• 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...

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.

We prove that, for any finite Blaschke product w=B(z) in the unit disk, corresponding Riemann surface over w–plane contains a one-sheeted disk of radius 0.5. Moreover, it with radial slit. apply this result to obtain universal lower estimate Bloch seminorm products.