Coarse grid correction by aggregation / disaggregation with application in image reconstruction

In algebraic reconstruction of images in computerized tomography we are dealing with rectangular, large, sparse and ill-conditioned linear systems of equations. In this paper we describe a two-grid algorithm for solving such kind of linear systems, which uses Kaczmarz's projection method as relaxation. The correction step is performed with a special “local” aggregation / disaggregation type procedure. In this respect, we have to solve a small sized minimization problem associated to each coarse grid pixel. The information so obtained is then “distributed” to the neighbour fine grid pixels. Some image reconstruction experiments are also presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inviscid Limit for Damped and Driven Incompressible Navier-Stokes Equations in $$\mathbb R^2$$

We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in . We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance.     

Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra I: A Priori Estimates

ABSTRACT

Let 𝒯 _k be a sequence of triangulations of a polyhedron Ω ? ? ⁿ and let S _k be the associated finite element space of continuous, piecewise polynomials of degree m. Let u _k  ∈ S _k be the finite element approximation of the solution u of a second-order, strongly elliptic system Pu = f with zero Dirichlet boundary conditions. We show that a weak approximation property of the sequence S _k ensures optimal rates of convergence for the sequence u _k . The method relies on certain a priori estimates in weighted Sobolev spaces for the system Pu = 0 that we establish. The weight is the distance to the set of singular boundary points. We obtain similar results for the Poisson problem with mixed Dirichlet–Neumann boundary conditions on a polygon.     

Perfluoroalkylation of Alkenes by Frustrated Lewis Pairs

The activation of perfluoroalkyl iodides by the frustrated Lewis pair tris(pentafluorophenyl)borane and tri‐tert‐butylphosphine is described. By abstraction of both a fluorine and an iodine atom, an iodophosphonium fluoroborate salt is formed. In the presence of alkenes the corresponding iodoperfluoroalkylation products are generated regioselectively. First mechanistic investigations support a radical mechanism.     

The Crystal Structure of Symplesite

Since the discovery of symplesite mineral in the late 19th century, a number of structural studies were performed. The crystal symmetry of this mineral was debated to be either monoclinic or triclinic. Even though this debate has ended, agreeing on the triclinic symmetry, no detailed crystal structure was reported so far. In the present contribution, we report on the crystal structure of symplesite. The crystal structure was solved and refined from high‐resolution laboratory X‐ray powder diffraction data, collected on a natural sample. Symplesite is shown to be isostructural to metavivianite (and possibly to ferrostrunzite).