Ein analogon zum Primzahlsatz für algebraische Funktionenkörper

LetF be an algebraic function field of one variable over a finite field . We prove that

Convective instability in a liquid-liquid system due to complexation with a crown ether

Periodic convective instability has been observed in a biphasic system during the complexation reaction of alkali picrate and dicyclohexano-18-crown-6 which undergoes mass transfer from the hexane phase into the aqueous phase. The convection was visualized by means of precipitated crystals that are formed in both phases by the complexation reaction. The fluid motion was observed with an optical microscope and further analyzed with the particle image velocimetry (PIV) technique. The partition at the extraction of cesium into the organic phase was followed by means of the radioactive isotope (137)Cs. The type of the hydrodynamic instability is governed by the alkali metal expressed via its stability constants for the complex formed. More stable complexes trigger a higher precipitation, thereby favoring a Raleigh-Taylor instability. Complexes with a lower stability constant induce Marangoni cells which show a pulsating character in a cubic container. Depending on the confinement of the experiment cell the fluid motion can also follow a back-and-forth movement. Possible mechanisms for the occurring oscillations are discussed.     

Using immobilized enzymes to reduce RNase contamination in RNase mapping of transfer RNAs by mass spectrometry

RNase (ribonuclease) mapping by nucleobase-specific endonucleases combined with mass spectrometry (MS) is a powerful analytical method for characterizing ribonucleic acids such as transfer RNAs. Typical free solution enzymatic digestion of RNA samples results in a significant amount of RNase being present in the sample solution analyzed by MS. In some cases, the RNase can lead to contamination of the high performance liquid chromatography and MS instrumentation. Here we investigate and compare several different approaches for reducing or eliminating contaminating RNase from the digested RNA sample before LC-MS analysis. Approaches using immobilized RNases were found to be most effective, with no enzyme carryover into the digested sample detected. Among the various options for immobilized RNases, we show that carbodiimide-based reactions can be used to couple RNases to carboxylic acid-terminated magnetic beads. The immobilized enzymes retain biological activity, are re-usable, and do not interfere with subsequent LC-MS analysis of the expected RNase digestion products. The use of immobilized RNases provides a simple approach for eliminating enzyme contamination in mass spectrometry-based RNase mapping experiments.     

Synthesis,Antioxidant, and Antimicrobial Activity of Novel Hydrazones,Arylidenes, and Heterocycles Using 3,5-Diphenylcyclohex-2-en-1-one

Russian Journal of General Chemistry - Reactions of 3,5-diphenylcyclohex-2-en-1-one (1) with several chemical reagents have led to a variety of novel biologically active hydrazones, arylidene...     

Complex formation of trivalent americium with salicylic acid at very low concentrations

For the first time, the complexation of americium(III) with salicylic acid was studied at trace metal concentrations using a 2.0 m Long Path Flow Cell for UV–vis spectroscopy. The detection limit of Am(III) in aqueous solution at pH 3.0 was found to be 5 × 10⁻⁹ M. Two Am(III)-salicylate complexes were formed at pH 5.0 in 0.1 M NaClO₄, indicated by a clear red shift of the absorption maximum. The absorption spectra obtained from spectrophotometric titration were analyzed by means of factor analysis and complex stabilities were calculated to be log β₁₁₀ = 2.56 ± 0.08 and log β₁₂₀ = 3.93 ± 0.19.     

Dynamical Field Inference and Supersymmetry

Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically-driven, dynamically-evolving field from finite data. It relies on information field theory (IFT), the information theory for fields. Here, the relations of DFI, IFT, and the recently developed supersymmetric theory of stochastics (STS) are established in a pedagogical discussion. In IFT, field expectation values can be calculated from the partition function of the full space-time inference problem. The partition function of the inference problem invokes a functional Dirac function to guarantee the dynamics, as well as a field-dependent functional determinant, to establish proper normalization, both impeding the necessary evaluation of the path integral over all field configurations. STS replaces these problematic expressions via the introduction of fermionic ghost and bosonic Lagrange fields, respectively. The action of these fields has a supersymmetry, which means there exists an exchange operation between bosons and fermions that leaves the system invariant. In contrast to this, measurements of the dynamical fields do not adhere to this supersymmetry. The supersymmetry can also be broken spontaneously, in which case the system evolves chaotically. This affects the predictability of the system and thereby makes DFI more challenging. We investigate the interplay of measurement constraints with the non-linear chaotic dynamics of a simplified, illustrative system with the help of Feynman diagrams and show that the Fermionic corrections are essential to obtain the correct posterior statistics over system trajectories.