Related papers: A higher order Weierstrass approximation theorem -…
We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.
In this paper, we prove a number of results providing either necessary or sufficient conditions guaranteeing that the number of real roots of real polynomials of a given degree is either less or greater than a given number. We also provide…
We provide a short proof of the intriguing characterisation of the convex order given by Wiesel and Zhang.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
This document presents an alternative proof of Sylvester's theorem stating that "the product of $n$ consecutive numbers strictly greater than $n$ is divisible by a prime strictly greater than $n$". In addition, the paper proposes stronger…
In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.
In this paper, we present a general method for obtaining addition theorems of the Weierstrass elliptic function $\wp(z)$ in terms of given parameters. We obtain the classical addition theorem for the Weierstrass elliptic function as a…
We establish some new theorems on pentagon and pentagram.
We give a counter example to the new theorem that appeared in the survey \cite{H} on Artin approximation. We then provide a correct statement and a proof of it.
We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.
In this article we show that some recent results on the existence of best proximity points can be obtained from the same result in fixed point theory.
The Stone-Weierstrass approximation theorem is extended to certain unbounded sets in $C^n$. In particular, on a locally rectifiable arc going to infinity, each continuous function can be approximated by entire functions.
We use Weierstrass Point Theory and Frobenius orders to prove the uniqueness (up to isomorphism) of some optimal curves.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
This is a literal word-for-word translation from the German of the article by Paul Koebe which contains a proof of Weierstrass's famous theorem characterizing all analytic functions which possess an algebraic addition theorem.
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…
As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals…
We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.