Let (M,g) be a complete two dimensional simply connected Riemannian manifold with Gaussian curvature K ≤ −1. If f is a compactly supported function of bounded variation on M then f satisfies the Sobolev inequality 4π Z

This paper mainly researches the speaking rate effect for segmental reduction in a phrase word. Four speakers spoke eight words with different speaking rates. The investigation includes the durational variation of each syllable, the durational variation of each semi-syllable and the total word duration variation. Different speakers’ material in read speech was explored at last.

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components of the original random structure. In this paper we build up on previous work and derive results in t...

It is shown constructively that a strongly extensional function of bounded variation on an interval is regulated, in a sequential sense that is classically equivalent to the usual one. This paper continues the constructive study of monotone functions and functions of bounded variation, begun in [3] and [4] (see also [5]). It can be read by anyone who appreciates the distinction between classica...

Let f(x) be a 1-periodic function of bounded variation having mean zero, and let (nk)k≥1 be an increasing sequence of positive integers. Then a result of Baker implies the upper bound ∣∣∣∑Nk=1 f(nkx)∣∣∣ = O (√N(logN)3/2+ε) for almost all x ∈ (0, 1) in the sense of the Lebesgue measure. We show that the asymptotic order of ∣∣∣∑Nk=1 f(nkx)∣∣∣ is closely connected with certain number-theoretic pro...

An algorithm for total variation regularized photoacoustic imaging.

Let (K,+, ∗) be an odd order presemifield with commutative multiplication. We show that the set of nonzero squares of (K, ∗) is a skewHadamard difference set or a Paley type partial difference set in (K,+) according as q is congruent to 3modulo 4 or q is congruent to 1 modulo 4. Applying this result to the Coulter–Matthews presemifield and the Ding–Yuan variation of it, we recover a recent cons...

Global weak solutions of bounded variation to systems of balance laws with non-local source are constructed by the method of vanishing viscosity. Suitable dissipativeness assumptions are imposed on the source terms to assure convergence of the method. Under these hypotheses, the total variation remains uniformly bounded and integrable in time, the vanishing viscosity solutions are uniformly sta...

The aim of this paper is to prove the existence of extension operators for SBV functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a non coercive homogenization problem.