Related papers: A variation of Gronwall's lemma
We give a counting based proof of the Graham Pollak Theorem
We investigate a variation of $q$-Wolstenholme's theorem, which extends the $q$-analogue of Wolstenholme's theorem due to Shi and Pan [Amer. Math. Monthly 114 (2007), 529--531]. The proof makes use of the Ramanujan sum and higher order…
We expose here a short proof of Cramer's theorem in R based on convex duality.
We prove a version of van der Corput's Lemma for polynomials over the p-adic numbers.
This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.
We provide new sufficient conditions under which Ryser's conjecture holds.
We give a probabilistic proof of the orbit-counting lemma.
We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.
A proposed solution to the Riemann Hypothesis
We present a generalization of a formula of higher order derivatives and give a short proof.
We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.
We provide a permutation-invariant version of the Koml\'os' theorem for non-negative random variables. The proof is quite elementary in the sense that it did not use the Axiom of Choice, and was based on a recent result in [3].
We give a proof of some small weight and level cases of Serre's conjecture.
Watson proved Kirkman's hypothesis (partially solved by Cayley). Using Lagrange Inversion, we drastically shorten Watson's computations and generalize his results at the same time.
We prove some vanishing conditions on the Gromov-Witten invariants of product of P1.
In this paper, we state as a conjecture a vector-valued Hopf-Dunford-Schwartz lemma and give a partial answer to it. As an application of this powerful result, we prove some Fe fferman-Stein inequalities in the setting of Dunkl analysis…
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.
In a preceding paper [E.J.ofProb.34,860-892,(2006)], we proved a sewing lemma which was a key result for the study of Holder continuous functions. In this paper we give a non-commutative version of this lemma with some applications.