Related papers: The Marker-Steinhorn Theorem

In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.

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 paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

In this note we give a detailed proof of a theorem of Aubin.

We give a new simpler proof of a theorem of Jayne and Rogers.

We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.

We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

We prove Burkholder inequality using Bregman divergence.

We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We use the Terwilliger algebra to provide a new approach to the Assmus-Mattson theorem. This approach also includes another proof of the minimum distance bound shown by Martin as well as its dual.

The paper gives a unified and simple proof of both theorems and Cousin's theorem.

In this paper we prove gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality. We apply the theorems to many examples of manifolds. We also prove a uniqueness theorem for the basic…

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

We give a short proof of Ahlfors' theorem on covering surfaces.

We prove an infinitary version of the Brauer-Schur theorem.