Hermitian quadratic eigenvalue problems of restricted rank

We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix . Of the n+r solutions that this problem admits, we show at least n-r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2r are nonreal occuring in possibly repeated conjugate pairs.     

Numerical computation of viscous profiles for hyperbolic conservation laws

Viscous profiles of shock waves in systems of conservation laws can be viewed as heteroclinic orbits in associated systems of ordinary differential equations (ODE). In the case of overcompressive shock waves, these orbits occur in multi-parameter families. We propose a numerical method to compute families of heteroclinic orbits in general systems of ODE. The key point is a special parameterization of the heteroclinic manifold which can be understood as a generalized phase condition; in the case of shock profiles, this phase condition has a natural interpretation regarding their stability. We prove that our method converges and present numerical results for several systems of conservation laws. These examples include traveling waves for the Navier-Stokes equations for compressible viscous, heat-conductive fluids and for the magnetohydrodynamics equations for viscous, heat-conductive, electrically resistive fluids that correspond to shock wave solutions of the associated ideal models, i.e., the Euler, resp. Lundquist, equations.

     

Numerical simulation of exciton dynamics in Cu(2)O at ultra-low temperatures within a potential trap

We have studied theoretically the relaxation behaviour of excitons in cuprous oxide (Cu(2)O) at ultra-low temperatures when excitons are confined within a potential trap by solving numerically the Boltzmann equation. As relaxation processes, we have included in this paper deformation potential phonon scattering, radiative and non-radiative decay and Auger decay. The relaxation kinetics has been analysed for temperatures in the range between 0.3 and 5?K. Under the action of deformation potential phonon scattering only, we find for temperatures above 0.5?K that the excitons reach local equilibrium with the lattice, i.e.?that the effective local temperature is coming down to the bath temperature, while below 0.5?K a non-thermal energy distribution remains. Interestingly, for all temperatures the global spatial distribution of excitons does not reach the equilibrium distribution, but stays at a much higher effective temperature. If we include further a finite lifetime of the excitons and the two-particle Auger decay, we find that both the local and the global effective temperature do not come down to the bath temperature. In the first case we find that a Bose-Einstein condensation (BEC) occurs for all temperatures in the investigated range. Comparing our results with the thermal equilibrium case, we find that BEC occurs for a significantly higher number of excitons in the trap. This effect could be related to the higher global temperature, which requires an increased number of excitons within the trap to observe the BEC. In the case of Auger decay, we do not find a BEC at any temperature due to the local heating of the exciton gas.     

Dediazoniations of Arenediazonium Ions in Homogeneous Solutions. Part XV. Products of dediazoniation of p-chlorobenzenediazonium tetrafluoroborate in weakly alkaline aqueous solutions

The products of decomposition of solutions of p-chlorobenzenediazonium tetrafluoroborate in aqueous buffer solutions (pH 9.0–10.3; ionic strength 0.1–0.5) at 20.0° have been analyzed quantitatively. Up to eleven low molecular weight compounds could be identified besides the major product, the complex polymeric diazo tar. The distribution of products is influenced by trace amounts of oxygen as well as by p-chlorophenol and the radical trapping reagent iodoacetic acid. Mechanisms of formation of the products are discussed.     

Zinkkomplexe eines neuen N,N, O‐Liganden

Zinc Complexes of a New N, N, O Ligand The tridentate ligand N, N(2‐dimethylaminoethyl)‐3, 5‐di‐tert.‐butyl‐salicylaldimine ( L H) results from the corresponding salicylic aldehyde and N, N‐dimethyl ethylenediamine. With zinc salts it forms the mononuclear halide complexes [ L ZnCl ˙ CH₃OH] ( 1 ) and [ L ZnI ˙ CH₃OH] ( 2 ) and the presumably polymeric acetate [ L ZnOCOCH₃] ( 3 ). With diethyl zinc and diphenylphosphoric acid it yields the phosphate complex [ L Zn‐OPO(OPh)₂ ˙ CH₃OH] ( 4 ). The coordination of the complexes, which is between trigonal bipyramidal and square pyramidal, and the character of the five donors in the phosphate complex represent the transition state of a hydrolytic substrate cleavage in a zinc enzyme.     

Method for Simultaneously Improving the Thermal Stability and Mechanical Properties of Poly(lactic acid): Effect of High-Energy Electrons on the Morphological, Mechanical, and Thermal Properties of PLA/MMT Nanocomposites

Nanocomposites derived from poly(lactic acid) (PLA) and organically modified montmorillonite (oMMT) have been cross-linked by high-energy electrons in the presence of triallyl cyanurate (TAC). The morphology of untreated and cross-linked PLA/MMT nanocomposites was characterized by wide-angle X-ray scattering (WAXS) and transmission electron microscopy (TEM). This treatment can improve both the thermal stability and the glass-transition temperatures of the PLA nanocomposites (e.g., PLA-MMT-TAC 30kGy, 50kGy, and 70kGy) because of the formation of cross-linking structures in the nanocomposites that will considerably reduce the mobility of polymers. Interestingly, at relatively low irradiation doses (e.g., 30 and 50 kGy) a good balance between tensile strength and elongation at break for the PLA nanocomposites could be achieved. These mechanical properties are superior to those of pure PLA. Therefore, combining nanotechnology and electron beam cross-linking is a promising new method of simultaneously improving the mechanical properties (toughness and tensile strength) and thermal stability of PLA.     

Zur Reaktion des Germaniums mit Germaniumtetrachlorid und zur Existenz der Oxidchloride GeOCl2 und GeOCl6 im Gleichgewicht

On the Reaction of Germanium with Germanium Tetrachloride and on the Existence of the Oxidechlorides GeOCl₂ and GeOCl₆ at the Equilibrium The above equilibrium was measured in a Gauge-manometer and the enthalpy of formation and the entropy for GeCl₂,g were derived from these results. From total pressure measurements and transport experiments of GeO₂ with GeCl₄ follows, that the oxidechlorides Ge₂OCl₆ and GeOCl₂ are not present in measurable concentrations, that means the enthalpy of formation of GeOCl₂ must be higher than ?327 kJ · mol^?1.