相关论文: A proof of Bertrand's theorem using the theory of …

We prove a certain relation between Legendre's conjecture and Bertrand's postulate in terms of a certain transformation of Legendre's function phi. We show a certain property of a prime.

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.

We prove a theorem of uppersemicontinuity for the metric entropy of meromorphic maps.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

Working from definitions and an elementarily obtained integral formula for the Euler-Mascheroni constant, we give an alternative proof of the classical Puiseux representation of the exponential integral.

We present a geometric characterization of the nonlinear smooth functions $V: R\to R$ for which the origin is a global isochronous center for the scalar equation $\ddot x=-V'(x)$. We revisit Stillinger and Dorignac isochronous potentials…

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.

In this note, we give a probabilistic interpretation of the Central Limit Theorem used for approximating isotropic Gaussians in [1].

We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…

We consider the rational potentials of the one-dimensional mechanical systems, which have a family of periodic solutions with the same period (isochronous potentials). We prove that up to a shift and adding a constant all such potentials…

We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $\dot x=-y+A(x,y), \dot y=x+B(x,y)$, where $A, B\in \mathbb{R}[x,y]$, which can be reduced to the Lienard type equation. Using the so-called C-algorithm we have found…

The paper contains an alternative proof of M. Kontsevich Formality 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 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…

A new generalization of the classical separate algebraicity theorem is suggested and proved.

We prove a power series ring analogue of the Dedekind-Mertens lemma. Along the way, we give limiting counterexamples, we note an application to integrality, and we correct an error in the literature.