This paper is a sequel to both Ash, Erd1⁄2os and Rubel [AER], on very slowly varying functions, and [BOst1], on foundations of regular variation. We show that generalizations of the Ash-Erd1⁄2os-Rubel approach –imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property – lead naturally to the main result of regular variation, th...

Let X be a compact subset of the complex plane with property that every relatively open has positive area and let $$A_0(X)$$ denote space VMO functions are analytic on X. is said to admit bounded point derivation order t at $$x_0 \in \partial X$$ if there exists constant C such $$|f^{(t)}(x_0)|\le \Vert f\Vert _{{\text {BMO}}}$$ for all in $${\text {VMO}}(X)$$ In this paper, we give necessa...

The more alcohol a person has consumed, the more mispronunciations occur. This study investigates how deaffrication surfaces in Bernese Swiss German when speakers are moderately intoxicated (0.05-0.08 % Vol.), whether these effects can be hidden, and whether a placebo effect interacting with mispronunciation occurs. Five participants reading a text were recorded as follows. In stage I, they rea...

This paper investigates production of the mid vowels /e, ɛ, ø, œ, o, ɔ/ by four speakers of New Caledonian French (NCF). Formant and durational properties of these vowels are examined with respect to the type of syllable in which they occur. Results point to general adherence to the loi de position in NCF, such that the close-mid vowels occur in open syllables and the open-mid vowels occur in c...

In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem fo...

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.