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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A New Technique for Preserving Conservation Laws

Foundations of Computational Mathematics - This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We...     

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.     

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.