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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Category equivalences of clones

This note was inspired by McKenzie's recent paper [8] whose main result is a characterization of categorical equivalence (for short category equivalence) between varieties. Here we use this result to define category equivalent clones and to describe all clones category equivalent to maximal clones. If one is interested in maximal clones only up to category equivalence it is sufficient to consider very simple maximal clones, essentially the same as considered in Jablonski's early papers about maximal clones [6]. The results we have found encourage us in our feeling that category equivalence could be a useful tool in clone theory.Dedicated to the memory of Alan Day.Presented by J. Sichler.     

Hybrid extension of Schottky space

Part of this work was written while the author was feliow of the Graduiertenkolleg Geometrie und Mathematische Physik at the University of Bochum, Germany.     

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.