Spin wave spectrum and exchange interactions in the antiferromagnetic garnet Ca3Cr2Ge3O12 by inelastic neutron scattering

We have measured the spin wave spectrum for the garnet Ca₃Cr₂Ge₃O₁₂ by means of inelastic neutron scattering. The data can be well described in the framework of linear spin wave theory if we assume a Heisenberg model with two exchange parameters up to the next nearest neighbours (J ₁ andJ ₂) and a staggered anisotropy field (A). A least squares fit to the observed dispersion relations yield the following values for these parameters: J ₁=–0.582(8)K,J ₂=0.416(4)K,A=0.25(8)K. Although symmetry requires that two nearest neighbour exchange constantsJ ₁ andJ ₁ ^' must be distinguished, only the average J ₁=(J ₁+3J ₁ ^' )/4 and the condition –0.35 K <J ₁=J ₁-J ₁ ^' <0.50 K could be deduced from the experiment. The most striking result is the positive value ofJ ₂. We discuss the implications for an understanding of superexchange mediated by more than one oxygen atom. In an extension of the conventional analysis we have calculated the integrated intensities in order to check the eigenvectors directly. Good agreement between observed and calculated intensities was obtained.     

On the separation of basic semialgebraic sets by polynomials

In this paper we show that two disjoint basic closed semialgebraic sets, defined over a real closed field R, can be separated by a polynomial, if one of them has dimension 2. Counterexamples are given in all higher dimensions.     

Electrical and optical properties of melting Au/Si eutectics on Si(111)

The Au/Si system exhibits an extremely low eutectic temperature of 363°?C. Thin gold films of 200 nm thickness were deposited on Si(111) single-crystals and the electrical and optical properties of the melting mixtures were investigated. The resistivity measurements were performed in situ in a combined LEED/Auger apparatus. A highly resolving spectroscopic ellipsometer was used for the optical analysis in the wavelength range 400–900 nm. The eutectic temperature was found to be lower than for bulk Au/Si samples. The structure analysis showed that small liquid Au/Si islands embedded in the silicon surface are formed by the melting process. Various heating/ cooling cycles show a characteristic hysteresis behaviour.     

Über die katalytische Hydrierung von Chinolen

Zusammenfassung Bei der katalytischen Hydrierung von freien Chinolen werden unter Wasserstoffaufnahme hydroaromatische Verbindungen gebildet, während bei den Chinolen andere Reduktionsmethoden, sowie bei den Chinolacetaten auch die katalytische Hydrierung zur Ausbildung von aromatischen Körpern führen.Unserem verehrten Lehrer, Herrn Prof. Dr.F. Wessely, in Dankbarkeit zum 60. Geburtstag gewidmet.     

Synthesis of silver molybdate clusters driven by laser-annealing

The synthesis of silver rich molybdate clusters is achieved by laser induced chemical reaction of coadsorbed MoO(3) and O(2) molecules on free silver clusters. The reactants MoO(3) and/or O(2) molecules condensed at low temperature (77 K-175 K) on free silver clusters. Then, the silver clusters together with their adsorbed molecules are flashed either ionized with a discharge or ionized and heated by a laser. Then they are cooled down by evaporation. The synthesized chemical compounds are analyzed by a high-resolution time-of-flight mass spectrometer. If only one type of reactant is adsorbed on the cluster, only one oxide molecule is stabilized on the metallic core after the heating and cooling cycle. On the contrary, the coadsorption of the two types of molecules MoO(3) and O(2) on Ag(n) (+), at 77 K, leads to complex aggregates that transform, after laser heating, into a molybdate rich metal clusters. These synthesized species cool down by evaporating silver atoms showing evidence of a binary oxide that is more stable than the metallic core. Moreover we demonstrate that for small size molybdate clusters, a stoichiometric composition may differ from the bulk one.     

HPLC-NMR of fatty alcohol ethoxylates

The application of HPLC-NMR for the analysis of a mixture of fatty alcohol ethoxylates (FAEs) is described. The use of the new generation, cryogenically cooled probes is investigated in respect of the sensitivity advantage that they provide. The FAE mixture is separated using liquid chromatography at the critical point of adsorption. The ability of the method to differentiate between the different end groups and the degree of polymerization of the mixture constituents is investigated. Both on-flow and stop-flow HPLC-NMR techniques were used together with two-dimensional NMR spectroscopy. The results are compared with those obtained by using an evaporative light scattering detector for the HPLC.     

Local products for relativistic quantum fields

A definition of local functions of generalized free fields is suggested. Their concrete form is determined in a fairly general setting by analysing realizations of locality. A huge class of new models of relativistic quantum fields results in this way.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

A geometrical approach to bifurcation for nonlinear boundary value problems

Summary In this note we use a new averaging method, which was introduced in [2], to explain the geometrical behaviour of systems governed by nonlinear boundary value problems of the formy+g(y)=K sin(t),y(0)=y(/)=0. We show by numerical computations that global features of the solutions (such as the number of solutions, their magnitude, bifurcation behaviour, etc.) agree in both the original and averaged model. As an example, the pendulum equation is discussed in detail.

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Zusammenfassung In dieser Arbeit benutzen wir eine neue, in [2] eingeführte Mittelwertmethode, um das geometrische Verhalten nichtlinearer Randwertprobleme der Formy+g(y)=K sin(t),y(0)=y(/)=0. zu erklären. Wir belegen durch numerische Untersuchungen, daß globale Eigenschaften der Lösungen (wie z. B. die Anzahl der Lösungen, ihre Größenordnung, das Verzweigungsverhalten usw.) in der originalen und genäherten Gleichung übereinstimmen. Als Beispiel wird die Pendelgleichung ausführlich diskutiert.

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Supported by the Deutsche Forschungsgemeinschaft under grant No. BA 735/3-1