In mathematics, proofs can be written down and shared. In cryptography, when people are trying to avoid revealing their ...

Bayes' theorem is a statistical formula used to calculate conditional probability. Learn how it works, how to calculate it ...

Abstract: We show that applying a generalization of the Cayley-Hamilton Theorem to a state-space representation of a single-output, multidimensional (mD), linear, shift-invariant, causal, autonomous ...

We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning ...

Abstract: This paper introduces the formal proof of the three mean value theorems of differentiation in detail. The differential mean value theorem is the core theorem of differential calculus, an ...

This book deals with fundamental problems, concepts, and methods of multiparameter stability theory with applications in mechanics. It presents recent achievements and knowledge of bifurcation theory, ...

This book attempts to bridge the gap between the principles of pure mathematics and the applications in physical science. After the Möbius inversion formula had been considered as purely academic, or ...