Zur Theorie der binomischen Differentialgleichungen

Ohne Zusammenfassung     

Susy-breaking without sliding vev

In the absence of gauge interactions the spontaneous breakdown of supersymmetry (Susy) is accompanied by a scalar field whose vacuum expectation value is not determined by the tree potential. Inclusion of the gauge interactions can fix this vev at the tree level. The situation is exemplified by a simpleSU(2)-model yielding nonvanishingF-andD-vevs.     

Factorizing the complete graph into factors with large star number

The graph G has star number n if any n vertices of G belong to a subgraph which is a star. Let f(n, k) be the smallest number m such that the complete graph on m vertices can be factorized into k factors with star number n. In the present paper we prove that $\text{c}{}_1{}^{\mathrm{n}}\text{k ≤ f(n, k) < c}{}_2{}^{\mathrm{n}}\text{k}$.     

The experimental gas-phase structures of 1,3,5-trisilylbenzene and hexasilylbenzene and the theoretical structures of all benzenes with three or more silyl substituents

The structures of 1,3,5-trisilylbenzene and hexasilylbenzene in the gas phase have been determined by electron diffraction, and that of 1,3,5-trisilylbenzene by X-ray crystallography. The structures of three trisilylbenzene isomers, three tetrasilylbenzenes, pentasilylbenzene and hexasilylbenzene have been computed, ab initio and using Density Functional Theory, at levels up to MP2/6-31G*. The primary effect of silyl substituents is to narrow the ring angle at the substituted carbon atoms. Steric interactions between silyl groups on neighbouring carbon atoms lead first to displacement of these groups away from one another, and then to displacement out of the ring plane, with alternate groups moving to opposite sides of the ring. In the extreme example, hexasilylbenzene, the SiCCSi dihedral angle is 17.8(8) degrees .     

Mechanism and kinetics of the catalytic CO-H2 reaction: An approach by chemical transients and surface relaxation spectroscopy

The aim of this paper is to demonstrate the importance of providing time-resolved information in catalysis research. Two truly in situ methods will be presented and compared for their merits and drawbacks: chemical transient kinetics (CTK) and pulsed field desorption mass spectrometry (PFDMS). The presentation will be given by way of example choosing the syngas (CO/H2) reaction over cobalt-based catalysts as a catalytic process. Despite numerous efforts in the past, the mechanism of this reaction is still under debate. In CTK the reaction is studied on a metal-supported catalyst under flow conditions in a pressure range extending from atmospheric pressure down to 100 Pa. Sudden changes in the partial pressures of the reactants then allow following the relaxation to either steady-state conditions ("transients") or cleanoff ("back transients"). In PFDMS short field pulses of several volts per nanometer are applied to a model catalyst which resembles a single metal particle grain (a "tip"). These pulses intervene during the ongoing reaction under flow conditions at pressures ranging from 10(-1) to 10(-5) Pa and cause field desorption of adsorbed species. This method is particularly suited to detect reaction intermediates in a time-dependent manner since the repetition frequency of the pulses can be systematically varied. It is shown that both methods lead to complementary results. While CTK allows conclusions on the mechanism of CO hydrogenation by following the time-dependent formation of hydrocarbon species, PFDMS provides insight into the initial steps leading to adsorbed CxHy species. A quantitative assessment of the CTK data allows the demonstration that the catalyst under working conditions is in an oxidized rather than metallic state. The initial steps to oxidation are also traced by PFDMS. Most importantly, however, CTK results allow formulation of a reaction mechanism that is common for both hydrocarbon and oxygenate formation and is based on the occurrence of a formate-type species as the most abundant surface intermediate.     

Summarizing complexity in high dimensions

High-dimensional, multispectral data on complex physical systems are increasingly common. As the amount of information in data sets increases, the difficulty of effectively utilizing it also increases. For such data, summary information is required for understanding and modeling the underlying dynamics. It is here proposed to use an extension of computational mechanics [C. R. Shalizi and J. P. Crutchfield, J. Stat. Phys. 104, 817 (2001)] to arbitrary spatiotemporal and spectral dimension, for providing such summary information. An example of the use of these tools to identify state evolution in the brain, an archetypal, complex biophysical system, serves as an illustration.     

Optimized hole injection with strong electron acceptors at organic-metal interfaces

The energy-level alignment at interfaces between three electroactive conjugated organic materials and Au was systematically varied by adjusting the precoverage of the metal substrate with the electron acceptor tetrafluoro-tetracyanoquinodimethane (F4-TCNQ). Photoelectron spectroscopy revealed that electron transfer from Au to adsorbed F4-TCNQ was responsible for lowering the hole-injection barrier by as much as 1.2 eV. This novel interface modification scheme is independent of the charge transfer complex formation ability of the organic materials with the electron acceptor.     

New measure of electron correlation

We propose to quantify the correlation inherent in a many-electron (or many-fermion) wave function psi by comparing it to the unique uncorrelated state that has the same 1-particle density operator as does /|psi>相似文献