In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Z
The norm of an integral operator occurring in the partial wave decomposition of an operator B introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that B is non-negative and has no eigenvalue at 0 when the nuclear charge does not exceed a specified critical value.
We present a real interpolation method involving broken-logarithmic functors. We obtain a variety of interpolation theorems for quasilinear operators on quasi-Banach spaces, including limiting cases. We present a number of Holmstedt's formulae corresponding to the broken-logarithmic functors and apply these to obtain reiteration theorems for interpolation… (More)
The approximation numbers of Hardy–type operators on trees. Abstract The Hardy operator Ta on a tree Γ is defined by (Taf)(x) := v(x) x a u(t)f (t)dt for a, x ∈ Γ. Properties of Ta as a map from L p (Γ) into itself are established for 1 ≤ p ≤ ∞. The main result is that, with appropriate assumptions on u and v, the approximation numbers an(Ta) of Ta satisfy… (More)
BACKGROUND AND PURPOSE The TRPC5 proteins assemble to create calcium-permeable, non-selective, cationic channels. We sought novel modulators of these channels through studies of natural products. EXPERIMENTAL APPROACH Intracellular calcium measurements and patch clamp recordings were made from cell lines. Compounds were generated by synthetic chemistry.… (More)
CONTEXT Health communication campaigns including mass media and health-related product distribution have been used to reduce mortality and morbidity through behavior change. The intervention is defined as having two core components reflecting two social marketing principles: (1) promoting behavior change through multiple communication channels, one being… (More)
In the model suggested by Smilansky  one studies an operator describing the interaction between a quantum graph and a system of K one-dimensional oscillators attached at different points of the graph. This paper is a continuation of  in which we started an investigation of the case K > 1. For the sake of simplicity we consider K = 2, but our argument… (More)
The paper analyses the decay of any zero modes that might exist for a massless Dirac operator H := α·(1/i)∇+Q, where Q is 4 × 4-matrix-valued and of order O(|x| −1) at infinity. The approach is based on inversion with respect to the unit sphere in R 3 and establishing embedding theorems for Dirac-Sobolev spaces of spinors f which are such that f and Hf lie… (More)