Ein Satz über geodätische Verbindbarkeit in normalhyperbolischen Räumen

Under certain conditions, two points of a normal hyperbolic manifold joined by a time-like curve can be joined by a time-like geodesic. These conditions are discussed, and some applications are given.     

On the occurrence of naked singularities in general relativity. II

It is shown that naked shell crossing singularities can occur in the gravitational collapse of a spherically symmetric ball of perfect fluid for a large family of equations of state in which the pressure has an (arbitrarily large) upper bound, and, moreover, that this behaviour is stable with respect to spherically symmetric perturbations of the initial data, as well as with respect to perturbations of the equation of state.Work supported by the Deutsche Forschungsgemeinschaft.     

Probing of energy gap distribution in superconducting tunnel junctions by low temperature scanning electron microscopy

A two-dimensional voltage image of the energy gap distribution of a superconducting tunnel junction was obtained by scanning the current biased junction with an electron beam and detecting the voltage change δV. The value of the energy gap at the point of irradiation was determined quantitatively from the δV σ(V) curves, where σ(V) is the electric conductance of the junction. Further the quasiparticle diffusion length was found by measuring the length of the transition between a high- and low-gap region generated by a double tunnel junction configuration. The theoretical predictions could be verified by investigating a double tunnel junction configuration, where the energy gap could be changed deliberately by quasiparticle injection.     

Tuning the shape anisotropy of silver nanoparticles using time-delayed laser pulse pair irradiations

Glass-embedded spherical silver nanoparticles were irradiated by pairs of delayed femtosecond laser pulses. The influence of intensity, relative polarization (parallel or orthogonal) and time delay between the pulses was investigated. We found a delay-dependent reversal of the orientation of prolate nanoparticles produced in the low-intensity regime: at very short time delays up to 10 ps between pulse pairs the polarization direction of the second-hitting pulse defines the particles’ symmetry axes; in an intermediate regime between 10 and 20 ps no optical dichroism is found at all; at more than 20 ps delay between the pulses, finally, the transformed nanoparticles are oriented along the polarization direction of the first-hitting pulse. Also, in the quite different situation of the high-intensity regime using parallel-polarized pulse pairs, where normally oblate particles are created, isotropic spectral changes (i.e., no dichroism) after irradiation were observed at delay times around 20 ps. The possible physical background of this apparently very special inter-pulse delay of around 20 ps is discussed.     

Structure and stability of molybdenum sulfide fullerenes

MoS2 nanooctahedra are believed to be the smallest stable closed-cage structures of MoS2, i.e., the genuine inorganic fullerenes. Here a combination of experiments and density functional tight binding calculations with molecular dynamics annealing are used to elucidate the structures and electronic properties of octahedral MoS2 fullerenes. Through the use of these calculations MoS2 octahedra were found to be stable beyond nMo > 100 but with the loss of 12 sulfur atoms in the six corners. In contrast to bulk and nanotubular MoS2, which are semiconductors, the Fermi level of the nanooctahedra is situated within the band, thus making them metallic-like. A model is used for extending the calculations to much larger sizes. These model calculations show that, in agreement with experiment, the multiwall nanooctahedra are stable over a limited size range of 104-105 atoms, whereupon they are converted into multiwall MoS2 nanoparticles with a quasi-spherical shape. On the experimental side, targets of MoS2 and MoSe2 were laser-ablated and analyzed mostly through transmission electron microscopy. This analysis shows that, in qualitative agreement with the theoretical analysis, multilayer nanooctahedra of MoS2 with 1000-25 000 atoms (Mo + S) are stable. Furthermore, this and previous work show that beyond approximately 105 atoms fullerene-like structures with quasi-spherical forms and 30-100 layers become stable. Laser-ablated WS2 samples yielded much less faceted and sometimes spherically symmetric nanocages.     

Fast Algorithms for Nonparametric Curve Estimation

Abstract

Naive implementations of local polynomial fits and kernel estimators require almost O(n ²) operations. In this article two fast O(n) algorithms for nonparametric local polynomial fitting are presented. They are based on updating normal equations. Numerical stability is guaranteed by controlling ill-conditioned situations for small bandwidths and data-tuned restarting of the updating procedure. Restarting at every output point results in a moderately fast but highly stable O(n ^7/5) algorithm. Applicability of algorithms is evaluated for estimation of regression curves and their derivatives. The idea is also applied to kernel estimators of regression curves and densities.     

Periodic solutions of certain hybrid delay-differential equations and their corresponding difference equations

In this paper we use a method due to Carvalho (A method to investigate bifurcation of periodic solution in retarded differential equations, J. Differ. Equ. Appl. 4 (1998), pp. 17–27) to obtain conditions for the existence of nonconstant periodic solutions of certain systems of hybrid delay-differential equations. We first deal with a scalar equation of Lotka–Valterra type; then a system of two equations in two unknowns that could model the interactions of two identical neurons. It will be seen that such solutions are determined by solutions of corresponding difference equations. Another paper in which this method is used is by Cooke and Ladeira (Applying Carvalho's method to find periodic solutions of difference equations, J. Differ. Equ. Appl. 2 (1996), pp. 105–115).

We first state Carvalho's result.     

The Chiral Trimer and a Metastable Chiral Dimer of Achiral Hexafluoroisopropanol: A Multi‐Messenger Study

1,1,1,3,3,3‐hexafluoro‐propan‐2‐ol aggregates preferentially into an achiral dimer of achiral monomers, but the trimer is found to prefer three metastable chiral monomer units arranged into a strained OH???O hydrogen‐bonded ring, which is reinforced by secondary CH???FC interactions. This is shown by a combination of infrared, microwave, and Raman spectroscopy in supersonic jet expansions and supported by high‐level quantum chemical calculations. It involves an activation of the monomers by >15 kJ mol^?1, clearly driven by the much stronger hydrogen‐bond interaction available to the gauche and even more to the cis monomer units.     

Optimization of anionic conductivity through the coexistence of ionomer cluster and backbone-backbone morphologies in anion exchange membranes

Random copolymers of poly(4-vinylpyridine) and polyisoprene were synthesized, and subsequently quaternized with 1-alkylbromides. The number of carbons on the pendant side-chain of the resultant comb-shaped polymer, n, ranged from 2–8. The comb-shaped polymers were crosslinked employing thiol-ene chemistry to give mechanically robust ion conducting membranes. Analysis by wide and medium-angle X-ray scattering show three morphology regimes that are dependent on the number of carbons on the pendant side-chains. When n = 2, ionomer cluster morphology was dominant, when n = 8 backbone-backbone morphology was dominant, and when n = 3–6, the membrane showed a coexistence of both ionomer cluster and backbone-backbone morphologies. Evaluation of the water uptake of the membranes showed a maximum water uptake per cation of 9.5 when n = 5 at 95% relative humidity (RH) and 60°C. Conductivity of the samples characterized by electrochemical impedance spectroscopy showed bromide conductivity as high as 110 mS/cm when n = 3 at 95% RH and 90°C.