Let B={Bt:t?0} be a real-valued fractional Brownian motion of index H?(0,1). We prove that the macroscopic Hausdorff dimension level sets Lx=t?R+:Bt=x is, with probability one, equal to 1?H for all x?R.

the impact resistance of new lightweight panel is studied. this panel consists of two thin metal layers bonded together by intermediate fiber/epoxy layers (mcm-sheets). to simulate a behavior of this kind of impact problem, explicit and implicit finite element software abaqus is used. in order to validate the finite element modeling, these results have been compared with experimental test resul...

We give a short and simple argument that proves, in a uniform way, the Auslander-Buchsbaum formula, relating depth and projective dimension, and the Auslander-Bridger formula, relating depth and G-dimension. Moreover, the same type of argument quickly reproves the fact that, in the degrees above the codepth, the syzygy modules of a finite module over a commutative local ring have no free summan...

Perceptual audio coders exploit two properties to achieve coding gain: perceptual irrelevancy and source redundancy. Recently, a two-dimensional modulation transform was introduced which efficiently extracts perceptual irrelevancy and source redundancy not accessible in a one-dimensional transform. In this paper, we propose an alternative modulation transform design with an octave-band non-unif...

We find a sharp combinatorial bound for the metric entropy of sets in R and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central Limit Theorem if the square root of its combinatorial dimension is integrable. 2. The uniform entropy is equivalent to the combinatorial dimension under minimal ...

The aim of this paper is to give sufficient conditions for a switched linear system defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function to be GUAS. We show that this property is equivalent to the uniform observability on [0,+∞) of a bilinear system defined on a subspace whose dimension is in most cases much smaller than the dimension of the switc...

The Vapnik-Chervonenkis dimension of a set K in R n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This has a number of consequences, including the optimal Elton's theorem and a uniform central limit theorem in the real valued case.