Related papers: A Visual Proof that $\pi^e < e^\pi$

A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and Y does not compute X. A real X is relatively simple and above if there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset Z of…

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

In this short note, we will show that the metric of Deligne's pairing is continous.

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

Assume that we are given two graphic sequences, $\pi_1$ and $\pi_2$. We consider conditions for $\pi_1$ and $\pi_2$ which guarantee that there exists a simple graph $G_2$ realizing $\pi_2$ such that $G_2$ is the subgraph of any simple graph…

Extending a result of Christiansen, we prove that every mutli-graph $G=(V,E)$ admits a proper edge colouring $\phi:E\to \{1,2,\dots\}$ which is local, that is, $\phi(e)\le \max\{d(x)+\pi(x),d(y)+\pi(y)\}$ for every edge $e$ with end-points…

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We prove several congruences for trinomial coefficients.

We give three new proofs of the triangle inequality in Euclidean Geometry. There seems to be only one known proof at the moment. It is due to properties of triangles, but our proofs are due to circles or ellipses. We aim to prove the…

Let $E$ be an elliptic curve defined over ${\mathbb Q}$. For a prime $p$ of good reduction for $E$, denote by $e_p$ the exponent of the reduction of $E$ modulo $p$. Under GRH, we prove that there is a constant $C_E\in (0, 1)$ such that $$…

We produce a new, shorter construction of a minor-universal planar graph.

In this note, I study a comparison map between a motivic and \'{e}tale cohomology group of an elliptic curve over $\mathbb{Q}$ just outside the range of Voevodsky's isomorphism theorem. I show that the property of an appropriate version of…

I prove lower bounds of some parameters of elliptic curve over finite field. There parameters are closely interrelated with cryptographic stability of elliptic curve.

This paper deals with a proof theory for a theory of $\Pi_{N}$-reflecting ordinals using a system of ordinal diagrams. This is a sequel to the previous one(APAL 129)in which a theory for $\Pi_{3}$-reflection is analysed proof-theoretically.

Short proof of the aperiodicity of the Robinson tile set.

We bring additional support to the conjecture saying that a rational cuspidal plane curve is either free or nearly free. This conjecture was confirmed for curves of even degree, and in this note we prove it for many odd degrees. In…

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

The article presents the proof of Casas-Alvero conjecture.

The author states an exact expression of the distribution of primes.