Ueber die Eigenschaft der Gammafunction keiner algebraischen Differentialgleichung zu genügen

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Bücherbesprechungen

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Tautomeric Equilibrium in Polyfluoroalkylated 5,6,7,8-Tetrahydrofurans by IR Spectroscopy

The tautomeric equilibrium in substituted 5,6,7,8-tetrahydroquinazolines was studied by IR spectroscopy. The effect of various substitutents in the pyrimidine ring and the solvent on the state of the tautomeric equilibrium was evaluated.     

A new approach to obtain the non-Condon factors in closed form for two one-dimensional harmonic oscillators

A simple algebraic approach to calculate general Franck-Condon overlaps is extended to evaluate non-Condon factors for two one-dimensional harmonic oscillators. The method is based on the use of eigenstates of the harmonic oscillator annihilation operator which allows to obtain in terms of a multi-dimensional Hermite polynomial the overlap of harmonic oscillator functions associated with different Born-Oppenheimer potentials. The presented approach is self-contained, only basic concepts of quantum mechanics associated with the harmonic oscillator system are needed. The obtained expression for the Franck-Condon overlaps is similar to the Ansbacher’s formula and equivalent to the one calculated by Malkin and Man’ko. However our final expression has the advantages that only real numbers are involved and it is straightforward to get the limit case of equal frequencies. Concerning the non-Condon factors two approaches leading to different formulas are considered, both of which reduce to triple sums of products of three Hermite polynomials.     

Ueber die Darstellung von Traubenzucker

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Complexes of Some Pyrido[1,2-a]pyrimidinium Perchlorates with Scandium,Yttrium, and Lanthanum. Crystal and Molecular Structure of 3-Chloro-9-Hydroxy-2,4-Dimethylpyrido[1,2-a]pyrimidinium Perchlorate

Complexes of scandium, yttrium, and lanthanum nitrates with 3-chloro-9-hydroxy-2,4-dimethylpyrido[1,2-a]pyrimidinium perchlorate (HL¹ClO₄) and 9-hydroxy-2,4-dimethylpyrido[1,2-a]pyrimidinium perchlorate (HL²ClO₄) were obtained. Their composition was formulated as Sc(LClO₄)₂(NO₃) and M(LClO₄)₂(NO₃)₂ (L = L¹ or L²; M = Y or La); structures for the complexes obtained were proposed. The crystal and molecular structure of HL¹ClO₄ was determined. Dissociation and complexation of HL¹ClO₄ and HL²ClO₄ in aqueous ethanol were studied using the spectroscopic method. Ligand dissociation and complexation constants were calculated. It was shown that a chlorine-containing organic ligand only slightly changes the composition and stability of the metal complexes.     

Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.