Related papers: On two extensions of Poncelet theorem
Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.
In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.
I study the sequences of Euler and Springer numbers from the point of view of the classical moment problem.
In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers…
The aim of this note is to provide a natural extension of Gelfond's constant $e^\pi$ using a hypergeometric function approach. An extension is also found for the square root of this constant. A few interesting special cases are presented.
The main result of the paper is an interesting relation between the solution of the truncated Exponential Moment problem and truncated Classical Moment problem, considered on the half-line or on a compact interval.
We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem.
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.
We isolate a combinatorial property of capacities leading to a construction of proper forcings. Then we show that many classical capacities such as the Newtonian capacity satisfy the property.
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.
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
We prove a variant of the standard Whitney extension theorem for $\mathcal C^m(\mathbb R^n)$, in which the norm of the extension operator has polynomial growth in $n$ for fixed $m$.
In this note we generalise a method of Perott to give new proofs that there are infinitely many prime numbers.
For the infinite-dimensional extension of the Dirichlet distribution, the super Poincare inequality does not hold based on the result in [14], so we establish the weighted super Poincare inequalities for this measure with respect to two…
In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.
We compare two henselisations of a residually discrete valuation domain. Our constructive proof that a certain natural morphism is an isomorphism is also a proof in classical mathematics. Although this isomorphism is implicitly accepted as…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
We establish some new theorems on pentagon and pentagram.
Paper withdrawn, see math-ph/0505072