The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Addendum to Birkhoff's Theorem

In spherically symmetric systems, in spite of Birkhoff's Theorem, the rates of clocks in vacuum regions on either side of moving mass shells must be continually readjusted to stay in synchrony. This shows up as time-dependence of the metric in terms of the globally meaningful time coordinate.     

Ground-state complex formation of perylene with pyromellitic dianhydride studied by static fluorescence quenching

The association of complex formation with static quenching in CT systems was investigated. Evaluation of the data made evident that the inner filter effect must be allowed for. Time-resolved and temperature-dependent stationary measurements of fluorescence led to the separation of dynamic and static quenching components. The static quenching constant is discussed with respect to the equilibrium constant of complex formation determined by absorption spectroscopy.     

Alkenylidenes in Organic Synthesis

Alkenylidenes R₂C?C: (= alkylidene carbenes) undergo regio- and stereoselective intramolecular C? H insertion reactions that are excellently suited for the synthesis of cyclopentenes. The 1, 2-shifts occurring with R?H and R?Ar are useful for the preparation of alkynes. Alkenylidenes are efficiently generated from carbonyl compounds by diazomethylation, from vinyl halides by α-elimination, from alkynyliodonium salts by addition of nucleophiles, and from alkynes by retro-1, 2-shifts. Specific applications of the various methods, particularly in the synthesis of natural products, are discussed.     

Isotrope Unterräume rationaler quadratischer Formen

Ohne ZusammenfassungDiese Arbeit wurde während eines Aufenthaltes von Schmidt in der Bundesrepublik Deutschland als Preisträger der Alexander von Humboldt-Stiftung geschrieben.     

A systematic elimination procedure for Ito stochastic differential equations and the adiabatic approximation

We study a class of nonlinear Ito stochastic differential equations (with possibly state dependent diffusion coefficients), in which the variables can be divided into linearly damped (slaved) variables s and linearly undamped variablesu (order parameters). We devise a systematic and constructive procedure to eliminate the slaved variables. We take explicit time and chance dependence of the slaved variables into account, the latter via a family of diffusion processesZ _t ^(v) . These act as fluctuating coefficients of the Center Manifolds _t=s(u _t, t,Z _t ^(v) (v=2, 3, ...)) and appear explicitly in the elimination procedure. We show how in the Ito calculus fluctuating and deterministic coefficients of the Center Manifold are more completely separated than in the previously treated Stratonovich case [1]. The adiabatic approximation is defined as a partial summation of the elimination expansion and the stochastic generalization ofs=0 is derived. We show how thus ambiguity of stochastic calculi is removed. Closed form summations are given in two examples. We briefly indicate the potential use of perturbation theory techniques in the systematic elimination procedure.