Boundary Harnack Principle for <Emphasis Type="Italic">p</Emphasis>-harmonic Functions in Smooth Euclidean Domains

We establish a scale-invariant version of the boundary Harnack principle for p-harmonic functions in Euclidean C ^1,1-domains and obtain estimates for the decay rates of positive p-harmonic functions vanishing on a segment of the boundary in terms of the distance to the boundary. We use these estimates to study the behavior of conformal Martin kernel functions and positive p-superharmonic functions near the boundary of the domain. H. A. was partially supported by Grant-in-Aid for (B) (2) (No. 15340046) Japan Society for the Promotion of Science. N. S. was partially supported by NSF grant DMS-0355027. X. Z. was partially supported by the Taft foundation.     

Wax treatment of wood slows photodegradation

Waxes and wax emulsions are one of the most important solutions for non-biocidal wood protection. Wax treated wood is designed for outdoor use, therefore it is of considerable importance to elucidate the influence of weathering on the photodegradation processes. It is presumed, that wax treatment will reduce water uptake and thus reduce or slow down photodegradation processes. In order to test this hypothesis, three types of wax emulsions at two different concentrations were vacuum impregnated into Norway spruce wood specimens: an emulsion of montan wax (LGE), an emulsion of polyethylene (WE1) and an emulsion of oxidized polyethylene (WE6) wax. The samples were exposed to artificial accelerated weathering (AAW) for 500 cycles. Before and after AAW colour, the contact angle of water and moisture content were determined. Chemical and morphological changes at exposed surfaces were also investigated with FTIR spectroscopy and SEM. In parallel, the uptake of wax emulsions and water into the axial surfaces of samples was determined with a tensiometer. The moisture content measurements showed that the best hydrophobic effect was achieved with LGE treated wood, where the lowest colour and FTIR changes were observed as well. These results were supported by tensiometer measurements as well. Presented data clearly showed that high loadings of waxes reduce or at least slow down weathering. Among tested waxes, montan wax was found the most effective.     

Concentration effects on the dynamics of liquid crystalline self-assembly: time-resolved X-ray scattering studies

A manifold of ordering transitions relevant to chemical and biological systems occur at interfaces from liquids to self-assembled soft solids like membranes or liquid crystals. In the present case, we were interested in understanding the phase transition from the microemulsion phase to the liquid crystal phase in terms of their driving forces, i.e., activation energy and entropy. The purpose of this work was to clarify the influence of concentration effects of the amphiphilic molecules on the nature of these self-assembly processes. By photosensitization of the model system (polyalkylglycolether (C(10)E(4)), water, decane, and cyclohexane) with laser dyes, we could effectively induce and control the phase transition through the absorption of optical photons. The photo transformation conditions were chosen in such a way that the system was in thermal equilibrium. By application of time-resolved photo small-angle X-ray scattering we could monitor the conversion process and demonstrate that the surfactant concentration has a direct impact on the activation energy, which is observable through the length of the induction time.     

Extragalactic background light: inventory of light throughout the cosmic history

The Extragalactic Background Light (EBL) stands for the mean surface brightness of the sky as we would see it from a representative vantage point in the intergalactic space outside of our Milky Way Galaxy. Averaged over the whole 4π solid angle it represents the collective light from all luminous matter radiated throughout the cosmic history. Part of the EBL is resolved into galaxies that, with the increasing detecting power of giant telescopes and sensitive detectors, are seen to deeper and deeper limiting magnitudes. This resolved part is now known to contribute a substantial or even the major part of the EBL. There still remains, however, the challenge of finding out to what extent galaxies too faint or too diffuse to be discerned individually, individual stars or emission by gas outside the galaxies, or – more speculatively – some hitherto unknown light sources such as decaying elementary particles are accounting for the remaining EBL. We review the recent progress that has been made in the measurement of EBL. The current photometric results suggest that there is, beyond the resolved galaxies, an EBL component that cannot be explained by diffuse galaxy halos or intergalactic stars.     

Itinerant antiferromagnetism of α-Titanium

The present study reports magnetic susceptibility, electrical resistivity and specific heat measurements on α-titanium. The experimental results indicate the existence of an anomaly in the temperature dependence of these parameters. The temperature dependence of the specific heat indicates that the anomaly observed in these parameters is a second order phase transition. The similarity between the temperature dependence of the magnetic susceptibility of α-titanium and of chromium suggests that α-titanium is an itinerant-electron antiferromagnet, such as chromium, with the Néel temperature at 276 ± 4 K.     

The magnetic behaviour of diluted CrAl alloys

Magnetic susceptibility as a function of temperature of binary CrAl alloys containing 0.7,1.07,1.35,1.59, 1.79,1.98, 2.18, 2.84, 3.74 and 4.36 at %A1 is investigated. Aluminium, by alloying, acts on the Néel temperature of pure chromium giving rise to a complicated phase diagram. The bahaviour of the magnetic susceptibility as a function of temperature, in the ordered phase, for the samples containing 1.28, 2.18 and 2.84 at %A1 is found to be temperature independent. In the paramagnetic region, for the samples containing between 1.07 and 2.84 at %A1, it is found a decrease of the magnetic susceptibility as a function of temperature.     

Metall-Komplexbildung von β-Hydroxythiophenderivaten III

The acidity constants of 2-acetyl-3-hydroxy-thiophene (III) and 3-acetyl-4-hydroxy-thiophene (IV) and the stability constants of their complexes with some bivalent metal ions have been determined. The stability of the chelates is discussed as a function of the respective bond orders of the α–β and β–β′ bonds of the thiophene ring.     

Self-adjunctions and matrices

It is shown that the multiplicative monoids of Temperley-Lieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronecker product of matrices. This self-adjunction underlies the orthogonal group case of Brauer's representation of the Brauer centralizer algebras.