Related papers: On a simple proof the Poincare Conjecture
We review the construction of flows associated to Tanaka's SDE from [9] and give an easy proof of the classification of these flows by means of probability measures on [0, 1]. Our arguments also simplify some proofs in the subsequent papers…
We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.
We consider a simplified model of a two-phase flow through a heterogeneous porous medium, in which the convection is neglected. This leads to a nonlinear degenerate parabolic problem in a domain shared in an arbitrary finite number of…
We first present a modern simple proof of the classical ergodic Birkhoff's theorem and Bourgain's homogeneous bilinear ergodic theorem. This proof used the simple fact that the shift map on integers has a simple Lebesgue spectrum. As a…
All known proofs of the PCP theorem rely on multiple "composition" steps, where PCPs over large alphabets are turned into PCPs over much smaller alphabets at a (relatively) small price in the soundness error of the PCP. Algebraic proofs,…
We introduce four new elementary short proofs of the famous K\"onig's theorem which characterizes bipartite graphs by absence of odd cycles.
In this paper, we prove a conjecture proposed by George Beck, which involves gap-free partitions and partitions with distinct parts.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it…
In this article we give a brief survey of breather and soliton solutions to the Ricci flow and prove a no breather and soliton theorem for homogeneous solutions.
We prove a uniform Sobolev inequality for Ricci flow, which is independent of the number of surgeries. As an application, under less assumptions, a non-collapsing result stronger than Perelman's $\kappa$ non-collapsing with surgery is…
The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).
In this paper we describe protocols which use a standard deck of cards to provide a perfectly sound zero-knowledge proof for Hamiltonian cycles and Flow Free puzzles. The latter can easily be extended to provide a protocol for a…
We present a simple inductive proof of the Lagrange Inversion Formula.
We give a simple proof of the $A_2$ conjecture proved recently by T. Hyt\"onen. Our proof avoids completely the notion of the Haar shift operator, and it is based only on the "local mean oscillation decomposition". Also our proof yields a…
The already proved Lum-Chua's conjecture says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle. In this paper, we provide a new proof by using a novel…
We prove that under a very general setting, a system of ODE passes the Painleve test if and only if there is a good change of variable, such that the pole singularity solutions are converted to regular power series, while the converted ODE…
We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining…
In this work, we introduce a method based on piecewise polynomial interpolation to enclose rigorously solutions of nonlinear ODEs. Using a technique which we call a priori bootstrap, we transform the problem of solving the ODE into one of…
We prove that for every countable discrete group $G$, there is a $G$-flow on $\omega^*$ that has every $G$-flow of weight $\leq\! \aleph_1$ as a quotient. It follows that, under the Continuum Hypothesis, there is a universal $G$-flow of…