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Gerd Herzog 《Numerical Functional Analysis & Optimization》2017,38(8):1008-1013
It is known that vector translations are contractive with respect to Thompson’s part metric. Here, we give a simple proof, based on a representation of Thompson’s metric through positive functionals. Moreover, we use contractivity of translations to prove a fixed point result for mappings that are Lipschitz continuous with respect to Thompson’s metric with Lipschitz constant r>1. The case r = 1 for order preserving or order reversing mappings has been recently studied by Lawson and Lim. We apply our result to a nonlinear boundary value problem. 相似文献
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Natural Abundance 15N NMR by Dynamic Nuclear Polarization: Fast Analysis of Binding Sites of a Novel Amine‐Carboxyl‐Linked Immobilized Dirhodium Catalyst 下载免费PDF全文
Torsten Gutmann Jiquan Liu Niels Rothermel Yeping Xu Eva Jaumann Mayke Werner Hergen Breitzke Snorri T. Sigurdsson Gerd Buntkowsky 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(9):3798-3805
A novel heterogeneous dirhodium catalyst has been synthesized. This stable catalyst is constructed from dirhodium acetate dimer (Rh2(OAc)4) units, which are covalently linked to amine‐ and carboxyl‐bifunctionalized mesoporous silica (SBA‐15?NH2?COOH). It shows good efficiency in catalyzing the cyclopropanation reaction of styrene and ethyl diazoacetate (EDA) forming cis‐ and trans‐1‐ethoxycarbonyl‐2‐phenylcyclopropane. To characterize the structure of this catalyst and to confirm the successful immobilization, heteronuclear solid‐state NMR experiments have been performed. The high application potential of dynamic nuclear polarization (DNP) NMR for the analysis of binding sites in this novel catalyst is demonstrated. Signal‐enhanced 13C CP MAS and 15N CP MAS techniques have been employed to detect different carboxyl and amine binding sites in natural abundance on a fast time scale. The interpretation of the experimental chemical shift values for different binding sites has been corroborated by quantum chemical calculations on dirhodium model complexes. 相似文献
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Isabel Rauscher Benjamin Bender Gerd Grözinger Oliver Luz Rolf Pohmann Michael Erb Fritz Schick Petros Martirosian 《Magnetic resonance imaging》2014
Objective
The purpose of this study was to implement clinically feasible imaging techniques for determination of T1, T1ρ, and T2 values of the ulnocarpal disc and to assess those values in a cohort of asymptomatic subjects at 3 tesla. Resulting values were compared between different age groups, since former histological findings of the ulnocarpal disc indicated frequent early degenerative changes of this tissue starting in the third decade of life, even in asymptomatic subjects.Materials and methods
Twenty-seven healthy subjects were included in this study. T1 measurements were performed using 3D spoiled gradient-echo (GRE) sequence with variable flip angle. A series of T1ρ and T2-weighted images was acquired by a 3D GRE sequence after suitable magnetization preparation. T1,T1ρ, and T2 maps of the ulnocarpal disc were calculated pixel-wise. Representative mean values from extended regions were analysed.Results
Mean T1 values of the ulnocarpal disc ranged from 722 ms in a 39 year-old subject to 1264 ms in a 65 year-old subject, T1ρ ranged from 9.2 ms (26 year-old subject) to 25.9 ms (65 year-old subject). Calculated T2 values showed a large range from 4.1 ms to 22.3 ms. T1ρ and T1 values tended to increase with age (p < 0.05), whereas T2 did not.Conclusions
MR relaxometry of the ulnocarpal disc is feasible, and T1,T1ρ, and T2 values show modest variance in asymptomatic subjects. The potential of relaxation mapping to reveal relevant structural changes in patients has to be investigated in further studies. 相似文献1000.
Martin Fischer Marianne Bader Robert Maiwald Andrea Golla Markus Sondermann Gerd Leuchs 《Applied physics. B, Lasers and optics》2014,117(3):797-801
We report on the demonstration of a light-matter interface coupling light to a single \(^{174}\hbox {Yb}^+\) ion in free space. The interface is realized through a parabolic mirror partially surrounding the ion. It transforms a Laguerre–Gaussian beam into a linear dipole wave converging at the mirror’s focus. By measuring the non-linear response of the atomic transition, we deduce the power required for reaching an upper-level population of \(1/4\) to be \(692\pm 20\,\hbox {pW}\) at half linewidth detuning from the atomic resonance. Performing this measurement while scanning the ion through the focus provides a map of the focal intensity distribution. From the measured power, we infer a coupling efficiency of \(7.2\pm 0.2\,\%\) on the linear dipole transition when illuminating from half solid angle, being among the best coupling efficiencies reported for a single atom in free space. 相似文献