Abstract: We consider second order nonlinear systems in control canonical form, where the functional relation between the control variable and the system acceleration is nonlinear, uncertain and ...

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 ...

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 ...

In this work, Fourier-series representation of a discontinuous function is used to highlight and clarify the controversial problem of finding the value of the function at a point of discontinuity.

Applied researchers often need to estimate confidence intervals for functions of parameters, such as the effects of counterfactual policy changes. If the function is continuously differentiable and ...

The present paper is devoted to the investigation of the properties of the space of distributions with discontinuous test functions of several variables. The consideration of discontinuous test ...

For nonparametric regression, where the regression function has discontinuity points, the kernel regression estimator and cross-validation are known to be affected by ...

In this part you do not have to sketch the graph and you may even be given the sketch of the graph to start with. For a quadratic equation of the form \(y = k{(x - a)^2} + b\), the following diagram ...