Graphing a piecewise defined function might seem daunting at first, but breaking down the process into manageable steps can make it significantly easier. A piecewise function, as the name suggests, is ...

Let $E$ be a set. Let $(A_i){1 \leq i \leq n}$ be a finite sequence of disjoint subsets of $E$, and let $(f_i){1 \leq i \leq n}$ be a finite sequence of real-valued ...

Abstract: We propose a novel characterization of piecewise-defined barrier functions for certifying forward invariant sets of piecewise continuous dynamical systems. Forward invariance is established ...

I just noticed that the textbook lacks an example relevant to this exercise group, which is a type of problem we frequently assess: Given a piecewise-defined function, we want to know if it is ...

Abstract: In this work, we study the sampling of piecewise smooth- graph signals that exhibit an inhomogeneous level of smoothness over the graph and are characterized by have abrupt, localized ...