Homogeneity and Canonical Connections of Isoparametric Manifolds

On every isoparametric submanifold M a connection with parallel second fundamental form is constructed geometrically such that M is an orbit of an s-representation if and only if the connection is a canonical one. If the rank of M is greater than one this connection is in case of homogeneity the canonical connection of the reductive decomposition given by the orbit of s-representation. This revised version was published online in June 2006 with corrections to the Cover Date.     

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     

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.     

MgF(3)(-) as a transition state analog of phosphoryl transfer

The formation of complexes between small G proteins and certain of their effectors can be facilitated by aluminum fluorides. Solution studies suggest that magnesium may be able to replace aluminum in such complexes. We have determined the crystal structure of RhoA.GDP bound to RhoGAP in the presence of Mg(2+) and F(-) but without Al(3+). The metallofluoride adopts a trigonal planar arrangement instead of the square planar structure of AlF(4)(-). We have confirmed that these crystals contain magnesium and not aluminum by proton-induced X-ray emission spectroscopy. The structure adopted by GDP.MgF(-) possesses the stereochemistry and approximate charge expected for the transition state. We suggest that MgF3(-) may be the reagent of choice for studying phosphoryl transfer reactions.