Related papers: A simple proof of Zeeman's theorem

We provide a short proof of the 1-dimensional flat chain conjecture.

We prove the following indistinguishability theorem for $k$-tuples of trees in the uniform spanning forest of $\mathbb{Z}^d$: Suppose that $\mathscr{A}$ is a property of a $k$-tuple of components that is stable under finite modifications of…

This paper offers a proof of the Coase theorem by formalizing the notion of ideal exchanges.

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact"…

A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

We prove some Liouville type theorems on smooth compact Riemannian manifolds with nonnegative sectional curvature and strictly convex boundary. This gives a nonlinear generalization in low dimension of the recent sharp lower bound of the…

We prove three results on the $a$-points of the derivatives of the Riemann zeta function. The first result is a formula of the Riemann-von Mangoldt type; we estimate the number of the $a$-points of the derivatives of the Riemann zeta…

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

The proof of the conjecture of the Birch and Swinnerton - Dyer is presented in the paper. The Riemann's hypothesis on the distribution of non-trivial zeroes of the zeta-function of Riemann, previously proven, is word to prove this…

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…

We obtain simple proofs of certain inequalites for bivariate means.

We present an elementary, short and simple proof of the validity of the Lindel\"of hypothesis about the Riemann zeta-function. The obtained estimate and classical results by Bohr-Landau and Littlewood disprove Riemann's hypothesis.

Consider the following nonlinear Neumann problem \[ \begin{cases} \text{div}\left(y^{a}\nabla u(x,y)\right)=0, & \text{for }(x,y)\in\mathbb{R}_{+}^{n+1}\\ \lim_{y\rightarrow0+}y^{a}\frac{\partial u}{\partial y}=-f(u), & \text{on…

We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.

We present the technique of derivation of a theory to obtain an $(n+1)f$-degrees-of-freedom theory from an $f$-degrees-of-freedom theory and show that one can calculate all of the quantities of the derived theory from those of the original…

We offer a self-contained proof of Lenagan's Theorem which does not rely on Goldie's Theorem