Enclosure results for second-order relative spectra by elementary means

Motivated by the general approach due to Shargorodsky we derive enclosure results for the second-order relative spectrum of bounded selfadjoint operators by studying quadratic operator pencils. The quality of the results is discussed by means of a simple example.

     

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.     

An abstract Szeg? theorem

Given a semi-group U(t) of bounded linear operators with bounded self-adjoint generator A we estimate the logarithm of the section determinants of U(t) in terms of A. When A is subject to an additional condition, which is related to so-called Følner sequences of orthogonal projections, this estimate implies a Szeg? type theorem for bounded, self-adjoint, and strictly positive operators. We show that the condition mentioned is satisfied when A is a Toeplitz operator or a compact operator.     

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.     

Influence of calcium on the self-assembly of partially hydrolyzed alpha-lactalbumin

Self-assembly of alpha-lactalbumin after partial hydrolysis by a protease from Bacillus licheniformis can result in nanotubular structures, which show many similarities to microtubules. Calcium plays a crucial role in this process. The objective of this investigation was to study the role of calcium in more detail. The kinetics of the hydrolysis step and the self-assembly step were monitored by respectively liquid chromatography-mass spectrometry and dynamic light scattering. The microstructure of the gels finally formed was investigated by transmission electron microscopy. This investigation demonstrates that calcium accelerated the kinetics of the self-assembly, but it had no effect on the hydrolysis kinetics. As a result of the accelerated self-assembly kinetics at a high calcium concentration, the time of gelation decreased as well. A minimum concentration of calcium needed to obtain the tubular alpha-lactalbumin structures was determined. Below R = 1.5 (mole calcium/mole alpha-lactalbumin), turbid gels with randomlike structure were obtained. Between R = 1.5 and R = 6, translucent gels with a fine stranded network of tubules were formed, while higher calcium concentrations had a negative effect on the tubule formation, resulting in amorphous structures. The optimum calcium concentration for alpha-lactalbumin nanotube formation seemed to be around R = 3.     

Laccase-catalyzed carbon-carbon bond formation: oxidative dimerization of salicylic esters by air in aqueous solution

The laccase catalyzed oxidative dimerization of salicylic esters, a rare example of a laccase-catalyzed carbon-carbon bond formation, was studied. This reaction allows the use of air as stoichiometric oxidant and proceeds in aqueous solution. The preparative scope and the mechanism of the method, which provides a new and convenient access to functionalized biaryls under mild conditions, were investigated.     

Definitive Proof for the Operation of Isotopically Sensitive Branching (‘Metabolic Switching’) in FeI-Mediated C?H Bond Activation in the Gas Phase Short Communication

Rigorous regio- and stereospecific labeling experiments are performed to demonstrate the operation of the previously suggested operation of ‘isotopically sensitive branching’ in Fe^I-mediated C? H bond activation. For the hexane-1,6-diol/Fe⁺-complex, it is shown that dehydrogenation involves specifically the central C(3)/C(4) position, and the study of the stereospecifically labeled D ,L - and meso-[3,4-D₂]-isotompomers 1e and 1f demonstrates that dehydrogenation proceedes via two competing pathways (i.e. ‘anti’- vs. ‘syn’-route). The contribution of these routes to the product formation is – due to a kinetic isotope effect – controlled by the relative configuration at the labeled positions C(3)/C(4). For the D ,L -form 1e , we estimate a ratio of 49:1 in favor of the ‘anti’-route; due to an isotope effect, this ratio drops to 4.3:1 for the meso-form 1f .     

Smooth projective translation planes

A projective plane is called smooth if both the point space and the line space are smooth manifolds such that the geometric operations are smooth. We prove that every smooth projective translation plane is isomorphic to one of the classical planes over , , or .Dedicated to Professor Dr. H. Salzmann on the occasion of his 65th birthday     

Gas Phase Catalysis by Metal Nanoparticles in Nanoporous Alumina Membranes

Nanoporous alumina membranes, loaded with palladium and ruthenium nanoparticles of various size, were used for gas phase hydrogenation of 1, 3‐butadiene and for oxidation of carbon monoxide, respectively. Those membranes contain 10⁹ ‐ 10¹¹ pores per cm², all running perpendicular to the surface. Membrane discs of 20 mm in diameter and only 60 μm thick, incorporated in a reactor in which the reactants can be pumped in a closed circuit through the pores, turned out to very actively catalyze hydrogenation of butadiene (Pd) and oxidation of CO (Ru). The activity of the Pd catalysts depends characteristically on the particles size, the gas flow, and of the educts ratio. As could be expected, larger particles are less active than smaller ones, whereas increasing gas flows in case of hydrogenation accelerates the reactions. Excessive hydrogen reduces selectivity with respect to the various butenes, but favours formation of butane.     

Synthesis of Chiral Cyclohexenones from α-Campholenic,Fencholenic, and β-Campholenic Derivatives

Summary. Optically active dimethylcyclohexenones, potential building blocks for enantioselective syntheses of various naturally active substances, were prepared. These compounds were obtained by oxidation with KMnO₄/Pb(OAc)₄ or ozonolysis of the corresponding cyclopentenic precursors, followed by aldol condensation. During the course of the preparation intermediate diols and chiral polyfunctional carbonyl derivatives were separated and identified analytically.