Ueber die Darstellung von Traubenzucker

Ohne Zusammenfassung     

On the recognition problem of quasi-homogeneous locally nilpotent derivations in dimension three

We give a criterion to decide if a given w-homogeneous derivation on A?k[X₁,X₂,X₃] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation.     

A Bicriterial Optimization Problem of Antenna Design

In this paper we consider a special optimization problem withtwo objectives which arises in antenna theory. It is shown that thisabstract bicriterial optimization problem has at least one solution.Discretized versions of this problem are also discussed, and therelationships between these finite dimensional problems and the infinitedimensional problem are investigated. Moreover, we presentnumerical results for special parameters using a multiobjectiveoptimization method.     

Time-resolved cavity ringdown spectroscopy on nanoparticle generation in a SiH4–H2 VHF plasma

Time-resolved cavity ringdown (τ-CRD) spectroscopy has been applied to monitor the silyl (SiH₃) radicals and nanoparticles in a pulsed very high frequency (VHF) silane-hydrogen plasma under microcrystalline silicon (μc-Si:H) deposition conditions. The measured cavity loss reveals four time intervals (I up to VI) in the first 4 s of the plasma pulse. By variation of the laser wavelength, it is demonstrated that the small cavity loss at 220 nm reflects the SiH₃ absorption in interval I. In intervals II and III, an additional cavity loss appears. This additional cavity loss corresponds to Rayleigh and Mie scattering by growing nanoparticles. Interval IV reflects the loss of nanoparticles between the electrodes during the afterglow of the plasma pulse. The evolution of the nanoparticle generation determined from the τ-CRD measurements are further confirmed by additional scanning electron microscopy analyses on the nanoparticles created in the plasma pulse.     

Mesoporous electrode material from alumina-stabilized anatase TiO2 for lithium ion batteries

A mesoporous electrode material whose structure is composed of anatase nanocrystals stabilized by alumina is reported. Powder X-ray diffraction shows the anatase phase only, but micro-Raman spectroscopy shows that the materials have a core-shell morphology with grains of bulk anatase covered by a thin rutile layer on the surface. This structure is unique when compared to analogous materials stabilized by zirconia (PNNL-1). Nitrogen adsorption isotherms demonstrate a monotonous increase in surface area and mesopore volume with increasing Al content. Thin film electrodes from these materials were characterized by lithium insertion electrochemistry. Cyclic voltammograms exhibit significant differences in Li accommodation in Al-free and Al-stabilized materials.     

Tantalum Clusters in Oxidic Matrices — Synthesis,Crystal Structure and Magnetic Properties of Eu1.83Ta15O32

The mixed‐valent oxotantalate Eu_1.83Ta₁₅O₃₂ was prepared from a compressed mixture of Ta₂O₅ and the metals in a sealed Ta ampoule at 1400 °C. The crystal structure was determined by means of single crystal X‐ray diffraction: space group R3¯, a = 777.2(6) pm and c = 3523.5(3) pm, Z = 3, 984 symmetrically independent reflections, 83 variables, R_F = 0.027 for I > 2σ (I). The structure is isotypic to Ba₂Nb₁₅O₃₂. The salient feature is a [Ta(+8/3)₆O₁₂ⁱO₆^a] cluster consisting of an octahedral Ta₆ core bonded to 12 edge‐bridging inner and six outer oxygen atoms. The clusters are arranged to slabs which are sandwiched by layers of [Ta(+5)₃O₁₃] triple octahedra. Additional Ta(+5) and Eu(+2) atoms provide the cohesion of these structural units. Twelve‐fold coordinated Eu(+2) atoms are situated on a triply degenerate position 33 pm displaced from the threefold axis of symmetry. A depletion of the Eu(+2) site from 6 to 5.5 atoms per unit cell reduces the number of electrons available for Ta‐Ta bonding from 15 to 14.67 electrons per cluster. Between 125 and 320 K Eu_1.83Ta₁₅O₃₂ is semi‐conducting with a band gap of 0.23 eV. The course of the magnetization is consistently described with the Brillouin function in terms of a M_mol/(N_Aμ_B) versus B/T plot in the temperature range 5 K — 320 K and at magnetic flux densities 0.1 T — 5 T. At moderate flux densities (< 1 T) the magnetic moment agrees fairly well with the expected value of 7.94 μ_B for free Eu (2+) ions with 4f⁷ configuration in ⁸S_7/2 ground state. Below 5 K, anisotropic magnetization measurements at flux densities B < 1 T point to an onset of an antiferromagnetic ordering of Eu spins within the layers and an incipient ferromagnetic ordering perpendicular to the layers.     

Solvothermale Synthese und Bestimmung der Kristallstrukturen von AgBiI4 und Ag3BiI6

Solvothermal Synthesis and Crystal Structure Determination of AgBiI₄ and Ag₃BiI₆ AgBiI₄ and Ag₃BiI₆ were synthesized by solvothermal reaction from AgI and BiI₃ in diluted HI‐solution (20 %) at a temperature of 160 °C. The greyish‐black crystals grow as octahedra (AgBiI₄) or hexagonal/trigonal platelets (Ag₃BiI₆). AgBiI₄ crystallizes in space group Fd3¯m with a = 1222.3(1) pm (300 K) and Z = 8 whereas Ag₃BiI₆ shows the space group R3¯m with a = 435.37(6) pm, c = 2081.0(4) pm (300 K) and Z = 1. Both crystal structures show stacking sequence abcabc… of hexagonal layers containing Iodine. Bismuth and silver are sharing octahedral sites with different mass ratio in both structures. The part of silver which could be localized varies with temperature. This behaviour indicates mobility of silver within the crystal structure. The ionic conductivity of AgBiI₄ is explored. AgBiI₄ and Ag₃BiI₆ show close structural relationship, with AgBiI₄ as a variant with a higher degree of order.