Absolute convergence factors of Lipschitz class functions for general Fourier series

The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions f ∈ Lip ⁡ 1 {f\in\operatorname{Lip}1} class provides absolute convergence of Fourier series. In particular, we found special conditions for the functions of orthonormal system (ONS), for which the above sequences are absolute convergence factors of Fourier series of functions of Lip ⁡ 1 {\operatorname{Lip}1} class. It is established that the resulting conditions are best possible in certain sense.

Non-Trivial Solutions of Non-Autonomous Nabla Fractional Difference Boundary Value Problems

In this article, we present a two-point boundary value problem with separated boundary conditions for a finite nabla fractional difference equation. First, we construct an associated Green’s function as a series of functions with the help of spectral theory, and obtain some of its properties. Under suitable conditions on the nonlinear part of the nabla fractional difference equation, we deduce two existence results of the considered nonlinear problem by means of two Leray–Schauder fixed point theorems. We provide a couple of examples to illustrate the applicability of the established results.

Degree of approximation of Fourier series of functions in Besov space by deferred Nörlund mean

In the present paper, we estimate the rate of convergence of Fourier series of functions by Deferred Nörlund mean in Besov space which is a generalization of [Formula: see text] space.

Fast Computation of Multi-Parametric Electromagnetic Fields in Synchronous Machines by Using PGD-Based Fully Separated Representations

A novel Model Order Reduction (MOR) technique is developed to compute high-dimensional parametric solutions for electromagnetic fields in synchronous machines. Specifically, the intrusive version of the Proper Generalized Decomposition (PGD) is employed to simulate a Permanent-Magnet Synchronous Motor (PMSM). The result is a virtual chart allowing real-time evaluation of the magnetic vector potential as a function of the operation point of the motor, or even as a function of constructive parameters, such as the remanent flux in permanent magnets. Currently, these solutions are highly demanded by the industry, especially with the recent developments in the Electric Vehicle (EV). In this framework, standard discretization techniques require highly time-consuming simulations when analyzing, for instance, the noise and vibration in electric motors. The proposed approach is able to construct a virtual chart within a few minutes of off-line simulation, thanks to the use of a fully separated representation in which the solution is written from a series of functions of the space and parameters coordinates, with full space separation made possible by the use of an adapted geometrical mapping. Finally, excellent performances are reported when comparing the reduced-order model with the more standard and computationally costly Finite Element solutions.

Assessing the Security of Campus Networks: The Case of Seven Universities

The network security situation of campus networks on CERNET (China Education and Research Network) has received great concern. However, most network managers have no complete picture of the network security because of its special management and the rapid growth of network assets. In this investigation, the security of campus networks belonging to seven universities in Wuhan was investigated. A tool called “WebHunt” was designed for campus networks, and with its help, the network security risks were found. Differently from existing tools for network probing, WebHunt can adopt the network scale and special rules of the campus network. According to the characteristics of campus websites, a series of functions were integrated into WebHunt, including reverse resolution of domain names, active network detection and fingerprint identification for software assets. Besides, WebHunt builds its vulnerability intelligence database with a knowledge graph structure and locates the vulnerabilities through matching knowledge graph information. Security assessments of seven universities presents WebHunt’s applicability for campus networks. Besides, it also shows that many security risks are concealed in campus networks, such as non-compliance IP addresses and domain names, system vulnerabilities and so on. The security reports containing risks have been sent to the relevant universities, and positive feedback was received.