Theory of aging in structural glasses

The random first-order transition theory of the dynamics of supercooled liquids is extended to treat aging phenomena in nonequilibrium structural glasses. A reformulation of the idea of "entropic droplets" in terms of libraries of local energy landscapes is introduced which treats in a uniform way the supercooled liquid (reproducing earlier results) and glassy regimes. The resulting microscopic theory of aging makes contact with the Nayaranaswamy-Moynihan-Tool nonlinear relaxation formalism and the Hodge-Scherer extrapolation of the Adam-Gibbs formula, but deviations from both approaches are predicted and shown to be consistent with experiment. The nonlinearity of glassy relaxation is shown to quantitatively correlate with liquid fragility. The residual non-Arrhenius temperature dependence of relaxation observed in quenched glasses is explained. The broadening of relaxation spectra in the nonequilibrium glass with decreasing temperature is quantitatively predicted. The theory leads to the prediction of spatially fluctuating fictive temperatures in the long-aged glassy state, which have non-Gaussian statistics. This can give rise to "ultraslow" relaxations in systems after deep quenches.     

Oxydation von Allylalkoholen mit Blei(IV)-acetat

Lead tetraacetate (LTA) oxidation of the allylic alcohols 1, 10, 14 and 19 leads to the formation of the epoxides 2, 11, 15 and 20 , products of a novel internal addition reaction of the electron deficient alcohol oxygen to the allylic double bond. In some cases ( 10, 14 ) the formation of a new type of acetoxylated enolethers ( 12, 16 ) is observed. The LTA oxidation of the allylic dienols 21 and 29 gives rise to the formation of the epoxyacetates 25 and 33 , products of a similar internal addition reaction. Furthermore, a variety of cyclization products ( 22, 23, 24, 26, 30, 31, 32 and 34 ) has been isolated whose formation requires an isomerisation of the allylic trans double bond to a cis one.     

Beiträge zur Chemie der Pyrrolpigmente, 38. Mitt.: Zur Assoziation von Gallenpigmenten

The long standing problem of solvent dependent absorption spectra of certain bile pigments such as bilirubindimethylester has been solved by measurement of molecular masses by means of vapour pressure osmometry. Using this method and the investigation of the concentration and temperature dependence of the absorption spectra on several model compounds an association equilibrium for pigments of the rubinoid structural type could be confirmed. Moreover the optical properties of the coexisting species and the corresponding equilibrium constants could be deduced by spectroscopic techniques. Verdinoid pigments lacking free carboxylic functions on the other hand tend to be monomeric in solution. A heteroassociated species involving equimolar amounts of a verdinoid and a rubinoid pigment could be verified existing on adsorbents like silicagel.

37. Mitt.:Falk, H., Thirring, K., Tetrahedron, im Druck.     

Halogenated 3-pyridylketones

The oxidation of 2,6-dichloro-3-benzylpyridines and bis(2,6-dichloro-3-pyridyl)methanes, respectively, was accomplished using chromic trioxide in a highly acidic medium. The synthesis of several phenyl-3-(2,6-dichloropyridyl)ketones and of bis(2,6-dichloro-3-pyridyl)ketone are reported.     

Perturbed sites and host—guest—host exciton cascade in the biphenyl isotopic mixed crystal phosphorescence

An interesting energy cascade is observed in the phosphorescence spectra of 1% biphenyl-h₁₀ in biphenyl-d₁₀ (2–15 K); strongly perturbed host sites, with energy levels below that of the protonated guest, quench the guest sites at higher temperatures (11–15 K). The identification of the perturbed sites is based on vibrational characteristics (both intensity and frequency), obtained with the help of phosphorescence spectra of biphenyl-h₁₀ and biphenyl-d₁₀ in an argon matrix, indicating an isotope dependent vibronic structure. A partial vibrational analysis is presented, resulting in confirmation of the first triplet state of biphenyl as orbitally ungerade. The dynamics of the triplet excitation are discussed, including several possible mechanisms explaining the non-Boltzmann nature of the low-temperature steady state.     

Ab initio SCF Calculation of the Fluoronium Ion: Geometry,electronic structure and vibrational constants

An ab initio SCF calculation of 42 points of the energy hypersurface of the fluoronium ion is presented using a contracted F(5s/3p), H(2s) gaussian basis set. In its equilibrium structure a bond length of 1.812 a.u. and a HFH bond angle of 127.2° are predicted. The calculated vibrational frequencies for H₂F⁺, HDF⁺, and D₂F⁺ are in good agreement with the experimental data.     

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Representations of double coset hypergroups and induced representations

The principal goal of this paper is to investigate the representation theory of double coset hypergroups. IfK=G//H is a double coset hypergroup, representations ofK can canonically be obtained from those ofG. However, not every representation ofK originates from this construction in general, i.e., extends to a representation ofG. Properties of this construction are discussed, and as the main result it turns out that extending representations ofK is compatible with the inducing process (as introduced in [7]). It follows that a representation weakly contained in the left-regular representation ofK always admits an extension toG. Furthermore, we realize the Gelfand pair (where are a local field andR its ring of integers) as a polynomial hypergroup on ℕ₀ and characterize the (proper) subset of its dual consisting of extensible representations.