Related papers: An Elementary proof for Bertrand's Postulate
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
We present a short and self-contained proof of the choosability version of Brooks' theorem.
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
A beautiful theorem due to J. L. F. Bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from French into English.
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
Myriad articles are devoted to Mertens's theorem. In yet another, we merely wish to draw attention to a proof by Hardy, which uses a Tauberian theorem of Landau that "leads to the conclusion in a direct and elegant manner". Hardy's proof is…
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 new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then…
This article provides a proof of the famous \textit{Prime Number Theorem} by establishing an analogous statement of the same in terms of the second \textit{Chebyshev Function} $\psi(x)$. We shall be extensively using complex analytic…
We give an elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves by using Kato's element.
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
We obtain some new inequalities of Chebyshev Type.
The goal of this notice is to present a proof of Bachet's conjecture based exclusively on the fundamental theorem of arithmetic. The novelty of this proof consists in its introduction of a partial order on rational integers through the…
We establish an unconditional effective Chebotarev density theorem that improves uniformly over the well-known result of Lagarias and Odlyzko. As a consequence, we give a new asymptotic form of the Chebotarev density theorem that can count…
In the present note a generalization of Borel-Cantelli Lemma is proposed.