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.     

Calculation ofn^3 S_1 (Q\bar Q) \to \gamma + (pseudo)scalar

The decays of³ S ₁ quarkonia into a photon and a scalar or pseudoscalar Higgs particle are examined, taking into account the bound-state dynamics in the framework of a nonrelativistic potential model. We find that for realistic quark potentials the naive calculation [1] overestimates the scalar rate. Numerical results are obtained for the \(\bar bb\) and \(\bar tt\) quark systems.     

Selective fluorescence quenching of 2,3-diazabicyclo[2.2.2]oct-2-ene by nucleotides

[reaction: see text] The fluorescence quenching of 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) by nucleotides has been studied. The quenching mechanism was analyzed on the basis of deuterium isotope effects, tendencies for exciplex formation, and the quenching efficiency in the presence of a molecular container (cucurbit[7]uril). Exciplex-induced quenching appears to prevail for adenosine, cytidine, and uridine, while hydrogen abstraction becomes competitive for thymidine and guanosine. Compared to other fluorescent probes, DBO responds very selectively to the type of nucleotide.     

Cycloadditionsreaktionen von Organometall-Komplexen : XV. [2 + 31- und [2 + 1]-Cycloadditionsreaktionen von Carbonylrhodium- und Carbonylcobalt-Komplexen mit Nitriloxiden und Aziden. Die Kristall- und Molekülstruktur von C5H5(PPr3) (C6H5)

The reaction of C₅H₅Rh(CO)(PⁱPr₃) (1] which is prepared from C₅H₅Rh(CO)₂ and neat P¹Pr₃, with the nitriloxides 2-RC₆H₄CNO (R = H, Cl) leads to the formation of the metallaheterocycles C₅H₅(P¹Pr₃) ) (2, 3) in 90–95% yield. Compound 1 reacts with tosylazide to give the C,N-bound isocyanate complex C₅ H₅(PⁱPr₃)Rh(η²-TosN=C=O) (6). Analogously, on treatment of C₅Me₅Co(CO)(PMe₃) with phenylazide the phenylisocyanate derivative C₅Me₅(PMe₃)Co(η²-PhN=C=O) (7) is formed. Protonation of 7 with CF₃CO ₂H affords the non-ionic carbamoylcobalt complex C₅Me₅(PMe₃)Co[C(O)NHPh](O₂CCF₃) (8). The X-ray structural analysis of 2 reveals the presence of an almost planar heterocycle in which the two Rh-C distances differ by 0.045 Å     

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.     

Ab initio calculations of small hydrides including electron correlation

Five different structures of CH₅ ⁺ and one structure of CH₅ ^– are calculated using a gaussian basis both in the SCF approximation and with the inclusion of electron correlation in the independent electron pair approximation (IEPA). While on SCF level the C _sstructure of CH₅ ⁺ has to lowest energy, the energy difference between the C _sand C _2vstructures becomes negligible if correlation is included. In contrast to this the approach of a proton to CH₄ at large and intermediate distances is most favorable towards a corner of the CH₄ tetrahedron which means a structure. The decomposition of CH₅ ⁺ into CH₃ ⁺ and H₂ requires 20kcal/mol on SCF level and 40 kcal/mol if correlation is included.