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.

     

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.     

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.     

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     

Asymmetric lithiation of 2-alkynyl aryl sulfides—Enantio- and diastereoselective formation of allenyl aryl sulfides and their application in nickel-catalyzed cross-coupling reactions

The enantio- and diastereoselective synthesis of allenyl aryl sulfides by asymmetric lithiation of 2-alkynyl (2-hetero)aryl sulfides is described. A dynamic thermodynamic resolution by selective crystallization of the intermediate lithium complexes derived from deprotonation, applying a bis(oxazoline) ligand, was achieved to give enantioselectivities up to 85% ee. Subsequent stereospecific nickel-catalyzed cross-coupling reactions with arylzinc reagents established a versatile access to threefold carbon-substituted allenes.     

Folding and unfolding of an elastinlike oligopeptide: "inverse temperature transition," reentrance, and hydrogen-bond dynamics

The temperature-dependent behavior of a solvated oligopeptide, GVG(VPGVG), is investigated. Spectroscopic measurements, thermodynamic measurements, and molecular dynamics simulations find that this elastinlike octapeptide behaves as a two-state system that undergoes an "inverse temperature" folding transition and reentrant unfolding close to the boiling point of water. A molecular picture of these processes is presented, emphasizing changes in the dynamics of hydrogen bonding at the protein/water interface and peptide backbone librational entropy.     

Optimisation of ambient and high temperature asymmetric flow field-flow fractionation with dual/multi-angle light scattering and infrared/refractive index detection

Asymmetric flow field-flow fractionation (AF4) enables to analyse polymers with very high molar masses under mild conditions in comparison to size exclusion chromatography (SEC). Conventionally, membranes for AF4 are made from cellulose. Recently, a novel ceramic membrane has been developed which can withstand high temperatures above 130 °C and chlorinated organic solvents, thus making it possible to characterise semicrystalline polyolefins by HT-AF4. Two ceramic membranes and one cellulose membrane were compared with regard to their quality of molar mass separation and the loss of the polymer material through the pores. Separating polystyrene standards as model compounds at different cross-flow gradients the complex relationship between cross-flow velocity, separation efficiency, the molar mass and peak broadening could be elucidated in detail. Moreover, the dependence of signal quality and reproducibility on sample concentration and mass loading was investigated because the evaluation of the obtained fractograms substantially depends on the signal intensities. Finally, the performance of the whole system was tested at high temperature by separating PE reference materials of high molar mass.     

Acceleration of Acetal Hydrolysis by Remote Alkoxy Groups: Evidence for Electrostatic Effects on the Formation of Oxocarbenium Ions

In contrast to observations with carbohydrates, experiments with 4‐alkoxy‐substituted acetals indicate that an alkoxy group can accelerate acetal hydrolysis by up to 20‐fold compared to substrates without an alkoxy group. The acceleration of ionization in more flexible acetals can be up to 200‐fold when compensated for inductive effects.     

Differential-Thermoanalyse von Ölen und Fetten im Temperaturbereich −100° bis +150°

A DTA apparatus is described which is suitable for investigations by thermal analysis in the temperature range from ?100° to +150°. While the system of measuring is a recent development, modified models of the DTA 02 Universal Apparatus manufactured wholesale in the German Democratic Republic are used. The experimental results demonstrate that this apparatus permits high-sensitivity oil and fat investigations by differential thermal analysis, with good zero-line behaviour. The problem of analysing oils and fats is also dealt with.