Consider the Cauchy problem for a hyperbolic n × n system of conservation laws in one space dimension: ut + f(u)x = 0, u(0, x) = ū(x). (CP ) Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions u = u(t, x) which have bounded variation along a suitable family of space-like curves.

Let X1, . . . , Xn be independent, integer valued random variables, with p th moments, p > 2, and let W denote their sum. We prove bounds analogous to the classical non-uniform estimates of the error in the central limit theorem, but now, for approximation of L(W ) by a translated Poisson distribution. The advantage is that the error bounds, which are often of order no worse than in the classic...

Abstract We prove that an optional process of non-exploding realized power variation along stopping times possesses almost surely làglàd paths. This result is useful for the analysis of some imperfect market models in mathematical finance. In the finance applications variation naturally appears along stopping times and not pathwise. On the other hand, if the power variation were only taken alon...

Let u = u(q) satisfy a hyperbolic equation with impulsive input: ∂ t u(x, t)−4u(x, t) + q(x)u(x, t) = δ(x1)δ(t) and let u|t<0 = 0. Then we consider an inverse problem of determining q(x), x ∈ Ω from data u(q)|ST and (∂u(q)/∂ν) |ST . Here Ω ⊂ {(x1, . . . , xn) ∈ R|x1 > 0}, n ≥ 2, is a bounded domain, ST = {(x, t); x ∈ ∂Ω, x1 < t < T + x1}, ν = ν(x) is the unit outward normal vector to ∂Ω at x ∈ ...

This paper studies the model of minimizing total variation with an L-norm fidelity term for decomposing a real image into the sum of cartoon and texture. This model is also analyzed and shown to be able to select features of an image according to their scales.

Assuming that a Nemytskii operator maps a subset of the space of bounded variation functions in the sense of Riesz into another space of the same type, and is uniformly continuous, we prove that the generator of the operator is an affine function.

We consider the problem of minimizing the size of a family of sets G such that every subset of {1, . . . , n} can be written as a disjoint union of at most k members of G, where k and n are given numbers. This problem originates in a real-world application aiming at the diversity of industrial production. At the same time, the question of finding the minimum of |G| so that every subset of {1, ....

Consider the sequences fX i g m i=1 and fY i g n j=1 of independent random variables , which take values in a nite alphabet, and assume that the variables X 1 ; X 2 ; : : : and Y 1 ; Y 2 ; : : : follow the distributions and , respectively. Two variables X i and Y j are said to match if X i = Y j. Let the number of matching subsequences of length k between the two sequences, when r, 0 r < k, mis...

Mid back vowels [o] and [ɔ] appear to be merging in the Catalan spoken in the region of Girona. In this brief paper, we present preliminary data on the production of these vowels in one of the 12 designated survey points for the study of the phenomenon, the area of Ter-Brugent. The first results in this area show that our speakers present an almost complete merger of the mid back vowel pair, an...

Most accounts of statistical learning (e.g., Saffran et al., 1996) assume that the learner computes cooccurrence statistics over units, such as syllables, that abstract away from the physical features of the input. This assumption need not hold when the units are underlearned, unfamiliar, or uncategorizable. We tested statistical learning with variable, unfamiliar units and show that if the fea...