rapid growth of the electrical vehicle (EV) market over the last decade has rendered the existence and accuracy of the business models of the EV charging market a critical factor for a company’s success. To address this issue, this paper presents a quantification framework for the business models of the core participants of the EV charging market, defining the factors that directly influence their revenues and costs and providing two sets of earnings before interest and taxes (EBIT) formulas: explicit and implicit. The explicit formulas would be useful for business analytics of the current participants of the EV charging market, while the implicit could be applied by the new entrants, to make reliable predictions based on the benchmark data. These formulas include factors that have not been previously addressed in the literature such as different prices per type of charger, the annual consumed amount of energy per charger and their utilization rate among others. Finally, this research applies the defined framework on an EBIT scenario of an archetypical charge point operator, based on real-life data.

FPGA Implementation of an Efficient FFT Processor for FMCW Radar Signal Processing

This paper presents the design and implementation results of an efficient fast Fourier transform (FFT) processor for frequency-modulated continuous wave (FMCW) radar signal processing. The proposed FFT processor is designed with a memory-based FFT architecture and supports variable lengths from 64 to 4096. Moreover, it is designed with a floating-point operator to prevent the performance degradation of fixed-point operators. FMCW radar signal processing requires windowing operations to increase the target detection rate by reducing clutter side lobes, magnitude calculation operations based on the FFT results to detect the target, and accumulation operations to improve the detection performance of the target. In addition, in some applications such as the measurement of vital signs, the phase of the FFT result has to be calculated. In general, only the FFT is implemented in the hardware, and the other FMCW radar signal processing is performed in the software. The proposed FFT processor implements not only the FFT, but also windowing, accumulation, and magnitude/phase calculations in the hardware. Therefore, compared with a processor implementing only the FFT, the proposed FFT processor uses 1.69 times the hardware resources but achieves an execution time 7.32 times shorter.

A system of nonlinear fractional BVPs with ϕ-Laplacian operators and nonlocal conditions

This work investigates the existence of multiple positive solutions for a system of two nonlinear higher-order fractional differential equations with ϕ-Laplacian operators and nonlocal conditions. A degenerate nonlinearity which obeys some general growth conditions is considered. The singularities are dealt with by approximating the fixed point operator. New existence results are presented by using the fixed point index theory. Examples of applications illustrate the theoretical results.

A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

Heat flux in general quasifree fermionic right mover/left mover systems

With the help of time-dependent scattering theory on the observable algebra of infinitely extended quasifree fermionic chains, we introduce a general class of so-called right mover/left mover states which are inspired by the nonequilibrium steady states for the prototypical nonequilibrium configuration of a finite sample coupled to two thermal reservoirs at different temperatures. Under the assumption of spatial translation invariance, we relate the 2-point operator of such a right mover/left mover state to the asymptotic velocity of the system and prove that the system is thermodynamically nontrivial in the sense that its entropy production rate is strictly positive. Our study of these not necessarily gauge-invariant systems covers and substantially generalizes well-known quasifree fermionic chains and opens the way for a more systematic analysis of the heat flux in such systems.

Construction of fixed point operators for nonlinear difference equations of non integer order with impulses

In this article, we establish a technique for transforming arbitrary real order delta difference equations with impulses to corresponding summation equations. The technique is applied to non-integer order delta difference equation with some boundary conditions. Furthermore, the summation formulation for impulsive fractional difference equation is utilized to construct fixed point operator which in turn are used to discuss existence of solutions.

How to Make the Charging Simple, Convenient and Efficient

With the large-scale application of electric vehicles (EV) in the world and also in China, the contradiction between the EV and charging stations has become more and more prominent. People always cannot easily find the charging stations or when they find them finally found they do not work. To connect the vehicle, charging station/pile and end-users for making the charging simple, convenient, efficient and visible is becoming very important. People need a platform to tell them where, when and how to charge for their EV. Matrix Mobility is focusing on realizing this comprehensive charging solution together with OEM, charging point operator (CPO), electric power company and parking lots by using big data analysis. Matrix Mobility installs the charging solution into the car unit before cars go off production line and meanwhile integrates the same function into OEM’s own APP with opening API to help end-users increase their charging experience.

A Convex Combination Approach for Mean-Based Variants of Newton’s Method

Several authors have designed variants of Newton’s method for solving nonlinear equations by using different means. This technique involves a symmetry in the corresponding fixed-point operator. In this paper, some known results about mean-based variants of Newton’s method (MBN) are re-analyzed from the point of view of convex combinations. A new test is developed to study the order of convergence of general MBN. Furthermore, a generalization of the Lehmer mean is proposed and discussed. Numerical tests are provided to support the theoretical results obtained and to compare the different methods employed. Some dynamical planes of the analyzed methods on several equations are presented, revealing the great difference between the MBN when it comes to determining the set of starting points that ensure convergence and observing their symmetry in the complex plane.