Related papers: A simple proof of Zeeman's theorem
In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
Liouville type theorems for the stationary Navier-Stokes equations are proven under certain assumptions. These assumptions are motivated by conditions that appear in Liouvile type theorems for the heat equations with a given divergence free…
A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…
This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and…
We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
In this note we examine Littlewood's proof of the prime number theorem. We show that this can be extended to provide an equivalence between the prime number theorem and the non-vanishing of Riemann's zeta-function on the one-line. Our…
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
We show that Thompson's $A\times B$-Lemma can be obtained as a consequence of the Brauer pair version of Brauer's Third Main Theorem.
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.
We prove some general results on the existence and uniqueness of solutions to the Liouville equation. Then, we discuss the sharpness and possible generalizations. Finally, we give several applications, arising in both mathematics and…
Following suggestions of T. H. Koornwinder, we give a new proof of Kummer's theorem involving Zeilberger's algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater. The…
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
We give a purely combinatorial proof of the density Hales--Jewett Theorem that is modeled after Polymath's proof but is significantly simpler. In particular, we avoid the use of the equal-slices measure and work exclusively with the uniform…