On Functions which are the Difference of two Bounded Convex Functions on (0, ∞)

The notion of HEWITT-STROMBERG dimension of separable metric spaces is introduced and some first results are presented. This dimension will be compared with the HAUSDORFF dimension and the metric dimension of separable metric spaces.     

On the Spectrum of the Reflection Operator on Conical Surfaces

We study the mapping properties of the reflection operator on a conical surface. This allows us to derive regularity results for the solution of the radiosity equation on conical surfaces in a scale of weighted Sobolev spaces. To motivate the calculations we first study the operator on a cylinder. Here we estimate the asymptotic behavior of the spectrum of the reflection operator by partial integration. This method works also for the conical case, but first we have to find a simple representation for some hypergeometric functions.     

A branch and bound algorithm for bound constrained optimization problems without derivatives

In this paper, we give a new branch and bound algorithm for the global optimization problem with bound constraints. The algorithm is based on the use of inclusion functions. The bounds calculated for the global minimum value are proved to be correct, all rounding errors are rigorously estimated. Our scheme attempts to exclude most uninteresting parts of the search domain and concentrates on its promising subsets. This is done as fast as possible (by involving local descent methods), and uses little information as possible (no derivatives are required). Numerical results for many well-known problems as well as some comparisons with other methods are given.     

Isotope effects on the enzymatic and nonenzymatic reactions of chorismate

The important biosynthetic intermediate chorismate reacts thermally by two competitive pathways, one leading to 4-hydroxybenzoate via elimination of the enolpyruvyl side chain, and the other to prephenate by a facile Claisen rearrangement. Measurements with isotopically labeled chorismate derivatives indicate that both are concerted sigmatropic processes, controlled by the orientation of the enolpyruvyl group. In the elimination reaction of [4-2H]chorismate, roughly 60% of the label was found in pyruvate after 3 h at 60 degrees C. Moreover, a 1.846 +/- 0.057 2H isotope effect for the transferred hydrogen atom and a 1.0374 +/- 0.0005 18O isotope effect for the ether oxygen show that the transition state for this process is highly asymmetric, with hydrogen atom transfer from C4 to C9 significantly less advanced than C-O bond cleavage. In the competing Claisen rearrangement, a very large 18O isotope effect at the bond-breaking position (1.0482 +/- 0.0005) and a smaller 13C isotope effect at the bond-making position (1.0118 +/- 0.0004) were determined. Isotope effects of similar magnitude characterized the transformations catalyzed by evolutionarily unrelated chorismate mutases from Escherichia coli and Bacillus subtilis. The enzymatic reactions, like their solution counterpart, are thus concerted [3,3]-sigmatropic processes in which C-C bond formation lags behind C-O bond cleavage. However, as substantially larger 18O and smaller 13C isotope effects were observed for a mutant enzyme in which chemistry is fully rate determining, the ionic active site may favor a somewhat more polarized transition state than that seen in solution.     

Ultrafast dynamics of isolated model photoactive yellow protein chromophores: "Chemical perturbation theory" in the laboratory

Pump-probe and pump-dump probe experiments have been performed on several isolated model chromophores of the photoactive yellow protein (PYP). The observed transient absorption spectra are discussed in terms of the spectral signatures ascribed to solvation, excited-state twisting, and vibrational relaxation. It is observed that the protonation state has a profound effect on the excited-state lifetime of p-coumaric acid. Pigments with ester groups on the coumaryl tail end and charged phenolic moieties show dynamics that are significantly different from those of other pigments. Here, an unrelaxed ground-state intermediate could be observed in pump-probe signals. A similar intermediate could be identified in the sinapinic acid and in isomerization-locked chromophores by means of pump-dump probe spectroscopy; however, in these compounds it is less pronounced and could be due to ground-state solvation and/or vibrational relaxation. Because of strong protonation-state dependencies and the effect of electron donor groups, it is argued that charge redistribution upon excitation determines the twisting reaction pathway, possibly through interaction with the environment. It is suggested that the same pathway may be responsible for the initiation of the photocycle in native PYP.     

X-ray reflectivity investigations of glass surfaces produced by float and draw techniques

Surfaces of soda-lime glass and borosilicate glass have been investigated by grazing incidence X-ray reflectivity (GIXR). Characteristic differences are obtained in dependence on the fabrication procedure, the composition and the cleaning procedure. Strong variation is recorded between the two soda-lime float glass surfaces while minor differences are analysed between the top and bottom side of borosilicate float glass. This is attributed to the reduced amount of tin diffused into the bottom side of the borosilicate glass surface. Different cleaning procedures generate characteristic changes on the glass surfaces which can be verified by GIXR. The results indicate that borosilicate float glass combines the merits of the good surface quality of float glass with the high chemical resistivity of borosilicate glass.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

Pilot study of capillary electrophoresis coupled to mass spectrometry as a tool to define potential prostate cancer biomarkers in urine

We describe the use of capillary electrophoresis (CE) coupled with mass spectrometry (MS) to identify single polypeptides and patterns of polypeptides specific for prostate cancer (CaP) in human urine. Using improved sample preparation methods that enable enhanced comparability between different samples, we examined samples from 47 patients who underwent prostate biopsy. Of this group, 21 patients had benign pathology and 26 with CaP, and these were used to define potential biomarkers, which allow discrimination between these two states. In addition, CE-MS data from these 47 urine samples were compared to that of 41 young men (control) without known or suspected clinical CaP to further confirm the polypeptides indicative for CaP. Upon crossvalidation of the same samples, several polypeptides were selected that enabled correct classification of the CaP patients with 92% sensitivity and 96% specificity. We then examined an additional 474 samples from patients with renal disease enrolled in other studies and found that 14 (3%) had polypeptides suggestive of CaP possibly indicating that they harbor clinical CaP. In conclusion, this early pilot study suggests that CE-MS of urine warrants further investigation as a tool that can identify putative biomarkers for CaP.