相关论文: A higher order Weierstrass approximation theorem -…

We produce an upper bound for the Hausdorff dimension of the graph of a Weierstrass-type function. Whilst strictly weaker than existing results, it has the advantage of being directly computable from the theory of hyperbolic iterated…

We prove some new results related to Tanaka's formula.

A new and elementary proof of a recent result of Laptev and Weidl is given. It is a sharp Lieb-Thirring inequality for one dimensional Schroedinger operators with matrix valued potentials.

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

We give a short proof of Ahlfors' theorem on covering surfaces.

We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

In this note we show that a special case of a recent result by Obus-Wewers (used as a black box) together with a deformation argument in characteristic $p$ leads to a proof of the Oort Conjecture in the general case. A boundedness result is…

We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.

The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.

We strengthen the Weierstrass approximation theorem by proving that any real-valued continuous function on an interval $I \subset \mathbb{R}$ can be uniformly approximated by a real-valued polynomial whose only (possibly complex) critical…

We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.

We give a new version of the open descent theory of Harari and Skorobogatov. As an application of the new version, we prove that some algebraic varieties satisfy strong approximation.

We prove the explicit formula for the probability of a run of r successes in n trials.

We prove the Aharoni Berger Conjecture

We give a complete self-contained proof of Statman's finite completeness theorem and of a corollary of this theorem stating that the $\lambda$-definability conjecture implies the higher-order matching conjecture.

We give a new proof of an important theorem by Nakazi using recent results by Sarason in his seminal paper on agebraic properties of truncated Toeplitz operators.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.

In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.