Towards an universal classification of scale invariant processes

We consider fields which take random values over several decades. Starting from physical examples, we postulate that scale is not an absolute quantity. We then establish the equivalence between two existing approaches based on scale symmetry arguments as general as possible. This yields a classification of log-infinitely divisible laws, possibly universal. The physical significance of the parameters entering in the classification is discussed. Received: 7 November 1997 / Received in final form: 26 March 1998 / Accepted: 30 March 1998     

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.     

The CeCl3·7H2O-NaI system as promoter in the synthesis of functionalized trisubstituted alkenes via Knoevenagel condensation

The arylidene malonates with two different geminal carboxylate functions, a suitable class of substrates of several synthetic and pharmacological studies, are easily available through Knoevenagel condensation of ethyl tert-butyl malonate and different aromatic aldehydes. The results have increased the potentialities of CeCl₃·7H₂O-NaI system as a type of water-tolerant green Lewis acid promoter for carbon-carbon bond forming procedures.     

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.