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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Mit 3 Abbildungen     

Spectres de Masse de Derives de l'Atractyloside. Determination du Nombre de Substituants par Combinaison d'Acetylation et de Silylation

Different transformations of the functions fixed on a heterocyclic molecule were made. It is thus possible to quickly determine the number of functions of each type present in the molecule: e.g. (i) all the functions are silylated and (ii) the alcohols are acetylated whilst the sulfates and acids are silylated. Mass spectra of atractylate, apoatractylate and gummiferine have been studied and the substituents are counted and enumerated.     

FeGa3 and RuGa3: Semiconducting Intermetallic Compounds

The intermetallic compounds FeGa₃ and RuGa₃ were prepared from the elements using a Ga flux and their structures were refined from single-crystal X-ray data. Both compounds crystallize with the FeGa₃ structure type (tetragonal, space group P4₂/mnm, Z=4). Electrical resistivity measurements revealed a semiconducting behavior for FeGa₃ and RuGa₃, which is in contrast to the good metallic conductivity observed for the isotypic compound CoGa₃. The origin of the different electronic properties of these materials was investigated by first-principle calculations. It was found that in compounds adopting the FeGa₃ structure type the transition metal atoms and Ga atoms interact strongly. This opens a d-p hybridization bandgap with a size of about 0.31 eV in the density of states at the Fermi level for 17-electron compounds (i.e., FeGa₃ and RuGa₃). The electronic structure of CoGa₃ (an 18-electron compound) displays rigid band behavior with respect to FeGa₃. As a consequence, the Fermi level in CoGa₃ becomes located above the d-p hybridization gap which explains its metallic conductivity.     

A novel phosphoramidite method for automated synthesis of oligonucleotides on glass supports for biosensor development

Two protocols for functionalization of glass supports with hexaethylene glycol (HEG)-linked oligonucleotides were developed. The first method (standard amidite protocol) made use of the 2-cyanoethyl-phosphoramidite derivative of 4,4′-dimethoxytrityl-protected HEG. This was first coupled to the support by standard solid-phase phosphoramidite chemistry followed by extension with a thymidylic acid icosanucleotide. Stepwise addition of the linker phosphoramidite graduated at 1% (relative to the total sites available) perstep at 50°C resulted in an optimal yield of immobilized oligonucleotides at a density of 2.24 × 10¹⁰ strands/mm². This observed loading maximum lies well below the theoretical maximum loading owing to nonspecific adsorption of HEG on the glass and subsequent blocking of reactive sites. Surface loadings as high as 3.73 × 10¹⁰/mm² and of excellent sequence quality were achieved with a reverse amidite protocol. The support was first modified into a 2-cyanoethyl-N,N-diisopropylphosphoramidite analog followed by coupling with 4,4′-dimethoxytrityl-protected HEG. This protocol is conveniently available when using a conventional DNA synthesizer. The reverse amidite protocol allowed for control of the surface loading at values suitable for subsequent analytical applications that make use of immobilized oligonucleotides as probes for selective hybridization of sample nucleic acids of unknown sequence and concentration.     

Silica-Based and Transition Metal-Based Inorganic-Organic Hybrid Materials—A Comparison

Organically substituted metal alkoxides can be prepared by reaction of the parent alkoxides with complexing organic compounds. The chemical and structural consequences of such substitutions are discussed in this article. Examples are given showing how functional organic moieties, such as polymerizable groups, can be incorporated into sol-gel materials via the complexing ligands. Major structural differences between silica-based and metal-based hybrid materials originate from the different charge/coordination number ratios of silicon and most metals. This results in a high tendency for the molecular building blocks to aggregate. In many cases, metal oxide clusters are formed which are capped by the organic ligands. Such surface-modified clusters are themselves very valuable condensed matter units for materials syntheses.