Die Klassengruppen quadratischer und kubischer Zahlkörper und die Selmergruppen gewisser elliptischer Kurven

For k∈?\0 we define the elliptic curve A_k, by the equation: Y²=X³+k. Let C(k) be the class group of \(K_o = Q(\sqrt[6]{k})\) . If k is a square we find a close connection between the elements of order 2 of the Selmer group of A_k and C(k); there is a corresponding connection between the elements of order 3 if k is a cube and satisfies some additional conditions. The main tool to prove the statements is the global and local Galois cohomology of elliptic curves; it seems remarkable that nearly no “explicit” number theory has to be used.     

STUDIEN ZUM VORGANG DER WASSERSTOFFÜBERTRAGUNG 511 RANEY-NICKEL ALS REAGENS ZUR HYDRIERENDEN ABSPALTUNG DES CHALKOGENATOMS AUS SCHWEFEL-, SELEN- UND TELLUR-VERBINDUNGEN

Abstract

Thioäther, Sulfoxide, Sulfone, organische Selenide und Telluride (R – Y – R': R, R', = Alkyl, Aryl, Y=S, SO, SO₂, Se, Te) werden an der Grenzfläche von Raney-Nickel hydrogenolysiert. Als Spaltprodukte entstehen die Verbindungen RH und R'H sowie eine Grenzflächenverbindung (Raney-Nickel-Y) (Y=S, Se, Te; S auch aus Sulfoxiden und Sulfonen. Letztere entbinden ebenfalls mit Mineralsäuren YH₂).

Die Größe und ‘Struktur’ der Oberfläche des Raney-Nickels entscheidet über die Hydrogenolysekapazität. Bei einer technischen Raney-Nickel-Probe liegt bei Diphenylsulfid die Sättigungsausbeute an Benzol bei 1,1 mmol/g Raney-Nickel. Die Sättigungskapazität hängt ab von der Struktur von R bzw. R' und dem Heteroatom Y. (Auch Benzylether können–wenn auch langsamer als Thioether–zu Toluol aufgespalten werden). Auf Grund bekannter Daten werden Vorstellungen entwickelt, die ein Bild über den topochemischen Verlauf der Hydrogenolyse von R–Y–R' vermitteln sollen.

Vergiftetes Raney-Nickel ist im Gegensatz zum aktivierten Raney-Nickel nicht mehr oder nur stark vermindert zur Isomerisierung, Disproportionierung und zum H-D-Austausch befähigt. Bei diesen Prozessen spielt offenbar der im Nickel strukturgebundene Wasserstoff eine wichtige Rolle.

Some thioethers, sulphoxides, sulphones, organoselenium and tellurium compounds (R–Y–R' R, R'= Alkyl, Aryl, Y?S, SO, SO₂, Se, Te) have been reductively cleaved on the surface of Raney-nickel. The products comprise RH and R'H, and a surface bound material (Raney-nickel-Y) (Y?S, also from sulphoxides and sulphones, Se, Te. The latter may be released as YH₂ on treatment with mineral acids).

The area and ‘structure’ of the surface determines the hydrogenolysis capacity of the catalyst. For technical quality Raney-nickel, the limiting yield of benzene from diphenylsulphide is 1.1 mmol/g. The limiting yield is dependent on the structure of R and R' and also the nature of Y. (Benzyl ethers may also be reduced to toluene, if somewhat slower than the corresponding thioether).

Proposal for the processes possibly involved at the surface during hydrogenolysis of R–Y–R' are put forward in the basis of consideration of the available experimental data.

Poisoned Raney-nickel (in contrast to the activated catalyst) is practically inactive as agent for isomerization, disproportionation, or H–D exchange, and hence surface bound hydrogen clearly plays an important role in these processes.     

Investigating Membrane-Mediated Antimicrobial Peptide Interactions with Synchrotron Radiation Far-Infrared Spectroscopy

Synchrotron radiation-based Fourier transform infrared spectroscopy enables access to vibrational information from mid over far infrared to even terahertz domains. This information may prove critical for the elucidation of fundamental bio-molecular phenomena including folding-mediated innate host defence mechanisms. Antimicrobial peptides (AMPs) represent one of such phenomena. These are major effector molecules of the innate immune system, which favour attack on microbial membranes. AMPs recognise and bind to the membranes whereupon they assemble into pores or channels destabilising the membranes leading to cell death. However, specific molecular interactions responsible for antimicrobial activities have yet to be fully understood. Herein we probe such interactions by assessing molecular specific variations in the near-THz 400–40 cm⁻¹ range for defined helical AMP templates in reconstituted phospholipid membranes. In particular, we show that a temperature-dependent spectroscopic analysis, supported by 2D correlative tools, provides direct evidence for the membrane-induced and folding-mediated activity of AMPs. The far-FTIR study offers a direct and information-rich probe of membrane-related antimicrobial interactions.     

Upper bound on the dark matter total annihilation cross section

We consider dark matter annihilation into standard model particles and show that the least detectable final states, namely, neutrinos, define an upper bound on the total cross section. Calculating the cosmic diffuse neutrino signal, and comparing it to the measured terrestrial atmospheric neutrino background, we derive a strong and general bound. This can be evaded if the annihilation products are dominantly new and truly invisible particles. Our bound is much stronger than the unitarity bound at the most interesting masses, shows that dark matter halos cannot be significantly modified by annihilations, and can be improved by a factor of 10-100 with existing neutrino experiments.     

Longitudinal-transverse separations of deep-inelastic structure functions at low Q2 for hydrogen and deuterium

We report on a study of the longitudinal to transverse cross section ratio, R=sigmaL/sigmaT, at low values of x and Q2, as determined from inclusive inelastic electron-hydrogen and electron-deuterium scattering data from Jefferson Laboratory Hall C spanning the four-momentum transfer range 0.06相似文献   

Correcting saturation effects of the arterial input function in dynamic susceptibility contrast-enhanced MRI: a Monte Carlo simulation

To prevent systematic errors in quantitative brain perfusion studies using dynamic susceptibility contrast-enhanced magnetic resonance imaging (DSC-MRI), a reliable determination of the arterial input function (AIF) is essential. We propose a novel algorithm for correcting distortions of the AIF caused by saturation of the peak amplitude and discuss its relevance for longitudinal studies. The algorithm is based on the assumption that the AIF can be separated into a reliable part at low contrast agent concentrations and an unreliable part at high concentrations. This unreliable part is reconstructed, applying a theoretical framework based on a transport-diffusion theory and using the bolus-shape in the tissue. A validation of the correction scheme is tested by a Monte Carlo simulation. The input of the simulation was a wide range of perfusion, and the main aim was to compare this input to the determined perfusion parameters. Another input of the simulation was an AIF template derived from in vivo measurements. The distortions of this template was modeled via a Rician distribution for image intensities. As for a real DSC-MRI experiment, the simulation returned the AIF and the tracer concentration-dependent signal in the tissue. The novel correction scheme was tested by deriving perfusion parameters from the simulated data for the corrected and the uncorrected case. For this analysis, a common truncated singular value decomposition approach was applied. We find that the saturation effect caused by Rician-distributed noise leads to an overestimation of regional cerebral blood flow and regional cerebral blood volume, as compared to the input parameter. The aberration can be amplified by a decreasing signal-to-noise ratio (SNR) or an increasing tracer concentration. We also find that the overestimation can be successfully eliminated by the proposed saturation-correction scheme. In summary, the correction scheme will allow DSC-MRI to be expanded towards higher tracer concentrations and lower SNR and will help to increase the measurement to measurement reproducibility for longitudinal studies.     

Influence of higher harmonics of the undulator in X‐ray polarimetry and crystal monochromator design

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel‐cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.