Particle ratios from a chiral SU(3) model

The measured particle ratios in central heavy-ion collisions are investigated within a chemical and thermal equilibrium chiral SU(3) σ?ω approach. Contrary to the commonly adopted non-interacting gas calculations, the chiral SU(3) model predicts modified effective hadron masses and effective chemical potentials in the medium and a transition to a chirally restored phase at high temperatures or chemical potentials. the influence of three different types of phase transitions is investigated. We show that the deduced freeze-out values considerably depend on the underlying model while the quality of the fit is approximately the same.     

Dielectric relaxation analysis of starch oligomers and polymers with respect to their chain length

Starch belongs to the polyglucan group. This type of polysaccharide shows a broad β-relaxation process in dielectric spectra at low temperatures, which has its molecular origin in orientational motions of sugar rings via glucosidic linkages. This chain dynamic was investigated for α(1,4)-linked starch oligomers with well-defined chain lengths of 2, 3, 4, 6, and 7 anhydroglucose units (AGUs) and for α(1,4)-polyglucans with average degrees of polymerization of 5, 10, 56, 70, and so forth (up to 3000; calculated from the mean molecular weight). The activation energy (E_a) of the segmental chain motion was lowest for dimeric maltose (E_a = 49.4 ± 1.3 kJ/mol), and this was followed by passage through a maximum at a degree of polymerization of 6 (E_a = 60.8 ± 1.8 kJ/mol). Subsequently, E_a leveled off at a value of about 52 ± 1.5 kJ/mol for chains containing more than 100 repeating units. The results were compared with the values of cellulose-like oligomers and polymers bearing a β(1,4)-linkage. Interestingly, the shape of the E_a dependency on the chain length of the molecules was qualitatively the same for both systems, whereas quantitatively the starch-like substances generally showed higher E_a values. Additionally, and for comparison, three cyclodextrins were measured by dielectric relaxation spectroscopy. The ringlike molecules, with 6, 7, and 8 α(1,4)-linked AGUs, showed moderately different types of dielectric spectra. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 188–197, 2004     

Electrochemical reduction of 1-([(4-halophenyl)imino]methyl)-2-naphthols in aprotic media.

The electrochemical reduction of 1-([(4-halophenyl)imino]methyl)-2-naphthols on graphite electrodes was studied using cyclic voltammetry, chronoamperometry, constant-potential coulometry and preparative constant-potential electrolysis techniques. The data revealed that the reduction on graphite was irreversible and followed an EC mechanism. The diffusion coefficients and the number of electrons transferred were determined using the chronoamperometric Cottrell slope and the ultramicro disc Pt-electrode steady-state current. The number of electrons was also determined by bulk electrolysis. The compounds were subjected to constant-potential preparative electrolysis and the electrolysis products were purified and identified by spectroscopic methods. Based on these findings, a mechanism for the electro-reduction process is proposed.     

Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal     

The linear polarization constant of R n

Summary He present work deals with estimations of the n-th linear polarization constant c(H)_n of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup_║y║=1 │1,y> ... n,y>│, where x₁, ... ,x_n are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) _n= n^n/2 remains open.     

Appropriate problems for learning and for performing—an issue for teacher training

Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities).     

Recombination of Au25+ with free electrons at low energies

The origin of the widely observed enhancement of rates for electron-ion recombination at very low energies is still unknown. We investigated the recombination of Au²⁵⁺ with free electrons in a merged-beams experiment at the UNILAC accelerator of the GSI in Darmstadt. At E _rel= 0 eV we found an enormous enhancement factor of 365 compared to the theory of radiative recombination. An increase of the electron density by a factor of 10 had not much influence on the measured rate coefficient. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Witt ring of a Brauer–Severi variety

For a Brauer–Severi variety X over a field k of characteristic not two, every symmetric bilinear space over X up to Witt equivalence is defined over k. Received: 2 February 1998