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 ...

A quadratic equation is drawn as a curve on a set of axes. This type of curve is called a parabola and it is symmetrical. To draw the graph we need coordinates. We generate these coordinates by ...

Abstract: A Lyapunov approach is developed in this paper for estimation of the magnitude of self-induced oscillations for systems with piecewise linear elements. The oscillatory trajectories are ...

Abstract: This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex ...

In the study of production scheduling to meet random fluctuations in supply and demand, a probabilistic measure of effectiveness can be used. This measure is a piecewise quadratic positive definite ...

We study the positive recurrence of piecewise Ornstein—Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes ...

Spiking neuron models simulate neuronal activities and allow us to analyze and reproduce the information processing of the nervous system. However, ionic-conductance models, which can faithfully ...