The relationship between the structures of Cu(II) complexes and their chemical transformations

The structures of compounds M ₂ ^I M^II(SEO₄)₂ (M^I=K, Tl; M^II=Cu and Ni), were studied using IR, electronic and EPR spectra. The results indicate a hexacoordination of both central atoms, and a bridging function of selenato groups, the mode of their coordination varies with M^I and M^II. The compound Tl₂Cu(SeO₄)₂ was prepared also in the amorphous glassy form, although with partial decomposition. It is presumed that in the homogeneous smaragd-green material -Cu-O-Cu-, -Cu-OSeO₂-Cu- and -Cu-OSeO₃-Cu- bridges are present simultaneously. The course of the thermal decomposition of the studied compounds depends on the nature of the M^I and M^II cations. According to powder X-ray patterns, the decomposition products do not contain individual oxides. Nearly complete removal of selenium was observed in the decomposition of hydrated ammonium double selenates of Ni(II) and Cu(II).

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Zusammenfassung Mittels IR-, Elektronen- und EPR-Spektren wurden die Strukturen der Verbindungen M ₂ ^I M^II (SeO₄)₂ mit M^I=K und Tl sowie M^II=Cu and Ni bestimmt. Die Ergebnisse zeigen eine Hexakoordination beider Zentralatome und eine Brückenfunktion der Selenatgruppen, deren Koordination sich mit M^I und M^II ändert. Die Verbindung Tl₂Cu(SeO₄)₂ wurde, wenn auch unter geringen Zerfalles, auch in einer amorphen Glasform hergestellt. Es wird angenommen, daß in den Smaragdgrün-Stoffen gleichzeitig-Cu-O-Cu-, -Cu-OSeO₂-Cu- und -Cu-OSeO₃-Cu- Brücken vorkommen. Der Verlauf der thermischen Zersetzung der untersuchten Verbindungen hängt von der Art der M^I und M^II-Kationen ab. In Bezugnahme auf Röntgenpulverdiffraktionsaufnahmen enthalten die Zersetzungsprodukte keine getrennten Oxide. Beim Zerfall von hydratierten Ammoniumdoppelselenaten von Ni(II) und Cu(II) wurde eine fast vollständige Abgabe von Selen beobachtet.

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M ₂ ^I Mⁱⁱ(SeO₄)₂, ⁱ — , , ⁱⁱ , - , . , - ^{i ii}. Tl₂Cu(SeO₄)₂ , . , ----, --OSeO₂- -Cu-OSeO₃-u-. ^{i ii}. , . .

     

Zero-sum block designs and graph labelings

Proving a conjecture of Aigner and Triesch, we show that every graph G = (V,E) without isolated vertices and isolated edges admits an edge labeling ξ: E → {0,1}^m with binary vectors of length m = [log₂ n] + 1 such that the sums. CALLING STATEMENT : (taken modulo 2 componentwise) are mutually distinct, provided that n is sufficiently large. The proof combines probabilistic arguments with explicitly constructed Steiner systems. © 1995 John Wiley & Sons, Inc.     

Analog of heat equation for gaussian measure of a ball in Hilberrt space

If _a,T is a Gaussian measure on a Hilbert space with meana and covariance operatorT, andr is a fixed positive number, then the functiong(a,T)= _a,T {xr} satisfies the equation

Perfect graph decompositions

Upper and lower bounds are given for the minimum number of perfect (induced or partial) subgraphs covering or partitioning the vertex set or the edge set of a graph ofn vertices. Also, weighted versions of the problems are investigated.Research supported in part by the OTKA Research Fund of the Hungarian Academy of Sciences, Grant No. 1812.     

Ball-Polyhedra

We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it contains every short circular arc of radius at least one, connecting them. The other objects of study are bodies obtained as intersections of finitely many balls of the same radius, called ball-polyhedra. We find analogues of several results on convex polyhedral sets for ball-polyhedra.     

Random field forward interest rate models,market price of risk and their statistics

In this paper we consider discrete time forward interest rate models. In our approach, unlike in the classical Heath–Jarrow–Morton framework, the forward rate curves are driven by a random field. Hence we get a general interest rate structure. Our aim is to give an overview of our results in such a model on the following questions: no-arbitrage conditions, maximum likelihood estimation of the volatility, as well as the joint estimation of the parameters and the asymptotic behaviour of the estimators, relationship with continuous models. Finally we give discussion on the practical problems of the estimation and we show several numerical results on the statistics of such models. This research has been supported by the Hungarian Scientific Research Fund under Grants No. OTKA–F046061/2004 and OTKA–T048544/2005.     

Asymptotic Inference for Unit Roots in Spatial Triangular Autoregression

A spatial autoregressive process with two parameters is investigated both in the stable and in the unstable case. It is shown that the limiting distribution of the least squares estimator of these parameters is normal and the rate of convergence is n ^3/2 if one of the key parameters equals zero and n otherwise.     

Line-graphs of cubic graphs are normal

A graph is called normal if its vertex set can be covered by cliques Q₁,Q₂,…,Q_k and also by stable sets S₁,S₂,…,S_l, such that S_i∩Q_j≠∅ for every i,j. This notion is due to Körner, who introduced the class of normal graphs as an extension of the class of perfect graphs. Normality has also relevance in information theory. Here we prove, that the line graphs of cubic graphs are normal.