Pointwise convergence problem of free Benjamin-Ono-Burgers equation

<abstract><p>In this paper, we show the almost everywhere pointwise convergence of free Benjamin-Ono-Burgers equation in $ H^{s}({\bf{R}}) $ with $ s &gt; 0 $ with the aid of the maximal function estimate.</p></abstract>

A Layered Middleware for OT/IT Convergence to Empower Industry 5.0 Applications

We are still in the midst of Industry 4.0 (I4.0), with more manufacturing lines being labeled as smart thanks to the integration of advanced ICT in Cyber–Physical Systems (CPS). While I4.0 aims to provision cognitive CPS systems, the nascent Industry 5.0 (I5.0) era goes a step beyond, aiming to build cross-border, sustainable, and circular value chains benefiting society as a whole. An enabler of this vision is the integration of data and AI in the industrial decision-making process, which does not exhibit yet a coordination between the Operation and Information Technology domains (OT/IT). This work proposes an architectural approach and an accompanying software prototype addressing the OT/IT convergence problem. The approach is based on a two-layered middleware solution, where each layer aims to better serve the specific differentiated requirements of the OT and IT layers. The proposal is validated in a real testbed, employing actual machine data, showing the capacity of the components to gracefully scale and serve increasing data volumes.

Coverage Control Optimization Algorithm for Wireless Sensor Networks Based on Combinatorial Mathematics

The traditional wireless sensor network coverage control optimization algorithm has the problems of long completion time, high energy consumption, and low coverage. A new algorithm based on combinational mathematics for wireless sensor network coverage control is proposed. The particle swarm optimization (PSO) algorithm is used to optimize the coverage control process of wireless sensor networks. Then, the combined mathematics method is used to detect the local convergence problem. Finally, the quasi-physical forces of quasi-gravity and Coulomb force are used to integrate the quasi-physical force into the particle. In the process of velocity evolution, the speed correction process of particle swarm optimization is optimized, which can effectively avoid the local convergence problem of the particle swarm optimization algorithm, reduce the repeated coverage, and expand the coverage. The experimental results show that compared with the traditional algorithm, the proposed algorithm has short completion time, low energy consumption, and high coverage.

Path planning of mobile robot based on particle swarm optimization algorithm

Aiming at the premature convergence problem of particle swarm optimization (PSO) due to the loss of population diversity in the late stage of search, this paper improves the traditional PSO and proposes the elite mean deviation induction strategy, which improves the convergence speed and accuracy of PSO. The experimental results show that the convergence speed and accuracy of the improved PSO are improved. The effectiveness of the improved algorithm is proved.

Existence and Convergence Results for Generalized Mixed Quasi-Variational Hemivariational Inequality Problem

The main purpose of this paper is threefold. One is to study the existence and convergence problem of solutions for a class of generalized mixed quasi-variational hemivariational inequalities. The second one is to study the existence of optimal control for such kind of generalized mixed quasi-variational hemivariational inequalities under given control u∈U. The third one is to study the relationship between the optimal control and the data for the underlying generalized mixed quasi-variational inequality problems and a class of minimization problem. As an application, we utilize our results to study the elastic frictional problem in a class of Hilbert spaces. The results presented in the paper extend and improve upon some recent results.

Healthcare Data Analysis Using Water Wave Optimization-Based Diagnostic Model

This paper presents a new diagnostic model for various diseases. In the proposed diagnostic model, a water wave optimization (WWO) algorithm was implemented for improving the diagnosis accuracy. It was observed that the WWO algorithm suffered from the absence of global best information and premature convergence problems. Therefore in this work, some improvements were proposed to formulate the WWO algorithm as more promising and efficient. The global best information issue was addressed by using an improved solution search equation and the aim of this was to explore the global best optimal solution. Furthermore, a premature convergence problem was rectified by using a decay operator. These improvements were incorporated in the propagation and refraction phases of the WWO algorithm. The proposed algorithm was integrated into a diagnostic model for the analysis of healthcare data. The proposed algorithm aimed to improve the diagnosis accuracy of various diseases. The diverse disease datasets were considered for implementing the performance of the proposed diagnostic model based on accuracy and F-score performance indicators, while the existing techniques were regarded to compare the simulation results. The results confirmed that the WWO-based diagnostic model achieved a higher accuracy rate as compared to existing models/techniques with most disease/healthcare datasets. Therefore, it stated that the proposed diagnostic model is more promising and efficient for the diagnosis of different diseases.

Nonsingular Global Fixed-Time Stabilization for Nonlinear Systems

Since existing results about fixed-time stabilization are only applied to strict feedback systems, this paper investigates the nonsingular fixed-time stabilization of more general high-order nonlinear systems. Based on a novel concept named coordinate mapping of time domain, a control method is first proposed to transform the nonsingular fixed-time convergence problem into the finite-time convergence problem of a transformed time-varying system. By extending the existing, adding a power integrator technique into the considered time-varying system, a periodic controller is constructed to stabilize the original system in fixed time. The results of simulations verify the effectiveness of the proposed method.

Pointwise convergence along a tangential curve for the fractional Schrödinger equation with 0 < m < 1

In this article, we study the pointwise convergence problem about solution to the fractional Schrödinger equation with 0 < m < 1 along the tangential curve and estimate the capacitary dimension of the divergence set. We extend the results of Cho and Shiraki in [8] for the case m > 1 to the case 0 < m < 1, which is sharp up to the endpoint.