Green Function Estimates and Harnack Inequality for Subordinate Brownian Motions

Let X be a Lévy process in, , obtained by subordinating Brownian motion with a subordinator with a positive drift. Such a process has the same law as the sum of an independent Brownian motion and a Lévy process with no continuous component. We study the asymptotic behavior of the Green function of X near zero. Under the assumption that the Laplace exponent of the subordinator is a complete Bernstein function we also describe the asymptotic behavior of the Green function at infinity. With an additional assumption on the Lévy measure of the subordinator we prove that the Harnack inequality is valid for the nonnegative harmonic functions of X.     

Dissipation anomaly and energy cascade in 3D incompressible flows

The purpose of this Note is to present a mathematical evidence of the dissipation anomaly in 3D turbulent flows within a general setting for the study of energy cascade in physical scales of 3D incompressible flows recently introduced by the authors.     

Multiphase‐Separated Polyurethanes Studied by Micro‐Raman Spectroscopy

Micro‐Raman spectroscopy has been used to investigate the chemical micro‐heterogeneity of multiphase‐separated poly(ether urethanes) (PETU). Analysis of PETU cross‐sections by means of micro‐Raman spectroscopy revealed the nearly complete absence of soft segments in AI aggregates (called globules). These aggregates are in the order of a few micrometers in size. The composition of the matrix and the AII aggregates (spherulites) was comparable.

Example of an AFM image (sample 706, scan size 25 μm, converted to monochromatic image).     

ChemInform Abstract: Single‐Crystal Structure Determination of NO2SbF6, XeF5SbF6 and XeF5Sb2F11.

The title compounds are prepared according to the literature and used for single crystal growth in a T‐shaped fluoroethylene‐hexafluoropropylene crystallization apparatus.