UNA generalizzazione del problema di burnside relativo all'esponente 4

An automorphism σ of order (a divisor of)n of the groupG is calledn-splitting if for everyg∈G. In this paper we prove that a 2-group admitting a 4-splitting automorphism, is locally finite.     

Solid-state NMR crystallography through paramagnetic restraints

Pseudocontact shifts (PCSs) measured by solid-state NMR spectroscopy (SS-NMR) on microcrystalline powders of a paramagnetic metalloprotein permit NMR crystallography. Along with other restraints for SS-NMR experiments, the protein molecular structure as well as the correct crystal packing are obtained.     

Photoreduction of Thiosulfate in Semiconductor Dispersions

Conduction band electrons produced by band gap excitation of TiO₂-particles reduce efficiently thiosulfate to sulfide and sulfite. \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm 2e}_{{\rm cb}}^ - ({\rm TiO}_{\rm 2}) + {\rm S}_{\rm 2} {\rm O}_3^{2 - } \longrightarrow {\rm S}^{2 - } + {\rm SO}_3^{2 - } $\end{document} This reaction is confirmed by electrochemical investigations with polycrystalline TiO₂-electrodes. The valence band process in alkaline TiO₂-dispersions involves oxidation of S₂O to tetrathionate which quantitatively dismutates into sulfite and thiosulfate, the net reaction being: \documentclass{article}\pagestyle{empty}\begin{document}$ 2{\rm h}^{\rm + } ({\rm TiO}_{\rm 2}) + 0.5{\rm S}_{\rm 2} {\rm O}_{\rm 3}^{{\rm 2} - } + 1.5{\rm H}_{\rm 2} {\rm O} \longrightarrow {\rm SO}_3^{2 - } + 3{\rm H}^{\rm + } $\end{document} This photodriven disproportionation of thiosulfate into sulfide and sulfite: \documentclass{article}\pagestyle{empty}\begin{document}$ 1.5{\rm H}_{\rm 2} {\rm O } + 1.5{\rm S}_{\rm 2} {\rm O}_{\rm 3}^{{\rm 2} - } \mathop \to \limits^{h\nu} 2{\rm SO}_3^{2 - } + {\rm S}^{{\rm 2} - } + 3{\rm H}^{\rm + } $\end{document} should be of great interest for systems that photochemically split hydrogen sulfide into hydrogen and sulfur.     

Research on heterocyclic compounds. XIII. Synthesis of 4,5-dihydro-5-oxo-3-isoxazoleacetic acid and related compounds

Some new 4,5-dihydro-5-oxoisoxazole derivatives were synthesized as part of a study to prepare potential antiinflammatory agents. The reaction of the diethyl ester of 3-oxopentanedioic acid with hydroxylamine afforded the 3-hydroxyimino derivative, which was then cyclized to the title compound. This reacted with diazomethane to give a couple of isomeric methyl derivatives, namely methyl 2,5-dihydro-2-methyl-5-oxo-3-isoxazoleacetate and methyl 5-methoxy-3-isoxazoleacetate. Reaction of these compounds with ammonia gave the corresponding acetamides. All compounds were characterized by elemental analysis, uv, ir, and ¹H-nmr spectra.     

On a class of second order Fuchsian hyperbolic equations

Summary We study a class of second order Fuchsian hyperbolic operators. The well-posedness of the Cauchy problem in a space of regular distributions is proved, together with results on the propagation of singularities of the solution. Moreover we give a representation formula for the distribution solutions of the homogeneous equation.     

A basic relation between invariants of matrices under the action of the special orthogonal group

The first fundamental theorem of invariant theory for the action of the special orthogonal group onm tuples of matrices by simultaneous conjugation is proved in [2]. In this paper, as a first step in the direction of establishing the second fundamental theorem, we study a basic identity betweenSO(n, K) invariants ofm matrices.