Über trilinear verwandte Felder als Raumbilder

Monatshefte für Mathematik -     

Berichtigung zu dem Aufsatze “Ueber Systeme höherer complexer Zahlen”

Ohne Zusammenfassung     

Bose-Einstein condensate coupled to a nanomechanical resonator on an atom chip

We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.     

Development and validation of a rapid LC-ESI-MS/MS method for quantification of fluoxetine and its application to MS binding assays

In the present study, a rapid and sensitive LC-ESI-MS/MS method for quantification of (S)-fluoxetine as a native marker in mass spectrometry (MS) binding assays addressing the human serotonin transporter (hSERT) was developed and validated. The concept of MS binding assays based on mass spectrometric quantification of a nonlabeled marker recently introduced by us represents a promising alternative to conventional radioligand binding without the drawbacks inherently connected with radioisotope labeling. For high-performance liquid chromatography (HPLC), a 20 × 2-mm RP-18 column with a mobile phase composed of acetonitrile and ammonium bicarbonate buffer (5 mmol L⁻¹, pH 9.5) at a ratio of 80:20 (v/v) and a flow rate of 800 μL min⁻¹ in an isocratic mode were used, resulting in a chromatographic cycle time of 60 s. Employing [²H₅]fluoxetine as internal standard enabled ESI-MS/MS quantification of (S)-fluoxetine between 3 nmol L⁻¹ and 50 pmol L⁻¹ (LLOQ) in matrix obtained from binding experiments without the need of any sample preparation. Validation of the method showed that linearity, intra-, and inter-batch accuracy as well as precision meet the requirements of the FDA guidance for bioanalytical method validation. Considering sensitivity and speed, the established method is clearly superior to those published for biological matrices so far. Furthermore, the method was transferred to other RP-18 columns of different lengths and respective validation experiments demonstrated its versatility and chromatographic robustness. Finally, the newly developed method was successfully applied to MS binding assays for hSERT. The affinity determined for (S)-fluoxetine in saturation experiments was in good agreement with literature data obtained in respective radioligand binding assays.     

Nickel hydrides supported by a non-innocent diphosphine arene pincer: mechanistic studies of nickel-arene H-migration and partial arene hydrogenation

Nickel hydrides supported by a terphenyl diphosphine were synthesized and found to undergo nickel-to-arene H-transfers. Some of the resulting complexes also undergo the reverse (C-to-Ni) H-migration, indicating the potential for storing H-equivalents in this type of pincer ligand. NMR spectroscopy, single crystal X-ray diffraction, and isotopic labeling studies investigating the mechanism of these processes are discussed.     

Series representations for densities functions of a family of distributions—Application to sums of independent random variables

Series representations for several density functions are obtained as mixtures of generalized gamma distributions with discrete mass probability weights, by using the exponential expansion and the binomial theorem. Based on these results, approximations based on mixtures of generalized gamma distributions are proposed to approximate the distribution of the sum of independent random variables, which may not be identically distributed. The applicability of the proposed approximations are illustrated for the sum of independent Rayleigh random variables, the sum of independent gamma random variables, and the sum of independent Weibull random variables. Numerical studies are presented to assess the precision of these approximations.