Über binäre Formen und die Correlationen mehrdimensionaler Räume

Ohne Zusammenfassung     

Construction der Hauptkrümmungshalbmesser und der Hanptkrümmungsrichtungen bei beliebigen Flächen

Ohne Zusammenfassung     

Die Reihenentwicklungen der Potentialtheorie

Ohne Zusammenfassung     

Zur Theorie der linearen Integrodifferentialgleichungen

Ohne Zusammenfassung     

The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

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The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

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In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.     

Stereoselective Syntheses of Benz[f]isoindoline-Derivatives by Intramolecular Cycloadditions of Styrenes to Olefins

The N-allyl-N-cinnamyl amide 10 undergoes thermal cyclization to a 2:1-mixture of the trans- and cis-benz(f)isoindolines 11a and 12a . By comparison, the thermolysis of the corresponding bis-cinnamylamide 14 proceeds in a highly stereoselective manner to give the cis-fused[4+2]-adduct 16a . Similarly, the trans-fused stereoisomeric adducts 30a and 31a were obtained with high stereochemical control on heating the N-allyl-N-diphenylallyl amide 28 . The thermal transformations 4 → 5 + 6a and 17 → 18a + 20a show the competitive formation of [2+2]-adducts. An alternative approach to (substituted) benz[f]isoindolines 16 via the all-cis-isomer 24a has been developed. The described structures have been assigned on the basis of spectral evidence, chemical correlations and by X-ray-diffraction study of the isomer 16b . These results illustrate the utility of substituent interactions in order to direct intramolecular cyclo-additions at will towards either endo- or exo-products.