Eine lokale Charakterisierung der Veronesemannigfaltigkeiten

We show that the Veronese submanifold of the standard sphere may be characterised by the property that the second fundamental form is-up to a constant factor-an isometric map from the symmetric product of the tangent space onto the normal space.     

Synthesis, structure and properties of pyrazole type tetrakis compounds

A series of pyrazole type tetrakis compounds has been synthesized by reaction of aromatic or heterocyclic dialdehydes and pyrazolone derivatives. Structure and tautomerism of the products were investigated by spectroscopic methods and X-ray analysis. Several tetrakis compounds form inclusion complexes with solvents like alcohols, ethers, and ketones in a definite ratio via hydrogen bonds.     

Bose-Einstein condensation in a cavity

The effect of the physically correct boundary conditions and the nonvanishing ground state energy on Bose-Einstein condensation of quantum particles confined to a cubic volumeV=L ³ is evaluated. The transition point is shifted towards higher temperatures by the confinement, the specific heat below the onset of condensation is no longer proportional toT ^3/2, and the pressure does depend on the volume. Precise expressions for the modification of the ground state population and for the shift of the condensation temperature are derived, together with an expansion of the internal energy and of the specific heat. Numerical computations confirm the accuracy of our analytical approximations.Dedicated to Herbert Wagner, whose work on quantum Fermi liquids proved to be also very stimulating for quantum Bose liquids.     

The product of powers in a finitep-group

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