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.     

EXCITED STATE BEHAVIOR OF PHYTOCHROME Pr

The primary excited state processes of phytochrome, the plant chromoprotein responsible for most photomorphogenetic responses, are investigated by picosecond intensity-dependent transmission measurements. At sufficient high excitation intensity (starting at photon flux densities of about 1′10²⁵ cm^?2 s^?l) a moderate bleaching of the absorption is observed. For the quantitative analysis of the experimental data a rate equation system approach for the energy levels responsible for the ultrafast transformation P_r→ lumi-R and the photon transport through the sample was utilized. The following was found for the excited state parameters of the phytochrome P_r: (1) an excited state absorption of the same order of magnitude as the ground state absorption (cross section: S?_exc= 4′10^?16 cm^?2 at 650 nm), (2) a fast relaxation of the higher excited singlet state on the femtosecond time scale.     

Identification of Peptide tumor markers in a tumor graft model in immunodeficient mice

The medical demand for useful biomarkers is large and still increasing. This is especially true for cancer, because for this disease adequate diagnostic markers with high specificity and sensitivity are still lacking. Despite advances in imaging technologies for early detection of cancer, peptidomic multiplex techniques evolved in recent years will provide new opportunities for detection of low molecular weight (LMW) proteome biomarker (peptides) by mass spectrometry. Improvements in peptidomics research were made based on separation of peptides and/or proteins by their physico-chemical properties in combination with mass spectrometric detection, respectively identification, and sophisticated bioinformatic tools for data analysis. To evaluate the potential of serological tumor marker detection by differential peptide display (DPD) we analyzed plasma samples from a tumor graft model. After subcutaneous injection of HCT-116 cells in immunodeficient mice and their growth to a palpable tumor, plasma samples were analyzed by DPD. The comparison of obtained mass spectrometric data allows discovery of tumor specific peptides which fit well into the biological context of cancer pathogenesis and show a strong correlation to tumor growth. The identified peptides indicate events associated with hyper-proliferation and dedifferentiation of cells from an epithelial origin, which are typical characteristics of human carcinomas. We conclude that these findings are a "proof of principle" to detect differentially expressed, tumor-related peptides in plasma of tumor-bearing mice.     

Characterizing Automorphism Groups of Ordered Abelian Groups

A proof is given of the following theorem, which characterizesfull automorphism groups of ordered abelian groups: a groupH is the automorphism group of some ordered abelian group ifand only if H is right-orderable. 2000 Mathematics Subject Classification20K15, 20K20, 20F60, 20K30 (primary); 03E05 (secondary).     

Isomerization and fragmentation of methylfuran ions and pyran ions in the gas phase

The mutual interconversion of the molecular ions [C₅H₆O]⁺ of 2-methylfuran (1), 3-methylfuran (2) and 4H-pyran (3) before fragmentation to [C₅H₅O]⁺ ions has been studied by collisional activation spectrometry, by deuterium labelling, by the kinetic energy release during the fragmentation, by appearance energles and by a MNDO calculation of the minimum energy reaction path. The electron impact and collisional activation mass spectra show clearly that the molecular ions of 1–3 do not equilibrate prior to fragmentation, but that mostly pyrylium ions [C₅H₅O]⁺ arise by the loss of a H atom. This implies an irreversible isomerization of methylfuran ions 1 and 2 into pyran ions before fragmentation, in contrast to the isomerization of the related systems toluene ions/cycloheptatriene ions. Complete H/D scrambling is observed in deuterated methylfuran ions prior to the H/D loss that is associated with an iostope effect k_H/k_D = 1.67–2.16 for metastable ions. In contrast, no H/D scrambling has been observed in deuterated 4H-pyran ions. However, the loss of a H atom from all metastable [C₅H₅O]⁺ ions gives rise to a flat-topped peak in the mass-analysed ion kinetic energy spectrum and a kinetic energy release (T₅₀) of 26 ± 1.5 kJ mol^?1. The MNDO calculation of the minimum energy reaction path reveals that methylfuran ions 1 and 2 favour a rearrangement into pyran ions before fragmentation into furfuryl ions, but that the energy barrier of the first rearrangement step is at least of the same height as the barrier for the dissociation of pyran ions into pyrylium ions. This agrees with the experimental results.