Related papers: A Visual Proof that $\pi^e < e^\pi$
In this very short note we prove a lower bound for the scalar curvature of certain steady gradient Ricci solitons.
We prove that five ways to define entry A086377 in the On-Line Encyclopedia of Integer Sequences do lead to the same integer sequence.
In this note we give a p-adic proof of Hodge symmetry for smooth, projective threefolds over complex numbers.
We show that the copolarity of pseudo-cones has analogous properties as the usual polarity of convex bodies.
For a specific class of surfaces of revolution S, the existence of a smooth map {\Phi} from a neighbourhood U of S to the Euclidean plane E2 preserving distances infinitesimally along the meridians and the parallels of S and sending the…
We claim to resolve the P=?NP problem via a formal argument for P=NP.
A result about projections of Gibbs measures from a particular class arising in economic modeling is proved.
Let $D$ be an directed graph on $p\geq 10$ vertices with minimum degree at least $p-1$ and minimum semi-degree at least $ p/2 -1$. We present a detailed proof of the following result [13]: The digraph $D$ is pancyclic, unless some extremal…
In the paper we prove (modulo the classification of finite simple groups) an analogue of the famous Baer-Suzuki theorem for the $\pi$-radical of a finite group, where $\pi$ is a set of primes
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
We give a new simpler proof of a theorem of Jayne and Rogers.
We provide two different proofs of an irreducibility criterion for the preimages of a transverse subvariety of a product of elliptic curves under a diagonal endomorphism of sufficiently large degree.For curves, we present an arithmetic…
Irreducible representations are the building blocks of general, semisimple Galois representations \rho, and cuspidal representations are the building blocks of automorphic forms \pi of the general linear group. It is expected that when an…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
The motivation and research design for repeating the EPF experiments are described in the paper.
This paper presents a proof of the following conjecture, stated by Nishizawa in [Appl. Math. Comput. 269, (2015), 146--154.]: for $\displaystyle 0<x<\pi/2$ the inequality $ \displaystyle \frac{\sin{x}}{x} \!>\! \left(\frac{2}{\pi} +…
In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of $\pi$ by using its rational approximation. In this approximation, both terms are constructed by using a…
We give a new analytical proof of the Morse index theorem for geodesics in Riemannian manifolds.
We give a new proof of Chen-Lin result with Li-Zhang method.