Strukturen caesiumhaltiger Fluoride. VII. Cs6Ni5F16 – eine neue Verbindung im System CsF/NiF2 und ihre Kristallstruktur

Structures of Caesium-containing Fluorides. VII. Cs₆Ni₅F₁₆ – a New Compound in the System CsF/NiF₂ and its Crystal Structure Single crystals of a more caesium-containing phase of composition Cs₆Ni₅F₁₆, forming in the course of solid state CsNiF₃ preparation, could be isolated and their structure determined: a = 618.4(1), b = 1. 455.5(2), c = 2145.1(2) pm, space group Cmca, Z = 4, R = 0.030 (1936 independent reflections). The structure contains chains of five face-sharing octahedra, which are connected at their ends via corners to form a zig-zag layer. The Ni? Ni distances within the chains are 264.1 and 270.2 pm, the average Ni? F distance is 202.0 pm. The caesium atoms exhibit 10-, 11-, and 12-coordination. The structural relations to 2L? CsNiF₃ and Cs₄Ni₃F₁₀ are discussed.     

Interplay between Auger and ionization processes in nanocrystal quantum dots

We study the interplay between Auger effects and ionization processes in the limit of strong electronic confinement in core/shell CdSe/ZnS semiconductor nanocrystal quantum dots. Spectrally resolved fluorescence decay measurements reveal a monotonic increase of the photoluminescence decay rate on excitation density. Our results suggest that Auger recombination accelerates ionization processes that lead to the occupation of dark, nonemissive nanocrystal states. A model is proposed in the quantized Auger regime describing these experimental observations and providing an estimate of the Auger assisted ionization rates.     

Congruence lattices ofp-algebras

T. Kartriák proved the following theorem:Every finite distributive lattice is the congruence lattice of a finite p-algebra. We provide a short proof, and a generalization, of this result.Presented by J. Berman.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.     

Graph products of groups and group spaces

An application of constructions from so-called Bass-Serre theory to group spaces in noncommutative geometry is discussed motivated by the question how to make visible the interplay of different structures coming together in the notion of a group space. A compact summary of basic notions and constructions from Bass-Serre theory up to the structure theorem is developed; it should serve as a brief guideline for further applications. Concluding prospects indicate a way for generalizing the methods from a categorical point of view.Dedicated to Professor Johannes André on the occasion of his 70th birthday     

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     

The Polynomials Associated with a Julia Set

We prove that, with two exceptions, the set of polynomials withJulia set J has the form {pⁿ:nN,} where p is one of these polynomialsand is the symmetry group of J. The exceptions occur when Jis a circle or a straight line segment.     

On isotone functions with the Substitution Property in distributive lattices

A universal algebra isaffine complete if all functions satisfying the Substitution Property are polynomials (composed of the basic operations and the elements of the algebra). In 1962, the first author proved that a bounded distributive lattice is affine complete if and only if it does not contain a proper Boolean interval. Recently, M. Ploica generalized this result to arbitrary distributive lattices.In this paper, we introduce a class of functions on a latticeL, we call themID-polynomials, that derive from polynomials on the ideal lattice (resp., dual ideal lattice) ofL; they are isotone functions and satisfy the Substitution Property. We prove that for a distributive latticeL, all unary functions with the Substitution Property are ID-polynomials if and only ifL contains no proper Boolean interval.The research of the first author was supported by the NSERC of Canada. The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.