We announce the extension of optimal regularity and Uhlenbeck compactness to general setting connections on vector bundles with non-compact gauge groups over non-Riemannian manifolds, including Lorentzian metric General Relativity. Compactness is essential tool mathematical analysis for establishing validity approximation schemes. Our proofs are based theory RT-equations $L^p$ curvature. Soluti...

Fundamental laws governing human mobility have many important applications such as forecasting and controlling epidemics or optimizing transportation systems. These mobility patterns, studied in the context of out of home activity during travel or social interactions with observations recorded from cell phone use or diffusion of money, suggest that in extra-personal space humans follow a high d...

First-order convergence in time and space is proved for a fully discrete semi-implicit finite element method the two-dimensional Navier–Stokes equations with L 2 initial data convex polygonal domains, without extra regularity assumptions or grid-ratio conditions. The proof utilises smoothing properties of analysis consistency errors, an appropriate duality argument, smallness numerical solution...

This letter proposes a fast implementation of the regularity-constrained discrete sine transform (R-DST). The original DST \textit{leaks} lowest frequency (DC: direct current) components signals into high (AC: alternating subbands. property is not desired in many applications, particularly image processing, since most natural images concentrate DC subband. characteristic filter banks whereby th...

A bipartite graph G = (V1 ∪ V2, E) is (δ, d)-regular if ̨̨ d− d(V ′ 1 , V ′ 2 ) ̨̨ < δ whenever V ′ i ⊂ Vi, |V ′ i | ≥ δ|Vi|, i = 1, 2.Here, d(V ′ 1 , V ′ 2 ) = e(V ′ 1 , V ′ 2 )/|V ′ 1 ||V ′ 2 | stands for the density of the pair (V ′ 1 , V ′ 2 ). An easy counting argument shows that if G = (V1 ∪ V2 ∪ V3, E) is a 3-partite graph whose restrictions on V1 ∪V2, V1 ∪V3, V2 ∪V3 are (δ, d)regular, then ...

The new class of Banach spaces, so-called asymptotic lp spaces, is introduced and it is shown that every Banach space with bounded distortions contains a subspace from this class. The proof is based on an investigation of certain functions, called enveloping functions, which are intimately connected with stabilization properties of the norm. 0 Introduction During the last year several problems ...

Dave Benson, in [2], conjectured that for any finite group G and any prime p the Castelnuovo-Mumford regularity of the cohomology ring, H(G,Fp), is zero. He showed that reg(H(G,Fp)) ≥ 0 and succeeded in proving equality when the difference between the dimension and the depth is at most two. The purpose of this paper is to prove Benson’s Regularity Conjecture as a corollary of the following result.

A celebrated result of Gowers states that for every > 0 there is a graph G such that every -regular partition of G (in the sense of Szemerédi’s regularity lemma) has order given by a tower of exponents of height polynomial in 1/ . In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter.

In this paper, we are interested in the minimization of the second eigenvalue of the Laplacian with Dirichlet boundary conditions amongst convex plane domains with given area. The natural candidate to be the optimum was the “stadium”, convex hull of two identical tangent disks. We refute this conjecture. Nevertheless, we prove existence of a minimzer. We also study some qualitative properties o...