Boundary functions for wavelets on a finite interval are often constructed as linear combinations of boundary-crossing scaling functions. An alternative approach is based on linear algebra techniques for truncating the infinite matrix of the Discrete Wavelet Transform to a finite one. In this article we show how an algorithm of Madych for scalar wavelets can be generalized to multiwavelets, giv...

We present alternative proofs of density versions of some combinatorial partition theorems originally obtained by H. Furstenberg and Y. Katznelson. These proofs are based on an extremal hypergraph result which was recently independently obtained by W. T. Gowers and B. Nagle, V. Rödl, M. Schacht, J. Skokan by extending Szemerédi’s regularity lemma to hypergraphs.

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...

We prove regularity criteria for harmonic heat flow and a liquid crystals model. Mathematics Subject Classifications: 35K55, 58E20

We prove the existence of many complete graphs in almost all sufficiently dense partitions obtained by an application of Szemerédi’s Regularity Lemma. More precisely, we consider the number of complete graphs K` on ` vertices in `-partite graphs where each partition class consists of n vertices and there is an ε-regular graph onm edges between any two partition classes. We show that for all β >...

In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis is based on the observation that the schemes are linear combinations of the Yosida approximation, ...

Periodic pattern mining is the problem that regards temporal regularity. There are many emerging applications in periodic pattern mining, including web usage recommendation, weather prediction, computer networks and biological data. In this paper, we propose a Progressive Timelist-Based Verification (PTV) method to the mining of periodic patterns from a sequence of event sets. The parameter min...

Abstract. We prove Strichartz estimates for the absolutely continuous evolution of a Schrödinger operator H = (i∇ + A) + V in R, n ≥ 3. Both the magnetic and electric potentials are time-independent and satisfy pointwise polynomial decay bounds. The vector potential A(x) is assumed to be continuous but need not possess any Sobolev regularity. This work is a refinement of previous methods, which...

In this paper we study Mean Field Game systems under density constraints as optimality conditions of two optimization problems in duality. A weak solution of the system contains an extra term, an additional price imposed on the saturated zones. We show that this price corresponds to the pressure field from the models of incompressible Euler’s equations à la Brenier. By this observation we manag...

We look at general brane worlds in six-dimensional Einstein-Gauss-Bonnet gravity. We find the general matching conditions for the brane world, which remarkably give precisely the four-dimensional Einstein equations for the brane, even when the extra dimensions are noncompact and have infinite volume. Relaxing regularity of the curvature in the vicinity of the brane, or having a thick brane, giv...