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 ...

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: We study representations of piecewise-smooth signals on graphs. We first define classes for smooth, piecewise-constant, and piecewise-smooth graph signals, followed by a series of ...

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 ...

An algorithmic solution to the biological effective dose (BED) calculation from the Lea-Catcheside formula for a piecewise defined function is presented. Data from patients treated for metastatic ...