This paper studies the celebrated KuramotoSakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets n-torus called winding cells. Second, analyze semicontractivity model, i.e., property that distance between trajectories decreases when measured according to a seminorm. establishes local Kuramoto-Sakaguchi which is equivalent contractiv...

• W1: Wasserstein-1-distance (see below). • TVW1: Our proposed total variation seminorm for ODF-valued functions (see below). Figure: Q-ball image of the corpus callosum, reconstructed from HARDI data of the human brain, (left) with added white Gaussian noise and (right) our Wasserstein-TV-based reconstruction using a Wasserstein data term. The noise is reduced substantially, while regions with...

In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the metric they define on the state space, to the extreme points of the state space. We characterize the Lipschitz norms which are determined by their metric on the ...

Abstract. We prove a BV estimate for scalar conservation laws that generalizes the classical Total Variation Diminishing property. In fact, for any smooth function Φ, we have that Φ(u) is TVD with the correct definition of the initial seminorm. We call this property Total Oscillation Diminishing. The reason being that it is in contradiction with the oscillations observed recently on some numeri...

Abstract Let ???? be a complex Hilbert space and A non-zero positive bounded linear operator on . The main aim of this paper is to discuss general method develop -operator seminorm -numerical radius inequalities semi-Hilbertian operators using the existing corresponding Among many other we prove that if S , T X ? ???? ( ), i.e., -adjoint exist, then <m:math xmlns:m="http://www.w3.org/1998/Math/...

We find the abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric defined by a seminorm two-dimensional subspace of algebra generating algebra. In terms structure constants and Minkowski support function unit ball which defines quasimetric, we establish criterion for strict abnormality these extremals.