Zur konstruktion bewerteter dicksonscher fastkörper

Zusammenfassung  After a short introduction to the valuation theory of nearfields, we give criteria for when a valuation of a skewfield F is also a valuation of the Dickson nearfield F^K which is derived from F by the coupling K on F. For the construction of examples, a rational function field F =K(t) is given. The set of all prolongations of a valuation v on K to F is well known. Sufficient conditions are given which guarantee that couplings K on F and elements are in this sense compatible so that w is a valuation of the Dickson nearfield F^K. Examples demonstrate the results.

     

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Ohne Zusammenfassung

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Book reviews

     

Linearly implicit time discretization of non-linear parabolic equations

We give a stability and error analysis of linearly implicitone-step methods for time discretization of non-linear parabolicequations. We derive precise error bounds for Rosenbrock andW-methods, and we explain the error reduction by Richardsonextrapolation of the linearly implicit Euler method which occursin spite of the breakdown of asymptotic expansions. The parabolicequations are studied in a Hilbert space framework that includessemilinear and quasilinear parabolic equations, and also stiffreaction-diffusion equations with reactions at different timescales.     

Pressure induced phase transition behaviour in f-electron based dialuminides

The rare-earth and actinide based compounds are endowed with several exotic physical and chemical properties due to the presence of f-electrons. These properties exhibit interesting changes under the action of various thermodynamic fields and hence continues to be a subject of extensive research. For instance, under pressure, the nature of f-electrons can be changed from localized to itinerant, leading to a variety of changes in their structural, physical and chemical properties. The present review on the high pressure phase transition behaviour of dialuminides of rare earths and actinides is an outcome of research in our laboratory during the last five years using a unique combination of a Guinier diffractometer and a diamond anvil cell built in-house. To bring out the correlations between the compressibility and structural behaviour with the electronic structure, we have also carried out electronic structure calculation. Further, the usefulness of Villars’ three parameter structure maps in predicting pressure induced structural transitions has been explored and this has been illustrated with the available phase transition data.     

Boson Stars: Rotation, Formation, and Evolution

Boson stars are descendants of the so-calledgeons of Wheeler, except that they are built from scalarparticles instead of electromagnetic fields. If scalarfields exist in nature, such localized configurations kept together by their self-generatedgravitational field can form within Einstein's generalrelativity. In the case of complex scalar fields, anabsolutely stable branch of such non-topologicalsolitons with conserved particle number exists. Thepresent surge of interest stems from the speculativepossibility that these compact objects could provide aconsiderable fraction of the non-baryonic part of dark matter. In any case, they may serve as aconvenient laboratory for studyingnumerically rapidly rotating bodies in generalrelativity and the generation of gravitational waves.Furthermore, we mention how to detect boson stars by gravitationallensing or gravitational redshift. Finally, we explorethe evolution of boson stars within scalar-tensortheories.     

Are Axidilaton Stars Massive Compact Halo Objects?

Boson stars built from a very light Kalb–Ramond axion, the dilaton or other moduli fields of effective string models could provide a considerable fraction of the non-baryonic part of dark matter. Gravitational microlensing of 0.5 M MACHOs within the halo of galaxies may indirectly "weighing" the mass of the constituent scalar particle, resulting in 10^–10 eV/c².     

Infrared matrix isolation and quantum chemical studies of the nitrous acid complexes with water

The 1:1 and 2:1 complexes between water and trans- and cis-isomers of nitrous acid have been isolated in argon matrices and studied using FTIR spectroscopy and DFT(B3LYP) calculations with a 6-311++G(2d,2p) basis set. The analysis of the experimental spectra indicate that 1:1 complexes trapped in solid argon involve very strong hydrogen bond in which acid acts as the proton donor and water as the proton acceptor. The perturbed OH stretches are −248, −228 cm⁻¹ red shifted from their free-molecules values in complexes formed by trans- and cis-HONO isomers, respectively. The calculated spectral parameters for the two complexes are in good agreement with experimental data. The calculations also predict stability of two more 1:1 weakly bound complexes formed by each isomer. In these the water acts as the proton donor and one of the two oxygen atoms of the acid as the acceptor. The experimental spectra demonstrate also formation of 2:1 complex between water and trans-HONO isomer in an argon matrix. The performed calculations indicate that the complex involves a seven-membered ring in which OH group of HONO forms very strong hydrogen bond with the oxygen atom of one water molecule and nitrogen atom acts as a weak proton acceptor for the hydrogen atom of the second water molecule of the water dimer. The observed perturbations of the OH stretch of trans-HONO (750 cm⁻¹ red shift) is much larger than that predicted by calculations (556 cm⁻¹ red shift); this difference is attributed to strong solvation effect of argon matrix on very strong hydrogen bond.     

High‐efficiency polymer solar cells based on phenylenevinylene copolymer with BF2‐azopyrrole complex and CN‐PC70BM with solvent additive

Power conversion efficiency (PCE) of phenylenevinylene‐based copolymer with BF₂ azopyrrole complex (PB)/modified PC₇₀BM, that is, CN‐PC₇₀BM bulk heterojunction solar cells improves from 2.16 to 4.90% using a processing additive and drying condition. The results demonstrate that a processing additive and drying condition provides an effective means to control both the surface roughness and finer interpenetrating networks to enhance the exciton dissociation into free charge carriers, charge transportation, and collection. Taking into the account of simple device fabrication process without thermal annealing, the PCE of the polymer solar cell can further improved by chloronapthalene (CN) additive under the fast drying condition. The average carrier lifetimes extracted from the impedance spectra and found to correlate with measured PCEs. At short circuit conditions and illumination, the average charge carrier lifetime was found vary from 16.8 to 32 μs with power conversion efficiencies ranging from 3.0 to 4.9%. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit

This paper discusses the convergence of kinetic variational inequalities to rate-independent quasi-static variational inequalities. Mathematical formulations as well as existence and uniqueness results for kinetic and rate-independent quasi-static problems are provided. Sharp a priori estimates for the kinetic problem are derived that imply that the kinetic solutions converge to the rate-independent ones, when the size of initial perturbations and the rate of application of the forces tend to 0. An application to three-dimensional elastic-plastic systems with hardening is given.