Related papers: A simple proof of Tong's theorem

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

This paper proposes a totally constructive approach for the proof of Hilbert's theorem on ternary quartic forms. The main contribution is the ladder technique, with which the Hilbert's theorem is proved vividly.

This is an exposition, in 12 pages including all prerequisites and a generalization, of Karamata's little known elementary proof of the Landau-Ingham Tauberian theorem, a result in real analysis from which the Prime Number Theorem follows…

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

In this note, we give short inductive proofs of two known results on $k$-extendible graphs based on a property proved in [Qinglin Yu, A note on $n$-extendable graphs. Journal of Graph Theory, 16:349-353, 1992].

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series…

This paper presents a short and simple proof of the Four-Color Theorem that can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has allowed it and the global structure of the proof are…

Kummer's test from 1835 states that the positive series $\sum_{n=1}^\infty a_n$ is convergent if and only if there is a sequence $\{ B_n\}_1^\infty$ of positive numbers such that $B_n\cdot \frac{a_n }{a_{n+1}} -B_{n+1}\geq 1 ,$ for all…

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.

There are several proofs now for the stability of Toom's example of a two-dimensional stable cellular automaton and its application to fault-tolerant computation. Simon and Berman simplified and strengthened Toom's original proof: the…

In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.

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

We give a new and short proof of a theorem on k-hypertournament losing scores due to Zhou et al. [G. Zhou, T. Yao, K. Zhang, On score sequences of k-tournaments, European J. Comb., 21, 8 (2000) 993-1000.]

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We give a direct geometric proof of the quantum Monk's formula which relies only on classical Schubert calculus.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.