Some results on the capitulation problem

Let K be an unramified abelian extension of a number field F with Galois group G. K corresponds to a subgroup H of the ideal class group of F. We study the subgroup J of ideal classes in H which become trivial in K. There is an epimorphism from the cohomology group H^?1(G, Cl_K) to J which is an isomorphism if G is cyclic; Cl_K is the ideal class group of K. Some results on the structure of J and Cl_K are obtained.     

A computer model of the interaction of acoustic surface waves with discontinuities

Surface acoustic waves are under active investigation in three fields of study: geophysics, electronics and non-destructive testing. While the mathematical features are the same for all three fields, the wavelengths, as well as the dimensions of the features, range over at least ten orders of magnitude.In this paper a brief review of available numerical techniques is presented and this is followed by discussion of a series of models which use finite difference methods to predict the reflected and transmitted signals from wide band pulses of ultrasonic Rayleigh waves incident on various surface-breaking features. The paper concludes with a comparison of analytical, numerical and experimental results.     

Distribution of stable isotopes in surface water along the Danube River in Serbia†

Stable hydrogen and oxygen isotopes were analysed in water samples from the River Danube and its tributaries during a longitudinal survey performed in August 2005 on Serbian territory. Danube river water data ranged from?80‰ to?66‰ for δ²H, and from?11.2‰ to?9.3‰ for δ¹⁸O with δ values increasing downstream. The isotopic signatures of the adjacent tributaries (the Tisza, the Sava and the Velika Morava) sampled at the locations close to their confluence with the Danube (Titel, Ostru?nica and Ljubi?evski most, respectively) just about the time of the campaign were enriched (?67‰ and?63‰ for δ²H, and?9.3‰ and?8.9‰ for δ¹⁸O) with respect to the Danube water because of their catchment effects. Hydrogen and oxygen stable isotope values were used in combination with measured physico-chemical and biological parameters to trace hydrological and transport processes in these river systems. The mixing relationships between the Danube main stream and its tributaries were estimated using the mass balance for isotopic composition and electrical conductivity as conservative parameters. Evidence of an incomplete mixing process at the ?enta location, 8 km below the confluence of the Tisza river, with its participation of 88% was shown by its oxygen-18 content. The correlations between river water isotope composition and physico-chemical and biological parameters are discussed.     

Controllable Synthesis of Few‐Layer Bismuth Subcarbonate by Electrochemical Exfoliation for Enhanced CO2 Reduction Performance

Two‐dimensional (2D) engineering of materials has been recently explored to enhance the performance of electrocatalysts by reducing their dimensionality and introducing more catalytically active ones. In this work, controllable synthesis of few‐layer bismuth subcarbonate nanosheets has been achieved via an electrochemical exfoliation method. These nanosheets catalyse CO₂ reduction to formate with high faradaic efficiency and high current density at a low overpotential owing to the 2D structure and co‐existence of bismuth subcarbonate and bismuth metal under catalytic turnover conditions. Two underlying fast electron transfer processes revealed by Fourier‐transformed alternating current voltammetry (FTacV) are attributed to CO₂ reduction at bismuth subcarbonate and bismuth metal. FTacV results also suggest that protonation of CO₂^.? is the rate determining step for bismuth catalysed CO₂ reduction.     

Diverged Plant Terpene Synthases Reroute the Carbocation Cyclization Path towards the Formation of Unprecedented 6/11/5 and 6/6/7/5 Sesterterpene Scaffolds

Sesterterpenoids are a relatively rare class of plant terpenes. Sesterterpene synthase (STS)‐mediated cyclization of the linear C₂₅ isoprenoid precursor geranylfarnesyl diphosphate (GFPP) defines sesterterpene scaffolds. So far only a very limited number of STSs have been characterized. The discovery of three new plant STSs is reported that produce a suite of sesterterpenes with unprecedented 6/11/5 and 6/6/7/5 fused ring systems when transiently co‐expressed with a GFPP synthase in Nicotiana benthamiana. Structural elucidation, feeding experiments, and quantum chemical calculations suggest that these STSs catalyze an unusual cyclization path involving reprotonation, intramolecular 1,6 proton transfer, and concerted but asynchronous bicyclization events. The cyclization is diverted from those catalyzed by the characterized plant STSs by forming unified 15/5 bicyclic sesterterpene intermediates. Mutagenesis further revealed a conserved amino acid residue implicated in reprotonation.     

Eigenvalue Asymptotics of the Stokes Operator for Fractal Domains

The leading asymptotic term for the function that counts theeigenvalues of the Stokes operator is determined for fairlygeneral underlying bounded domains. Moreover, the remainderis estimated in terms of the fractality of the boundary of thedomain. The results obtained resemble corresponding ones forthe Dirichlet Laplacian. 1991 Mathematics Subject Classification:35P20.     

Crystal structure of Pt(S2COEt)2

The crystals of Pt(S₂COEt)₂ are orthorhombic, Pbca, with (at 20°C)a=7.799(3),b=7.368(6),c=20.588(7) Å.D _cale=2.46g cm^–3 forZ=4. The platinum atom resides on a crystallographic center of inversion and is bound to the four sulfur atoms of the xanthato ligand in a square planar geometry. The Pt–S distances are 2.313(6) and 2.320(7)Å with an intraligand S–Pt–S angle of 75.1(2)°.     

Azetidine,pyrrolidine and hexamethyleneimine at 170 K

The crystal structures of the cyclic amines azetidine (C₃H₇N), pyrrolidine (C₄H₉N) and hexamethyleneimine (homopiperidine, C₆H₁₃N), of the series (CH₂)_nNH, with n = 3, 4 and 6, respectively, have been determined at 170 K, following in situ crystallization from the melt. These structures provide crystallographic data to complete the homologous series of cyclic amines (CH₂)_nNH, for n = 2–6. Azetidine and pyrrolidine contain chains propagating along 2₁ screw axes, in which the molecules are linked by co-operative N—H...N hydrogen bonds. Azetidine has two molecules in its asymmetric unit, while pyrrolidine has only one. Hexamethyleneimine contains tetrameric hydrogen-bonded rings formed about crystallographic inversion centres, with two molecules in its asymmetric unit. The observation of crystallographically distinct molecules in the hydrogen-bonded chains of azetidine and cyclic hydrogen-bonded motifs in hexamethyleneimine is consistent with expectations derived from comparison with monoalcohols forming chains or rings by co-operative O—H...O hydrogen bonds. The next member of the cyclic amine series, heptamethyleneimine, forms a cubic plastic phase on cooling from the melt.