Ein verschärfter und verallgemeinerter Satz von Alexandrov

In this paper we prove the following theorem: Suppose that n≥3 and 1≤jn $$(\forall a,b) d(a,b) : = \sum\limits_{\nu = 1}^j { (a_\nu - b_\nu )^2 - \sum\limits_{\nu = j + 1}^n { (a_\nu - b_\nu )^2 .} }$$ If a function f:?ⁿ→?ⁿ satisfies the condition: (*) $$(\forall x,y \in \mathbb{R}^n ) d(f(x),f(y)) = 0 \Leftrightarrow d(x,y) = 0,$$ then f is affine. Moreover, f preserves distances up to a constant factor C≠0, i.e. d(f(x),f(y))=C·d(x,y) for every x,y. In contrast to Alexandrov's result [1] we do not assume that f is bijective, and we also do not assume that j=n?1. A very important part of our proof will be the discussion of a functional equation.     

Plateau's problem for surfaces of prescribed mean curvature in given regions

Plateau's problem for surfaces of prescribed mean curvature will be considered in regions which are not necessarily H-convex.     

Chernklassen semi-stabiler Rang-3-vektorbündel auf kubischen Dreimannigfaltigkeiten

It is shown that the third Chern-number of a semistable Rk-3-vector bundle on a smooth hypersurface of degree 3 in ₄ can be bounded by the first and the second Chern-number of the bundle.     

Coordination compounds of disulphur dinitride

Summary Coordination compounds of the S₂N₂ molecule including methods for their preparation, reactivities, i.r. data, structures, and aspects of chemical bonding are reviewed. Methods of synthesis include reactions of S₂N₂, S₄N₄ or (NSCl)₃ with metal halides, metal complexes such as carbonyls, or even metals themselves. In all cases, the planar S₂N₂ ring is coordinated, usuallyvia both, of its nitrogen atoms so that S₂N₂ acts as a bridging ligand between two metal centres; short contact distances imply that halogen atoms linked to the metal atoms show some interaction with the sulphur atoms. The stability of S₂N₂ is greatly enhanced by coordination. In the i.r. spectra, two characteristic S₂N₂ vibrations assist identification of the S₂N₂ species, a ring stretching mode being observable atca. 850 cm^–1 and the out-of-plane deformation at 450–490 cm^–1.     

Eine semiempirische Gleichung zur Beschreibung des Lösungsmitteleinflusses auf Statik und Kinetik chemischer Reaktionen. Teil I

A model has been developed for calculating the enthalpy, entropy and free energy change associated with the creation of cavities in a liquid the size of which corresponds to the volume occupied by a solvent molecule. The molar enthalpy change H _cav equals the molar enthalpy of vaporization of the liquid, the free energy change G _cav is given by G _cav=–RT ln (V _m ·p _eq /RT) (V _m =molar volume,p _eq =equilibrium vapor pressure) and is related to the standard free energy of vaporization. This relationship provides an estimate of the free energy of cavity formation required to accomodate a substrate in the liquid. It has been shown, that the free energy of solvation of a substrate can be dissected into different contributions accounting for (1) the concentration dependence of partial molar free energy quantities, (2) the formation of holes in the solvent, (3) the existence of specific, short range solute-solvent interactions and (4) the dielectric polarization of the medium. Application of this concept leads to an equation of the general form G ^S –G ^R =a(DN ^S –DN ^R )+b(AN ^S –AN ^R )+c(G _vp ^oS –G _vp ^oR ), where G represents the free energy of reaction or activation,DN the donor number,AN the acceptor number and G _vp ^o the standard free energy of vaporization of a solventS and a reference solventR, resp.

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