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.     

Thick grids with circular apertures: A comparison of theoretical and experimental performance

In this paper a comparison between a rigorous electromagnetic model for transmission through a hexagonal array of circular waveguides in a series of thick, metallic screens and experimental measurements in the far infrared is made. It is found that there is excellent agreement between theory and experiment when the frequency is below that where any diffracted orders propagate. The agreement is still very good above this frequency. Below a frequency approximately equal to the cut-off frequency of the circular waveguides little power is transmitted. As the thickness of the screen is increased, this decrease in transmission becomes more abrupt. Also, for thick screens, resonances appear in the transmission spectrum which are analogous to those which appear in the spectra of two grids separated by a distance comparable to the wavelength of the radiation being used.     

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.     

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.     

Mesoscopic chiral reshaping of the Ag(110) surface induced by the organic molecule PVBA

We report scanning tunneling microscopy observations on the restructuring of a Ag(110) surface induced by the molecule 4-[trans-2-(pyrid-4-yl-vinyl)]benzoic acid (PVBA). Our data reveal that the surface undergoes a mesoscopic step faceting following exposure to submonolayer coverages and thermal activation. A sawtooth arrangement evolves implying long-range mass transport of substrate atoms and forming a regular arrangement of kink sites. Its formation is associated with the molecules' functional headgroups forming carboxylates with [100] Ag microfacets at step edges, and eventually operating to reshape the surface morphology. Interestingly, the resulting microfacets act as chiral templates for the growth of supramolecular PVBA structures. Theoretical modeling based on ab initio results indicates that chiral recognition processes discriminating between the two enantiomers of adsorbed PVBA molecules occur in this process.     

Platinum(II) 1,10-phenanthroline complexes of acetylides containing redox-active groups

The new diimine ligand 3,8-di-n-pentyl-4,7-di(phenylethynyl)-1,10-phenanthroline (1) was used for the synthesis of a range of Pt(II) complexes, viz.[Pt(1)Cl2], [Pt(1)(C triple bond C-Ph)2], [Pt(1)(C triple bond C-Fc)2] and [Pt(1)(C triple bond C-p-C6H4-C triple bond C-Fc)2](Fc = ferrocenyl). Crystal structure analyses were performed for [Pt(1)Cl2] and [Pt(1)(C triple bond C-Ph)2] and revealed that the di(acetylide)pi-tweezer of the latter binds a molecule of chloroform through C-H...pi hydrogen bonds. The redox and optical properties of 1 and its complexes were investigated by (spectro-)electrochemistry, UV-Vis and luminescence spectroscopy, and an energy level diagram was derived for [Pt(1)(C triple bond C-Fc)2] and related compounds on the basis of the data collected. The ferrocenyl-substituted Pt(II) complexes are donor-sensitiser assemblies. Intramolecular quenching of the photoexcited Pt(II) diimine unit leads to very short luminescence lifetimes for [Pt(1)(C triple bond C-p-C(6)H(4)-C triple bond C-Fc)2](2 ns) and [Pt(1)(C triple bond C-Fc)2](0.3 ns), as opposed to [Pt(1)(C triple bond C-Ph)2](0.7 micros). Excimer formation has been observed for [Pt(1)(C triple bond C-Ph)(2)] at room temperature in dichloromethane and at low temperatures in frozen glassy dichloromethane and 2-methyltetrahydrofuran solution, but not in the solid state.     

Platinum‐Promoted Ga/Al2O3 as Highly Active,Selective, and Stable Catalyst for the Dehydrogenation of Propane

A novel catalyst material for the selective dehydrogenation of propane is presented. The catalyst consists of 1000 ppm Pt, 3 wt % Ga, and 0.25 wt % K supported on alumina. We observed a synergy between Ga and Pt, resulting in a highly active and stable catalyst. Additionally, we propose a bifunctional active phase, in which coordinately unsaturated Ga³⁺ species are the active species and where Pt functions as a promoter.     

Highly Efficient Trityl-Nitroxide Biradicals for Biomolecular High-Field Dynamic Nuclear Polarization

Dynamic nuclear polarization (DNP) is a powerful method to enhance the sensitivity of solid-state magnetic nuclear resonance (ssNMR) spectroscopy. However, its biomolecular applications at high magnetic fields (preferably>14 T) have so far been limited by the intrinsically low efficiency of polarizing agents and sample preparation aspects. Herein, we report a new class of trityl-nitroxide biradicals, dubbed SNAPols that combine high DNP efficiency with greatly enhanced hydrophilicity. SNAPol-1, the best compound in the series, shows DNP enhancement factors at 18.8 T of more than 100 in small molecules and globular proteins and also exhibits strong DNP enhancements in membrane proteins and cellular preparations. By integrating optimal sensitivity and high resolution, we expect widespread applications of this new polarizing agent in high-field DNP/ssNMR spectroscopy, especially for complex biomolecules.     

Phase coherent photorefractivity in ZnSe single quantum wells

We observe an efficient phase coherent photorefractive effect in ZnSe single quantum wells for ultrashort light pulses resonant to the excitonic transition. The effect is attributed to the formation of an electron grating in the quantum well induced by the interference of coherent excitons that preserve phase and polarization of the incident light fields. All characteristic features of the diffracted signal are explained and reproduced by numerical calculations that are based on the optical Bloch equations for a three-level system.