Knowledge of a truncated Fourier series expansion for a discontinuous 2^-periodic function, or a truncated Chebyshev series expansion for a discontinuous nonperiodic function defined on the interval [-1, 1], is used in this paper to accurately and efficiently reconstruct the corresponding discontinuous function. First an algebraic equation of degree M for the M locations of discontinuities in e...

This research aims to explain users’ discontinuous usage behavior in social network context. With system features increasing, information flooding and personal network expanding of SNSs, users begin to emerge social network fatigue, and ultimately express discontinuous usage intention. To explain this phenomenon, we develop a research model based on a cognition-affection-conation framework. Thi...

In this paper, we develop stability, dissipativity, and optimality notions for dynamical systems with discontinuous vector fields. Specifically, we consider dynamical systems with Lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving Filippov set-valued maps specifying a set of directions for the system velocity and admitting Filipp...

A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the relaxation of the system toward its stationary system. Bases on the first behavior, static phase transitions (discontinuous changes in the stationary profil...

A tutorial on solutions, nonsmooth analysis, and stability Discontinuous dynamical systems arise in a large number of applications. In optimal control problems, open-loop bang-bang controllers switch discontinuously between extreme values of the inputs to generate minimum-time trajectories from the initial to the final states [1]. Thermostats implement on-off controllers to regulate room temper...

1 Tankers moored at an oil production center.