We analyze the central discontinuous Galerkin (DG) method for time-dependent linear conservation laws. In one dimension, optimal a priori L error estimates of order k+1 are obtained for the semidiscrete scheme when piecewise polynomials of degree at most k (k ≥ 0) are used on overlapping uniform meshes. We then extend the analysis to multidimensions on uniform Cartesian meshes when piecewise te...

We study simple random walk on the uniform spanning tree on Z2. We obtain estimates for the transition probabilities of the random walk, the distance of the walk from its starting point after n steps, and exit times of both Euclidean balls and balls in the intrinsic graph metric. In particular, we prove that the spectral dimension of the uniform spanning tree on Z2 is 16/13 almost surely.

We calculate the growth rate of the small-amplitude perturbations superimposed on a one-dimensional soliton that is fully coherent in the self-trapping dimension, yet uniform and partially incoherent in the other transverse dimension. Such solitons become transversely stable only if the correlation distance is below a specific threshold value. We show that this threshold for transverse instabil...

We consider continuous SL(2,R)-cocycles over a minimal homeomorphism of a compact set K of finite dimension. We show that the generic cocycle either is uniformly hyperbolic or has uniform subexponential growth.

Rademacher complexity is a measure of the richness of a class of real-valued functions. In this sense, it is similar to the VC dimension. In fact, we will establish a uniform deviation bound in terms of Rademacher complexity, and then use this result to prove the VC inequality. Unlike VC dimension, however, Rademacher complexity is not restricted to binary functions, and will also prove useful ...

— By using the slope method, we obtain an explicit uniform estimation for the density of rational points in an arithmetic projective variety with given degree and dimension, embedded in a given arithmetic projective space. Résumé. — On obtient, en utilisant la méthode de pentes, une estimation uniforme et explicite de la densité des points rationnels dans une variété arithmétique projective de ...

We provide several constructions of self-affine probability measures on the unit square with uniform marginals. These constructions include and extend constructions of previous authors and are parameterized in a natural way. In addition, for each different construction we determine the dimension of the parameter space and thus the level of flexibility (for instance, for approximation purposes) ...

In this paper we propose an extension of grayscale histogram equalization for color images. For aesthetic reasons, previously proposed color histogram equalization techniques do not generate uniform color histograms. Our method will always generate an almost uniform color histogram thus making an optimal use of the color space. This is particularly interesting for pseudo-color scientific visual...

In this work we quantify the degree to which star-forming events are clumped. We apply a precise and accurate technique to calculate the correlation dimension Dc of the distribution of HII regions in a sample of disk galaxies. Our reliable results are distributed in the range 1.5 ∼< Dc ∼< 2.0. We get significant variations in the fractal dimension among galaxies, contrary to a universal picture...

In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show that the mass is invariant under the flow in dimension three (similar results hold in higher dimension with more assumptions). A consequence of this result is the following. Let (M, g) be an ALE manifold of dimension n...