New research has found ChatGPT-5.2 can generate original mathematical proofs, introducing “vibe-proving” as a new AI ...

Abstract: This note studies the linear quadratic (LQ) optimal control of continuous-time linear time-invariant systems with random gains imposed on the input channels. We start from the indefinite LQ ...

Abstract: This note surveys a novel algebraic-topological version of the max-flow-min-cut (MFMC) theorem for directed networks with capacity constraints. Novel features include the encoding of ...

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable ...

👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which ...

👉 Learn about Descartes' Rule of Signs. Descartes' rule of the sign is used to determine the number of positive and negative real zeros of a polynomial function. Knowing the number of positive and ...

This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and ...