Austauschreaktionen an komplexgebundenen liganden von elementen der IV. Hauptgruppe : III. Darstellung von halogen-, pseudohalogen- und hydridokomplexen des typs π-C5H5Fe(CO)2SiX3

The complexes CpFe(CO)₂SiBr₃, CpFe(CO)₂SiI₃, CpFe(CO)₂SiBr₂(OMe), and CpFe(CO)₂SiI(NH-cyclo-C₆H₁₁)₂ are prepared by the reaction of CpFe(CO)₂SiR₃ (R = OMe, NH-cyclo-C₆H₁₁) with HBr, HI and CH₃I. Treating CpFe(CO)₂SiCl₃ with a large excess of NaN₃, KOCN or KSCN yields the first tri-pseudohalogensilyl—transition-metal-complexes. The compounds are characterized by IR and mass spectra. A new method of preparation of the already known complex CpFe(CO)₂SiH₃ is described starting from CpFe(CO)₂SiCl₃ and LiAlH₄.     

Isomerization and fragmentation of methyl benzofuran ions and chromene ions in the gas phase

The rearrangement of the molecular ions of the isomeric 2- and 3-methyl benzofurans (1 and 2), 2H-chromene (3) and 4H-chromene (4) has been studied as a further example of the isomerization of oxygen-heteroaromatic radical cations via a ring expansion/ring contraction mechanism well documented for molecular ions of alkyl benzenes. The ions 1⁺˙?4⁺˙ fragment mainly by H loss into identical chromylium ions a. The process exhibits consistently a large kinetic energy release and an isotope effect k_H/k_D, which arise from a rate-determining energy barrier of the last dissociation step. Differences of the kinetic energy releases, the isotope effects and the appearance energies of the methyl benzofuran ions and the chromene ions indicate a large energy barrier also for the initial hydrogen migration during the rearrangement of the methyl benzofuran ions. This is substantiated by an MNDO calculation of the minimum energy reaction path. In contrast to the behaviour of alkyl benzene ions, a unidirectional isomerization of the methyl benzofuran ions by ring expansion takes place but no mutual interconversion of the molecular ions of methyl benzofurans and chromenes.     

On the Homeomorphism Groups of Cantor's Discontinuum and the Spaces of Rational and Irrational Numbers

The paper shows that the homeomorphism groups of, respectively,Cantor's discontinuum, the rationals and the irrationals haveuncountable cofinality. It is well known that the homeomorphismgroup of Cantor's discontinuum is isomorphic to the automorphismgroup Aut B of the countable, atomless boolean algebra B. Soalso Aut B has uncountable cofinality, which answers a questionposed earlier by the first author and H. D. Macpherson. Thecofinality of a group G is the cardinality of the length ofa shortest chain of proper subgroups terminating at G. 2000Mathematics Subject Classification 20B22, 20E15.     

Nonparametric Statistical Methods and the Pricing of Derivative Securities

In this review paper we summarise several nonparametric methods recently applied to the pricing of financial options. After a short introduction to martingale-based option pricing theory, we focus on two possible fields of application for nonparametric methods: the estimation of risk-neutral probabilities and the estimation of the dynamics of the underlying instruments in order to construct an internally consistent model.     

Decimals and almost–periodicity

We give conditions on sequences of real numbers so that their leading digit in the decimal-representation appears in an almost-periodic way. Examples are given by solutions of linear recurrences, such as the Fibonacci-sequence. Received: 8 August 2005