Zur Axiomatik der Geometrie. I

Ohne ZusammenfassungBis auf Nr. 8 und 9 im wesentlichen, mit Ausnahme der Anmerkungen, vorgetragen auf der Kissinger Mathematikertagung, September 1927, vgl. Jahresber. d. Deutsch. Mathem. Vergg.37 (1928), 2. Abt., S. 3 Auf Anregung von Herrn P. Bernays hin oder veranlaßt durch die neuesten Arbeiten der Herren P. Finsler und B. Baer sind zur ursprünglichen Fassung der vorliegenden Arbeit aus dem September 1927 Nr. 8 und 9, sowie die Anmerkungen²³),²⁴),²⁶) hinzugekommen.     

Local Entropy Conditions in Transonic Potential Flow Problems

The transonic potential flow problem is handled as a variational problem over a closed convex set which is given by a bound for the gas velocity and by a local entropy condition. It can be shown that the minimum problem has a solution though the functional need not be convex and the given set is not compact. Furthermore, the convergence of an approximation method (KATCHANOV'S method) for the solution to the corresponding variational inequality is proved.     

Preparation of micro- and nanopatterns of polymer chains grafted onto flexible polymer substrates

In this work a simple novel method for preparing micro- and nanoscale patterns of polymer chains grafted onto flexible polymer substrates is described. A combination of the two techniques of radiation grafting and "grafting-from" has been made. This combination makes it possible to prepare grafted structures having micro- or nanoscale lateral dimensions that are determined by the electron beam or X-ray irradiation patterns used. The height of the grafted features can be controlled by the irradiation dose or such grafting reaction conditions as time, temperature, or monomer concentration. Our first results for nanopatterned samples demonstrate resolution comparable to those of other polymer-based lithography processes.     

Rhodium and palladium β-diketonate determination with on-line supercritical fluid extraction-high performance liquid chromatography via solid phase extraction

 An on-line system of supercritical fluid extraction (SFE) and high performance liquid chromatography (HPLC) via solid phase extraction (SPE) is described for the determination of palladium and rhodium 2,2,6,6-tetramethyl-3,5-heptanedione-(thd) as well as rhodium-acetylacetonate-(acac) and benzylacetonate-(bzac) chelates. The chelates were extracted with supercritical CO₂ from sand and humic acid, concentrated on SPE cartridges and analysed with HPLC. Two cartridge materials were tested and compared to off-line trapping. The percentage of the breakthrough and cartridge retained material were measured in liquid dichloromethane. The SFE conditions could be optimized to separate metal chelates during the extraction. The supercritical fluid (SF) behaviour of different ligands on rhodium were investigated. Received: 19 July 1996/Revised: 11 December 1996/Accepted: 14 December 1996     

Characteristic behavior of macro-, semimicro- and microelectrodes in voltammetric and chronoamperometric measurements

The advantages of microelectrodes such as the improvement of signal-to-noise ratio, the ability to perform electrochemical measurements in high resistive solutions and small RC-time constants give the possibility of an extended use for voltammetric and chronoamperometric techniques in analytical chemistry. In this comparative study, the microelectrode properties of three selected electrodes were examined. The characterization of a RAM-microarray electrode, an epoxy-impregnated carbon electrode and a conventional glassy carbon macroelectrode was performed by cyclic voltammetry at different scan rates, by DP-voltammetric measurements using different concentrations of supporting electrolyte and by transient measurements. It could be shown, that in comparison to the microarray electrode and to the glassy carbon macroelectrode, respectively, the results obtained by using the epoxy-impregnated carbon electrode are caused by its semimicroelectrode character.     

Ultrahigh field MAS NMR dipolar correlation spectroscopy of the histidine residues in light-harvesting complex II from photosynthetic bacteria reveals partial internal charge transfer in the B850/His complex.

Low-temperature 15N and 13C CP/MAS (cross-polarization/magic angle spinning) NMR has been used to analyze BChl-histidine interactions and the electronic structure of histidine residues in the light-harvesting complex II (LH2) of Rhodopseudomonas acidophila. The histidines were selectively labeled at both or one of the two nitrogen sites of the imidazole ring. The resonances of histidine nitrogens that are interacting with B850 BChl a have been assigned. Specific 15N labeling confirmed that it is the tau-nitrogen of histidines which is ligated to Mg2+ of B850 BChl molecules (beta-His30, alpha-His31). The pi-nitrogens of these Mg2+-bound histidines were found to be protonated and may be involved in hydrogen bond interactions. Comparison of the 2-D MAS NMR homonuclear (13C-13C) dipolar correlation spectrum of [13C6,15N3]-histidines in the LH2 complex with model systems in the solid state reveals two different classes of electronic structures from the histidines in the LH2. In terms of the 13C isotropic shifts, one corresponds to the neutral form of histidine and the other resembles a positively charged histidine species. 15N-13C double-CP/MAS NMR data provide evidence that the electronic structure of the histidines in the neutral BChl a/His complexes resembles the positive charge character form. While the Mg...15N isotropic shift confirms a partial positive charge transfer, its anisotropy is essentially of the lone pair type. This provides evidence that the hybridization structure corresponding to the neutral form of the imidazole is capable of "buffering" a significant amount of positive charge.     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).     

Synthesis and absolute configuration of clemastine and its isomers (author's transl)]

Synthesis and Absolute Configuration of Clemastine and its Isomers. Condensation of 4-chloro-α-methylbenzhydrylalkohol ( 1 ) with 2-(2-chloroethyl)-1-methylpyrrolidine ( 2 ) gave an isomeric mixture of 2-[2-(p-chloro-α-methyl-=-phenylbenzyloxy)ethyl]-1-methylpyrrolidine ( 3 ) and 4-(p-chloro-=-phenylbenzyloxy)-1-methyl-hexahydroazepin ( 4 ). The separation of the four possible optically active isomers of 3 is described and their absolute configuration established by degradation to (R)- and (S)-1-methyl-2-pyrrolidineethanol ( 6 ), respectively, and by an X-ray cristallographic analysis of the quarternary methiodide of the isomer 3-A . Clemastine (3-A) is (+)-(2R)-2-[2-((αR)-(p-chloro-α-methyl-α-phenylbenzyloxy)ethyl)]-1-methylpyrrolidine.     

Structural constraints from proton-mediated rare-spin correlation spectroscopy in rotating solids

A novel solid-state NMR concept is introduced that allows for the detection of through-space proton-proton contacts in high spectral resolution. The proposed method not only can be utilized to infer sequential assignments and backbone or side chain conformation in solid-phase polypeptides, but it also provides information about the three-dimensional arrangement of the molecule of interest. As a result, the molecular structure can be studied without additional restrictions regarding sample labeling or magic angle spinning rates.