The Berezin transform and radial operators

We analyze the connection between compactness of operators on the Bergman space and the boundary behaviour of the corresponding Berezin transform. We prove that for a special class of operators that we call radial operators, an oscilation criterion is a sufficient condition under which the compactness of an operator is equivalent to the vanishing of the Berezin transform on the unit circle. We further study a special class of radial operators, i.e., Toeplitz operators with a radial symbol.

     

A New Approach to Chalcogen–Nitrogen π-Heterocyclic Radicals

This paper gives a brief overview of a new approach to chalcogen–nitrogen heterocyclic π-radicals, particularly 1,2,3- and 1,3,2-benzodithiazolyls, based on thermolysis or photolysis of closed-shell precursors (such as 1,3,2,4-benzodithiadiazines and their 1-Se congeners, 1,2,4,3,5- and 1,3,5,2,4-benzotrithiadiazepines, and some other sulfur–nitrogen rings and cages). The approach allows obtaining radicals hardly accessible or inaccessible in other ways, especially, fluorinated radicals. The identity of radicals prepared is confirmed by electron paramagnetic resonance spectroscopy in combination with density functional theory calculations.     

Transfer of electron density as a result of hydrogen bond formation

It has been found that the amount of charge transfer between donor and acceptor molecules in four sets of hydrogen‐bonded complexes may be adequately described as an exponential function of the equilibrium distance between the hydrogen atom and the nearest atom of the acceptor molecule. The exponential factors of the transfer are of the same order but somewhat larger than the factors found otherwise in the investigations of dynamic electron transfer. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The multivariate N-Component resolution problem with minimum assumptions

The present state of the minimum assumption multivariate component resolution theory is outlined. Some new developments are presented: limiting function domains; the analytical expression for the limiting function; efficient algorithms for defining the FIRPOL and INNPOL hyperpolyhedrons. A very low resolution data set is analyzed.