Algebraic composition operators

The focus of this paper is on the following problem. Given a linear space F of complex-valued functions on a set X and a polynomial p(z), is there an algebraic composition operator on F whose characteristic polynomial equals p(z)? We show that the supply of all the polynomials p(z) for which the answer to this question is affirmative depends heavily on the structure of the space F.     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

Lower bounds for the discrepancy of triples of inversive congruential pseudorandom numbers with power of two modulus

This paper deals with the inversive congruential method with power of two modulusm for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that there exist parameters in the inversive congruential method such that the discrepancy of the corresponding point sets in the unit cube is of an order of magnitude at leastm ^–1/3. The method of proof relies on a detailed analysis of certain rational exponential sums.     

Gibt es nichttriviale absolut-normale Körpererweiterungen?

Ohne Zusammenfassung     

CuAl2Cl8. Darstellung und Kristallstruktur

CuAl₂Cl₈. Preparation and Crystal Structure. Crystals of CuAl₂Cl₈ have been prepared. Their remission spectrum agrees with that of gaseous CuAl₂Cl₈. The crystal structure (P2₁/c;a = 6.614, b = 7.376, c = 12.319 Å; β = 94.11°) shows a molecular lattice with Cu in square planar coordination, which is completed to a stretched octahedron (as in solid CuCl₂) by two Cl atoms from neighbour molecules. Al has tetrahedral coordination.     

Zur Katalysierten Verflüchtigung von rotem Phosphor und von Claudetit

The Catalysed Volatilization of Red Phosphorus and of Claudetite The catalysis of the volatilization of P_red (as P₄) by AlCl_3,g, and of the volatilization of claudetite (as As₄O₆) by I_2,g is observed by mass spectrometry.     

Der chemische Transport von Platin mit Chlor. Experimentell bearbeitet mit Marita Trenkel

The Chemical Transport of Platinum with Chlorine Experiments show that the chemical transport of platinum by means of chlorine within a temperature gradient at temperatures below ≈ 1000°K goes into the hot temperature region, but at higher temperatures in the reverse direction. From the thermodynamic discussion it can be seen, that the platinum content of the gas phase at low temperatures is governed by the exothermic formation of Pt₆Cl_12,g, and at higher temperatures by the endothermic formation of PtCl_3,g and PtCl_2,g. The platinum content of the gas phase passes a minimum at ≈ 1000°K, if P(Cl₂) = 3.5 atm. This result is in agreement with the observed inversion of the transport direction.     

Die Gasmolekeln Pd2Al2Cl10 und PdAlCl5 als Begleiter von PdAl2Cl8

Gas Molecules Pd₂Al₂Cl₁₀ and PdAlCl₅ as Accompanists of PdAl₂Cl₈ Mass spectrometric observations using a double cell showed that the reaction of gaseous Al₂Cl₆ with solid PdCl₂ besides the known gaseous complex PdAl₂Cl₈ gives PdAlCl₅ and the unexpected complex Pd₂Al₂Cl₁₀. For the equilibrium (with ΔCp? ?1 cal/K) ΔH°(298) = 7.5 kcal/Mol and ΔS°(298) = 5.3 ± 2 cl have been obtained.