Domination of uniformly continuous semigroups

We prove that a bounded operator on a Banach lattice, satisfying a growth condition, is regular. Also, we prove that the generator of a C ₀-semigroup on such a lattice for which such an operator exists is bounded.     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

Structural and spectroscopic studies of silylated cyclo- and bicyclosilanes

A number of cyclo-and bicyclosilanes have been prepared and structurally characterized by X-ray crystallography and Raman spectroscopy. 1,1,4,4- and 1,1,3,3-tetrakis(trimethylsilyl)octamethylcyclohexasilanes were found to exhibit unusual twist- and twisted boat-conformations. The UV absorption properties of all compounds were studied and found to show absorption maxima red shifted compared to the parent compound dodecamethylcyclohexasilane. Dedicated to Prof. Mitsuo Kira on the occasion of his reception of the Wacker Silicon Award 2005 and in recongnition of his numerous outstanding achievements in organosilicon chemistry.     

Fluorine containing poly(amide-imide)s: synthesis and formation of Langmuir-Blodgett monolayers

Soluble fluorine containing poly(amide-imide)s, PAI(1-4), were synthesized from diimide-dicarboxylic acid, 2,2-bis[N-(4-carboxyphenyl)-phthalimide-1,4-yl]hexafluoropropane with various diamines by direct polycondensation in N-methyl-2-pyrrolidone (NMP) containing CaCl₂ and using triphenyl phosphite and pyridine as condensing agents. The polymers were readily soluble in aprotic polar solvents such as NMP, N,N-dimethylacetamide, dimethyl sulfoxide and tetrahydrofuran. Their Langmuir monolayers were studied at the air/water interface. The monolayers were generally stable at the water surface and could be reproducibly transferred onto solid substrates to build up Langmuir-Blodgett (LB) multilayers. The LB mono- and multilayers were characterized by ultra-violet/visible spectroscopy (UV-Vis), surface plasmon resonance, atomic force microscopy.     

NONLINEAR LASERSPECTROSCOPIC INVESTIGATIONS OF THE PIGMENT-PIGMENT INTERACTION WITHIN THE LIGHT-HARVESTING COMPLEX OF PHOTOSYSTEM II

Using a pump and test beam technique in the frequency domain with pump pulses in the nanosecond time range, the nonlinear transmission properties were investigated at room temperature in photosystem (PS) II membrane fragments and isolated light-harvesting chlorophyll a/b-protein preparations (LHC II preparations). In LHC II preparations and PS II membrane fragments, respectively, pump pulses of 620 nm and 647 nm cause a transmission decrease limited to a wavelength region in the nearest vicinity of the pump pulse wavelength (full width at half maximum ' 0.24 nm). In contrast, at 670 nm neither a transmission decrease nor a narrow band feature were observed. The data obtained for PS II membrane fragments and LHC II preparations at shorter wavelengths (620 nm, 647 nm) were interpreted in terms of excited state absorption of whole pigment-protein clusters within the light-harvesting antenna of photosystem II. The interpretation of the small transmission changes as homogeneously broadened lines led to a transversal relaxation time for chlorophyll in the clusters of about 4 ps.     

Über Glasbildung und Eigenschaften von Chalkogenidsystemen. IX. Zur Struktur der GeS/GeS2- und GeSe/GeSe2-Gläser

Glass Formation and Properties of Chalcogenide Systems. IX. On the Structure of GeS/GeS₂ and GeSe/GeSe₂ Glasses Mole volume, glass transition temperature, and coefficient of thermal expansion were measured on glasses prepared by standardized conditions. Near the composition Ge₂S₃ and Ge₂Se₃ the properties show a singularity or point of inflexion, respectively. Random models of structure are inconsistent with such a behaviour. A model of higher chemical order is proposed which can explain the observed dependence of the glass properties on composition and is in accordance with radial distribution studies.