Combining rearrangement techniques with Gromov’s proof (via optimal mass transportation) of the 1-Sobolev inequality, we prove a sharp quantitative version of the anisotropic Sobolev inequality on BV (R). As a corollary of this result, we also deduce a sharp stability estimate for the anisotropic 1-log-Sobolev inequality.

Abstract. A lower bound on the misclassification probability for a finite number of classes is obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. This bound, which is shown to be exact in a certain rather strong sense, is based on an exact upper bound on the difference between the maximum and the mean of a finite set of real numbers...

We introduce the Bounded Axiom A Forcing Axiom(BAAFA). It turns out that it is equiconsistent with the existence of a regular Σ2-correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom(BPFA).

This paper shows that realised power variation and its extension called realised bipower variation that we introduce here is somewhat robust to rare jumps. We demonstrate that in special cases realised bipower variation estimate integrated variance in stochastic volatility models, thus providing a model free and consistent alternative to realised variance. Its robustness property means that if ...

Are Wage and Employment Effects Robust to Alternative Minimum Wage Variables? A national minimum wage cannot explain variation in wages or employment across regions. Identification of the effect of the minimum wage separately from the effect of other variables on wages or employment requires regional variation. Many minimum wage variables with regional variation have been suggested in the liter...

In this paper, we establish some generalizations of weighted trapezoid inequality for mappings of bounded variation, and give several applications for r − moment, the expectation of a continuous random variable and the Beta mapping.

4 Casper-Emil T. Pedersen*, Kirk E. Lohmueller, Niels Grarup, Peter Bjerregaard, 5 Torben Hansen, Hans R. Siegismund*, Ida Moltke*, and Anders Albrechtsen* 6 7 Department of Biology, Section for Computational and RNA Biology, University of 8 Copenhagen, 2200 Copenhagen N, Denmark 9 10 Department of Ecology and Evolutionary Biology, University of California, Los 11 Angeles, CA 90095, United Stat...

We prove that the family of functionals (Iδ) defined by Iδ(g) = ∫∫ RN×RN |g(x)−g(y)|>δ δ |x− y|N+p dx dy, ∀ g ∈ L(R ), for p ≥ 1 and δ > 0, Γ-converges in L(R ), as δ goes to 0, when p ≥ 1. Hereafter | | denotes the Euclidean norm of R . We also introduce a characterization for BV functions which has some advantages in comparison with the classic one based on the notion of essential variation o...

For the nite volume method applied to scalar hyperbolic conservation law in two space dimensions, the uniform BV estimate for an approximate solution is not available on unstructured grids. Therefore the convergence proofs are based on methods which needs less regularity, e.g. on the Young measure theory. In this contribution we discuss the so-called ((t)-condition which serves as a suitable re...

When the random intersection graph G(n,m, p) proposed by Karoński, Scheinerman, and Singer-Cohen in [8] is compared with the independent-edge G(n, p), the evolutions are different under some values of m and equivalent under others. In particular, when m = nα and α > 6, the total variation distance between the graph random variables has limit 0.