Double coset density in classical algebraic groups

We classify all pairs of reductive maximal connected subgroups of a classical algebraic group that have a dense double coset in . Using this, we show that for an arbitrary pair of reductive subgroups of a reductive group satisfying a certain mild technical condition, there is a dense -double coset in precisely when is a factorization.

     

Radiative spectra of thermal electromagnetic noise induced by planar realistic dielectrics

Spectral characteristics of stochastic fields and their spatial derivatives in various planar structures composed by lossy materials described by realistic dielectric functions are numerically calculated based on solutions to the problems of multipolar electromagnetic fields in a plane layered geometry. A displacement of the maximum of the spectral power densities for spatial derivatives of fluctuating fields to the high-frequency domain, a resonant increase in the density of states of the fluctuating fields at the frequencies of interface excitations and interference modes for the radiative part of the spectra, the influence of geometry on the density of states, and other peculiarities are found by numerical calculations and graphically demonstrated. Interpretations of the above effects are provided.     

Necessary conditions for constrained optimization problems with semicontinuous and continuous data

We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.

     

An L2 model for selfadjoint elliptic differential operators with constant coefficients on bounded domains

The selfadjoint realization of a second order elliptic differential expression with Dirichlet boundary conditions is shown to be unitarily equivalent to the maximal multiplication operator with the independent variable in an explicit L² model space. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weibel-induced filamentation during an ultrafast laser-driven plasma expansion

The development of current instabilities behind the front of a cylindrically expanding plasma has been investigated experimentally via proton probing techniques. A multitude of tubelike filamentary structures is observed to form behind the front of a plasma created by irradiating solid-density wire targets with a high-intensity (I ~ 10(19) W/cm(2)), picosecond-duration laser pulse. These filaments exhibit a remarkable degree of stability, persisting for several tens of picoseconds, and appear to be magnetized over a filament length corresponding to several filament radii. Particle-in-cell simulations indicate that their formation can be attributed to a Weibel instability driven by a thermal anisotropy of the electron population. We suggest that these results may have implications in astrophysical scenarios, particularly concerning the problem of the generation of strong, spatially extended and sustained magnetic fields in astrophysical jets.     

Understanding the Mechanocatalytic Conversion of Biomass: A Low‐Energy One‐Step Reaction Mechanism by Applying Mechanical Force

On the way to establishing biomass as a renewable and environmentally friendly source to cover the ever‐increasing global demand on energy and chemicals, one great challenge is the efficient depolymerization of cellulose. Enhanced conversion rates have been discovered in ball‐milling experiments, thus opening a mechanocatalytic approach. However, an understanding of the impact of mechanical forces on the acid‐catalyzed cleavage of glycosidic bonds at the molecular level is still missing. Herein, we contribute such fundamental insight based on atomistic modeling. Mechanically stressing the macromolecular backbone radically changes the depolymerization pathway from a complex high‐barrier reaction upon thermal activation to a low‐energy single‐step mechanocatalytic process. In addition to revealing a regioselective increase in basicity under a mechanical force, our results provide molecular‐level explanations of the experimental findings and might therefore guide rational ways to improve such mechanocatalytic processes.     

Exhaustive computational search of ionic-charge clusters that mediate interactions between mammalian cytochrome P450 (CYP) and P450-oxidoreductase (POR) proteins

In this work, a model for the interaction between CYP2B4 and the FMN domain of rat P450-oxidoreductase is built using as template the structure of a bacterial redox complex. Amino acid residues identified in the literature as cytochrome P450 (CYP)–redox partner interfacial residues map to the interface in our model. Our model supports the view that the bacterial template represents a specific electron transfer complex and moreover provides a structural framework for explaining previous experimental data.We have used our model in an exhaustive search for complementary pairs of mammalian CYP and P450-oxidoreductase (POR) charge clusters. We quantitatively show that among the previously defined basic clusters, the 433K–434R cluster is the most dominant (32.3% of interactions) and among the acidic clusters, the 207D–208D–209D cluster is the most dominant (29%). Our analysis also reveals the previously not described basic cluster 343R–345K (16.1% of interactions) and 373K (3.2%) and the acidic clusters 113D–115E–116E (25.8%), 92E–93E (12.9%), 101D (3.2%) and 179E (3.2%).Cluster pairings among the previously defined charge clusters include the pairing of cluster 421K–422R to cluster 207D–208D–209D. Moreover, 433K–434R and 207D–208D–209D, respectively the dominant positively and negatively charged clusters, are uncorrelated. Instead our analysis suggests that the newly identified cluster 113D–115E–116E is the main partner of the 433K–434R cluster while the newly described cluster 343R–345K is correlated to the cluster 207D–208D–209D.     

Selective extraction and elution of weak bases by in-line solid-phase extraction capillary electrophoresis using a pH step gradient and a weak cation-exchange monolith

A polymer monolith bearing weak cation-exchange functionality was prepared for the purpose of demonstrating pH-selective extraction and elution in in-line solid-phase extraction-capillary electrophoresis (SPE-CE) utilising a model set of cationic analytes, namely imidazole, lutidine and 3-phenylpropanamine. Optimization of the electrolyte conditions for efficient elution of the adsorbed analytes using a moving pH boundary required that the capillary and monolith be filled with 44 mM sodium acetate at high pH (pH 6) and a low pH electrolyte of 3 mM sodium acetate pH 3 was placed in the electrolyte vials. This combination allowed the adsorbed analytes to be simultaneously eluted and focused into narrow bands, with peak widths of the eluted analytes having a baseline width of 1.2 s immediately after the monolith. Using these optimum elution conditions, the versatility of the SPE-CE approach was demonstrated by removing unwanted adsorbed components after extraction with a wash at a different pH and also by selecting a pH at which only some of the model weak bases were ionised. The analytical performance of the approach was evaluated and the relative standard deviation for peak heights, peak area and migration times were in the ranges of 1.4-5.3, 1.2-3.3 and 0.4-1.2% respectively. Analytes exhibited linear calibrations with r(2) values ranging from 0.996 to 0.999 over two orders of magnitude. Analyte pre-concentration provided excellent sensitivity, and limits of detection for the analyte used in this study were in the range 8.0-30 ng ml(-1), which was an enhancement of 63 when compared to normal hydrodynamic injection occupying 1.3% of the capillary of these bases in water.