Scientific Research Publishing

A Note on Discontinuous Functions with Continuous Second Iterate

This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous functions.
Scientific Research Publishing

A Note on Discontinuous Functions with Continuous Second Iterate ()

1 Department of Mathematics, Binzhou University, Shandong, China. 2 Department of Mathematics, Neijiang Normal University, Sichuan, China. of functions [1] - [7] , computing the n-th iterate of ...
IEEE

Direct Weight Optimization applied to discontinuous functions

Abstract: The Direct Weight Optimization (DWO) approach is a nonparametric estimation approach that has appeared in recent years within the field of nonlinear system identification. In previous work, ...
IEEE

Lyapunov Functions, Stability and Input-to-State Stability Subtleties for Discrete-Time Discontinuous Systems

Abstract: In this note we consider stability analysis of discrete-time discontinuous systems using Lyapunov functions. We demonstrate via simple examples that the classical second method of Lyapunov ...
Europe PMC

Robust Finite-Time Stabilization of Fractional-Order Neural Networks With Discontinuous and Continuous Activation Functions Under Uncertainty.

This paper is concerned with robust finite-time stabilization for a class of fractional-order neural networks (FNNs) with two types of activation functions (i.e., discontinuous and continuous ...
Europe PMC

Factorization of products of discontinuous functions applied to Fourier-Bessel basis.

The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of ...