We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse ...

For irrational Laplace transforms, the generalized final value theorem provides the analogous result. Finally, we point to a detailed analysis of the final value theorem for piecewise continuous ...

In this article, we study how the choices of c relate to varying the right endpoint b. In particular, we ask: When we can write c as a continuous function of b in some interval? As we explore this ...

It covers a number of directions, including completeness theorem and compactness theorem for hyperidentities; the characterizations of the Boolean algebra of n-ary Boolean functions and the bounded ...

Prerequisite: MTH 311 Description: This is a comprehensive and rigorous course in the study of real valued functions of one real variable. Topics include sequences of numbers, limits and the Cauchy ...

The first theorem that we prove is an asymptotic approximation result for continuous functions on manifolds using the RVFL network construction presented in Section 3.3.1.

Quantum annealing (QA) can be competitive to classical algorithms in optimizing continuous-variable functions when running on appropriate hardware, show researchers from Tokyo Tech. By comparing ...

In this section, we prove our main result, the impossibility theorem, splitting the proof into the cases of continuous time (Theorem 1) and discrete time (Theorem 2).

Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of ...