Related papers: A note on the Lee-Yang circle theorem

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.

In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…

In this paper we present a short and elementary proof for the error in Simpson's rule.

This paper presents a new, significantly simpler proof of one of the main results of applied pi-calculus: the theorem that the concepts of observational and labeled equivalence of extended processes in applied pi-calculus coincide.

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

In this short note, we point out a mistake in G.Cybenko's proof of his version of the universal approximation theorem which has been widely cited. This mistake might not be easily fixable along the idea of his proof and it also leads to an…

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

We present a simpler proof of Naji's characterization of circle graphs.

We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.

The aim of this note is to give a proof of the Schottky theorem in general domains in $\mathbb{C}^n$. The proof is short and works for the cases $n = 1$ and $n > 1$ at the same time.

These are notes on de Jong's proof of the period=index theorem over fields of transcendence degree two. They are actually about the simplified proof sketched by de Jong in the last section of his paper. These notes were meant as support for…

This note gives a short proof on characterizations of a forest to be equitably k-colorable.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

In this short note,we correct a well-known counter example of the famous book of Dacorogna[2].

The goal of this short note is to provide simple proofs for the "folklore facts" on the sample complexity of learning a discrete probability distribution over a known domain of size $k$ to various distances $\varepsilon$, with error…

This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…

The aim of this work is to establish the celebrated Denjoy-Wolff Theorem in the context of generalized Loewner chains. In contrast with the classical situation where essentially convergence to a certain point in the closed unit disk is the…

The theory of random real numbers is exceedingly well-developed, and fascinating from many points of view. It is also quite challenging mathematically. The present notes are intended as no more than a gateway to the larger theory. They…