Neue Redoxserien auf der Basis von Übergangsmetallkomplexen heterocyclischer Arensulfonylhydrazone

New Redox Series Based on Transition Metal Complexes of Heterocyclic Arenesulfonylhydrazones Heterocyclic bidentate arenesulfonylhydrazones (2-acetylpyridine-p-toluenesulfonylhydrazone ? APSH? H, 2-acetylquinoline-p-toluenesulfonylhydrazone ? ACSH? H) with transition metal ions afford tetrahedral 1,2-complexes M^II(APSH)₂ and M^II(ACSH)₂. In most cases the E-isomers of APSH^? and ACSH^? are coordinated, five-membered chelate rings are formed with the pyridine and hydrazone nitrogen atoms as donor atoms. In the complexes Zn(APSH)₂ and Cu(APSH)₂ probably the Z-isomer of APSH^? is present with the pyridine and the sulfonylamide nitrogen atoms as a donor set, yielding a six-membered chelate ring. These proposals are based on the magnetic moments, the ligand field spectra, and the binding energies (ESCA). Normally the complexes M^II(APSH)₂ and M^II(ACSH)₂ are reduced in two reversible steps. For Fe(APSH)₂ and Fe(ACSH)₂ a third anodic wave, but for Cu(APSH)₂ only one wave is observed. Relations between redox properties and structure of the new complexes are discussed, and the redox series are compared with that of the M(dipy)₃ⁿ⁺-type complexes.     

Coloring linear hypergraphs: the Erdős–Faber–Lovász conjecture and the Combinatorial Nullstellensatz

Designs, Codes and Cryptography - The long-standing Erdős–Faber–Lovász conjecture states that every n-uniform linear hypergaph with n edges has a proper vertex-coloring using...     

Almost block independence and bernoullicity of ℤ d -actions by automorphisms of compact abelian groups

Summary We prove that a ^d -action by automorphisms of a compact, abelian group is Bernoulli if and only if it has completely positive entropy. The key ingredients of the proof are the extension of certain notions of asymptotic block independence from -actions to ^d -action and their equivalence with Bernoullicity, and a surprisingly close link between one of these asymptotic block independence properties for ^d -actions by automorphisms of compact, abelian groups and the product formula for valuations on global fields.Oblatum 20-X-1994     

Wiener-Wintner return-times ergodic theorem

We state a new ergodic theorem, combining the Wiener-Wintner theorem and Bourgain’s theorem concerning the convergence of ergodic averages along return-times sequences. We consider ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {e^{in\theta } \cdot f'(S^n y) \cdot f(T^n x)} $$ and we show that the behaviour of these averages characterizes an algebraC of functions, which contains the Kronecker algebra and has interesting properties, linked with multiple recurrence ergodic theorems.     

Orientations of chain groups

We prove generalizations to chain groups, of Minty's Arc Colouring Lemma and its extension, the well-known Farkas Lemma. In these the orientation of the edges is replaced by an arbitrary chain.A function on a chain groupN isrepresentable if there exists a chainR such that (X)=R·X for allXN. Anorientation is a chain with values ±1. We prove that for a regular chain group a linear function that is representable by an orientation for each chainXN locally, is representable by an orientation globally.     

(Z)-1-[2-(Triarylstannyl)vinyl]-1-cycloheptanols: Synthesis, characterization, halodemetallation and crystal structures

The synthesis and characterization by ¹H, ¹³C, ¹¹⁹Sn NMR and ¹¹⁹Sn Mössbauer spectroscopy of (Z)-1-[2-(triphenylstannyl)vinyl]-1-cycloheptanol,

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(1), and (Z)-1-[2-tri-p-tolylstannyl)vinyl-1-cycloheptanol,

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(2), are described, together with their halodemetallation by I₂, Br₂ and ICIl to yield derivatives of the types

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(Ar = phenyl or p-tolyl, N = 1, 2; X = I, Br, Cl, respectively). The solid-state structures of four compounds have been determined by X-ray diffraction analysis. In the crystals of

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(1) and

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(2) the Sn atom has a tetrahedral geometry distorted towards trigonal bipyramid as a consequence of a close intramolecular contact with the hydroxyl O(1) atom of 2.742(3) Å and 2.768(3) Å, respectively. A trigonal bipyramidal geometry is found in

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(12) and

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(4), in which significant Sn---O(1) interactions are noted [2.437(8) Å and 2.407(8) Å, respectively].     

Modelling of the processes of ultrafine SiO2 production under thermal plasma conditions

The production of ultrafine silica particles is examined by modelling the processes in a flow plasma reactor. The model is based on the authors' experimental data on silica sand processing by use of thermal arc plasma. The free-molecular coagulation is assumed to be the dominant process for particle growth. This is carried out at fast cooling of the vapour, during its mixing with oxygen. The particle size distribution functions are calculated, and the influence of the chemical monomer generation and the mixing on their behavior is investigated. Comparison of the calculated and the experimental mean particle size is made.List of symbols C _nl collision frequency function, cm³/s - d _m mean median diameter, nm - F _LN(d) integral form of the particle size distribution function,% - g(t) mixing function - k Boltzmann's constant - k ₁,k,k rate coefficients, cm³/s - k ₂,k ₃ rate coefficiens, cm⁶/s - m mass of the monomer, g - M number of groups - T absolute temperature, K - T ₀ temperature of the hot vapour, K - T _E temperature of SiO₂ condensation, K - t time, s - t _m mixing time, s - t _c colling time, s - z ₀ monomer concentration, cm^–3 - z _n ,z _l concentrations of particles in groups, cm^–3 - z _n total number concentration of particles (n=0, 1, M), cm^–3 - z _n /(z _n )(log d _n+1 –logd _n) differential form of particle size distribution function - w _i reaction rates (i=1, 2, 3), cm^–3/s - , cooling rates, K/s - coefficient of proportionality - _SiO conversion rate of SiO,% - coefficient determined from the cooling rate, s^–1 - mass density of the particles, g/cm³ - standard deviation The authors gratefully acknowledge Prof. L. S. Polak from the Institute of Petrol Chemical Synthesis, Russian Academy of Science, for helpful discussions.