Asymptotic regularity of solutions to Hartree–Fock equations with Coulomb potential

We study the asymptotic regularity of solutions to Hartree–Fock (HF) equations for Coulomb systems. To deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo‐differential operators on conical manifolds. First, the non‐self‐consistent‐field case is considered, which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator, which guarantee ellipticity for the local part of the Fock operator on the open stretched cone ?₊ × S². This proves the existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed‐point approach based on Cancès and Le Bris analysis of the level‐shifting algorithm, we show via another bootstrap argument that the corresponding self‐consistent‐field solutions to the HF equation have the same type of asymptotic regularity. Copyright © 2008 John Wiley & Sons, Ltd.     

Identification of poliovirions and subviral particles by capillary electrophoresis

Poliovirions, purified from infected cell extracts with anion-exchange chromatography, can be analyzed and identified by CE in untreated fused silica capillaries using UV detection. Other subviral particles can be eluted as well from the same infected cell extract using a higher salt concentration buffer on the ion-exchange chromatography. Virions can be identified because of their conversion into empty capsids upon heating at 56°C. As a result of heating, the viral genome is released from the capsid. Here, we show that during this incubation some intermediate particles were found. The latter were identified by enzymatic peak shift analysis. The high salt concentration eluate subviral particles were analyzed with preincubation affinity CE together with their sensitivity for RNase and proteinase K treatment. Electropherograms of the higher salt concentration eluate display a mixture of at least four different subviral particles. One particle proved to have an [N1, H] antigenicity and was resistant to RNase and proteinase K digestion. The remaining particles were all sensitive to proteinase K treatment. This CE method proved to be valuable in the detection, identification and analysis of poliovirions and poliovirus particles offering an alternative powerful, cheap, fast and easy analysis method.     

Parameters affecting the separation of intact proteins in gradient-elution reversed-phase chromatography using poly(styrene-co-divinylbenzene) monolithic capillary columns

An experimental study was performed to investigate the effects of column parameters and gradient conditions on the separation of intact proteins using styrene-based monolithic columns. The effect of flow rate on peak width was investigated at constant gradient steepness by normalizing the gradient time for the column hold-up time. When operating the column at a temperature of 60 °C a small C-term effect was observed in a flow rate range of 1–4 μL/min. However, the C-term effect on peak width is not as strong as the decrease in peak width due to increasing flow rate. The peak capacity increased according to the square root of the column length. Decreasing the macropore size of the polymer monolith while maintaining the column length constant, resulted in an increase in peak capacity. A trade-off between peak capacity and total analysis time was made for 50, 100, and 250 mm long monolithic columns and a microparticulate column packed with 5 μm porous silica particles while operating at a flow rate of 2 μL/min. The peak capacity per unit time of the 50 mm long monolithic column with small pore size was superior when the total analysis time is below 120 min, yielding a maximum peak capacity of 380. For more demanding separations the 250 mm long monolith provided the highest peak capacity in the shortest possible time frame.     

An Alternative to the Gauge Theoretic Setting

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner’s representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation.     

Effects of natural sounds on the perception of road traffic noise

Recent studies show that introducing sound from water features in urban open spaces may reduce the loudness of road traffic noise, but it is not clear in which situations this measure also improves overall soundscape quality. This work describes a listening experiment on loudness, pleasantness, and eventfulness of stimuli that combine road traffic noise with fountain or bird sound at different sound levels. Adding fountain sound reduced the loudness of road traffic noise only if the latter had low temporal variability. Conversely, adding bird sound significantly enhanced soundscape pleasantness and eventfulness, more than what was achieved by adding fountain sound.     

Bondi-Metzner-Sachs Symmetry,Holography on Null-surfaces and Area Proportionality of “Light-slice” Entropy

It is shown that certain kinds of behavior, which hitherto were expected to be characteristic for classical gravity and quantum field theory in curved spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography on event horizons and an area proportionality of entropy, have in fact an unnoticed presence in Minkowski QFT.     

On the Parameterization of Rational Ringed Surfaces and Rational Canal Surfaces

Ringed surfaces and canal surfaces are surfaces that contain a one-parameter family of circles. Ringed surfaces can be described by a radius function, a directrix curve and vector field along the directrix curve, which specifies the normals of the planes that contain the circles. In particular, the class of ringed surfaces includes canal surfaces, which can be obtained as the envelopes of a one-parameter family of spheres. Consequently, canal surfaces can be described by a spine curve and a radius function. We present parameterization algorithms for rational ringed surfaces and rational canal surfaces. It is shown that these algorithms may generate any rational parameterization of a ringed (or canal) surface with the property that one family of parameter lines consists of circles. These algorithms are used to obtain rational parameterizations for Darboux cyclides and to construct blends between pairs of canal surfaces and pairs of ringed surfaces.