Die polarographische Bestimmung von Verunreinigungen in reinstem Indium

Zusammenfassung Es wird eine spurenanalytische Methode zur Bestimmung von Verunreinigungen in hochreinem Indium beschrieben. Die Elemente Blei, Eisen, Cadmium, Kupfer, Thallium, Wismut und Zink werden durch Isopropylätherextraktion aus Halogensäuren angereichert und polarographisch bestimmt. Die Bedingungen zur extraktiven Anreicherung werden eingehend behandelt. Zur Vermeidung von Einschleppungen wird weitgehend im geschlossenen System gearbeitet. Die Bestimmung der genannten Elemente ist bis 10^–6% mit einer Genauigkeit von besser als ± 10% möglich.     

Carbon-carbon bond formation in palladium(II)-catalyzed allylic oxidation: a novel oxidative carbocyclization of allene-substituted olefins

A new efficient palladium(II)-catalyzed oxidative carbocyclization has been developed. It was found that allene-substituted olefins 1 cyclized in the presence of 1 mol % Pd(O2CCF3)2 and p-benzoquinone (2 equiv) to give bicyclic ring systems 2 in good to excellent yields. The cyclization constitutes a new type of carbon-carbon bond forming reaction between an allene and an olefin under oxidative conditions.     

Total cross section for inclusive electron scattering in the lowQ 2 region

Absolute cross sections for inclusive electron scattering on H, D, Be, Al, and Si have been measured in the kinematical region 0.08 (GeV/c)²<Q ²<1.0 (GeV/c)² and 0.3 GeV<v<6.5 GeV. The measurements have been performed at incident energies of 3, 5, 6, and 7 GeV and at the fixed scattering angle of 10°. A careful treatment of radiative corrections due to elastic electron nucleus scattering, quasielastic and inelastic scattering on the bound nucleons has been applied to the measured cross sections. The comparison of the nuclear cross sections with the elementary ones leads to a value ofA _eff<A with a rapid onset of this effect at small values of the scaling variablex′.     

On Wong-Zakai approximation of stochastic differential equations

An approximation theorem of stochastic differential equations driven by semimartingales is proved, based on approximation of semimartingales by a sequence of processes with piecewise monotonic sample functions.     

Zur simultanen Diophantischen Approximation. I

An important problem in the field of Diophantine Approximation was solved in 1891 byHurwitz. He could show that any irrational number can be approximated by infinitely many rationals in such a way that the modulus of the difference multiplied with the square of the denominator is less than 5^–1/2, and there 5^–1/2 is best possible.-The generalization of this problem in the direction of simultaneous Diophantine Approximation is still unsolved.Furtwängler in 1925 gave lower bounds for the maximum difference, conjecturing that these were best possible.-Here it is shown that in the two dimensional caseFurtwängler's bounds are indeed best possible for certain irrationals lying in cubic number fields which are not totally real. Yet by considering totally real cubic fields we are led to replaceFurtwängler's conjecture by a new one.     

A criterion for the affine equivalence of cell complexes inR d and convex polyhedra inR d+1

A criterion is given that decides, for a convex tilingC ofR ^d , whetherC is the projection of the faces in the boundary of some convex polyhedronP inR ^d+1. Its applicability is restricted neither by the properties nor by the dimension ofC. It turns out to be conceptually simpler than other criteria and allows the easy examination of various classes of cell complexes. In addition, the criterion is constructive, that is, it can be used to constructP provided it exists.Research was supported by the Austrian Fonds zur Foerderung der wissenschaftlichen Forschung.     

The analog of electric and magnetic fields in stationary gravitational systems

Newtonian and Machian aspects of the stationary gravitational field are brought into formal analogy with a stationary electromagnetic field. The electromagnetic vector potential equals (up to a factor) the timelike Killing vector field. The current density is given by the contraction of the Killing vector with the Ricci tensor. A coordinate-dependent split in electric and magnetic field vectors is given, and some results of classical electrodynamics are used to illustrate the analogy. In the linearized theory, the usual Maxwell equations are obtained. The analogy also holds from the point of view of particle motion. The geodesic equation is brought into a special form that exhibits an analog to the Lorentz force. Two examples (which have played an important role in the theoretical discovery of Machian effects) are considered.     

New Triterpenoid Saponins from Achyrantes aspera Linn.

Two new bisdesmosidic triterpenoid saponins, i.e. 1 and 2 , were isolated, besides the three known saponins 3 – 5 , from the MeOH extract of the aerial parts of Achyranthes aspera Linn. (Amaranthaceae). Their structures were elucidated as β‐D ‐glucopyranosyl 3β‐[O‐α‐L ‐rhamnopyranosyl‐(1→3)‐O‐β‐D ‐glucopyranuronosyloxy]machaerinate ( 1 ) and β‐D ‐glucopyranosyl 3β‐[O‐β‐D ‐galactopyranosyl‐(1→2)‐O‐α‐D ‐glucopyranuronosyloxy]machaerinate ( 2 ) by NMR spectroscopy, including 2D‐NMR experiments (machaerinic acid=3β,21β‐dihydroxyolean‐12‐en‐28‐oic acid). The other saponins were identified as β‐D ‐glucopyranosyl 3β[O‐α‐L ‐rhamnopyranosyl‐(1→3)‐O‐β‐D ‐glucopyranuronosyloxy]oleanolate ( 3 ), β‐D ‐glucopyranosyl 3‐β‐[O‐β‐D ‐galactopyranosyl‐(1→2)‐O‐β‐D ‐glucopyranuronosyloxy]oleanolate ( 4 ), and β‐D ‐glucopyranosyl 3β‐[O‐β‐D ‐glucopyranuronosyloxy]oleanolate ( 5 ) (oleanolic acid=3β‐hydroxyolean‐12‐en‐28‐oic acid).