On the support of the Ashtekar-Lewandowski measure

We show that the Ashtekar-Isham extension of the configuration space of Yang-Mills theories is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that is contained in a zero measure subset of with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on . Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the extended configuration space .     

Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

On the number of triple points of the tangent developable

We study the singularities of the tangent developable of a generic curve in ³ and prove that if the curve has no torsion zero points, the number of triple points of that surface must be even.     

Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.     

Studium des gegenseitigen Einflusses der Bindungen in Thiocyanat-Kupfer(II)-Komplexen mit Methyl- und Dimethylpyridinen mittels Infrarotspektroskopie

The infrared spectra of thiocyanato-copper(II) complexes of the type Cu(NCS)₂ L ₂ with all isomeric picolines and lutidines (L) as well as those of the type Cu(NCS)₂ L ₃ withL=3- and 4-picoline, 3,4- and 3,5-lutidine were measured. The behaviour of the (CN) stretching vibrations of the Cu(NCS)₂ L ₂ complexes led to conclusions on the different kind of coordination of the NCS groups in dependence on the ligandL. The mutually conditioned strength of the Cu–NCS and Cu–N(L) bonds in the equatorial plane, especially in the presence of ligandsL with the steric effect, was determined from the frequency shift of the Cu–NCS and Cu–N(L) stretching vibrations with regard to the vibrations for Cu(NCS)₂(pyridine)₂.

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Mit 1 Abbildung     

Ligandenfeldspektren einiger Cyanato-Kupfer(II)-Komplexe des Typs Cu(NCO)2 L 2 mit Liganden aus der Chinolin- und Isochinolingruppe Cyanato-Kupfer(II)-Komplexe mit organischen Liganden, 7. Mitt.

Zusammenfassung Die Ligandenfeldspektren der Komplexe des Typs Cu(NCO)₂ L ₂ (L=Ligand der Chinolin- bzw. Isochinolingruppe) im festen Zustand wurden aufgenommen. Das Spektrum des Komplexes Cu(NCO)₂(Chin)₂ weist eine einzige Bande auf und deutet auf eine pseudooktaedrische Struktur. Die Spektren der übrigen Komplexe enthalten hingegen neben den Hauptbanden auch Schultern bzw. ist die anwesende Bande zusammengesetzt, so daß diese Spektren mit einer planaren Struktur im Einklang sind. Die annähernden Werte für den Parameter 10Dq wurden berechnet; sie liegen im Bereich von 7,1 bis 7,8 kK.

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Ligand field spectra of some cyanato-copper(II) complexes with ligands from the quinoline- and isoquinoline group

The ligand field spectra of complexes of the type Cu(NCO)₂ L ₂ (L=ligand from the quinoline or isoquinoline group) in the solid state were recorded. Only the spectrum of Cu(NCO)₂(Quin)₂ exhibits a single band and indicates a pseudooctahedral structure, while the spectra of the remaining complexes also contain shoulders in addition to the main band, or this band is composite, thus being in accordance with a planar structure. The approximate values of the parameter 10Dq were calculated and found to be in the range of 7.1 to 7.8 kK.

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6. Mitt.:M. Quastlerová-Hvastijová, J. Kohout undJ. Gao, Z. anorg. allgem. Chem., im Druck.