A topological aspect of Sobolev mappings

Let be a connected open set, . We give a sufficient condition for a mapping , , to have the property that sgn is almost everywhere of one sign. Following the work of Müller, Spector, and Tang [MST], we give an application of our results to the theory of non-linear elasticity. Received: 13 October 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001     

Backward particle production in neutrino neon interactions

Backward proton and pion production is studied in ν and \(\bar v\) charged current interactions in neon. The results are compared with other experiments and theory. The complete backward proton data is compatible with protons produced by reinteractions in the nucleus. However in events with only one proton, muon variables appear correlated to those for the backward proton, as expected by the two-nucleon correlation model.     

Coherent single pion production by antineutrino charged current interactions and test of PCAC

The cross section for coherent production of a single π^? meson in charged current antineutrino interactions on neon nuclei has been measured in BEBC to be (175±25) 10^?40 cm²/neon nucleus, averaged over the energy spectrum of the antineutrino wide band beam at the CERN SPS; this corresponds to (0.9±0.1) % of the total charged current \(\bar v_\mu \) cross section. The distributions of kinematical variables are in agreement with theoretical predictions based on the PCAC hypothesis and the meson dominance model; in particular, theQ ² dependence is well described by a propagator containing a massm=(1.35±0.18) GeV. The absolute value of the cross section is also in agreement with the model. This analysis thus provides a test of the PCAC hypothesis in the antineutrino energy range 5–150 GeV.     

Efficient method for visualization and isolation of proteins resolved in polyacrylamide gels

Polyacrylamide gel electrophoresis is a popular method used to purify proteins for reconstitution experiments, amino acid composition and sequence determinations. In this report we describe methods that will be of general use in the isolation and characterization of proteins and the benefits of substituting boric acid for glycine in the electrophoresis tray buffers. We also describe how proteins resolved in a variety of gel systems (including those containing sodium dodecyl sulfate) may be rapidly visualized with 8-anilino-1-naphthalene sulfonic acid and efficiently transferred to a second gel for two-dimensional gel analysis, or isolated by electroelution for subsequent characterization.     

Synthese und Strukturuntersuchungen von Ba2H[α-FeO4W12O36] · 26 H2O

Synthesis and Structure Studies of Ba₂H[α-FeO₄W₁₂O₃₆] · 26 H₂O The heteropolyanion compound Ba₂H[α-FeO₄W₁₂O₃₆] · 26 H₂O (I) crystallizes in the tetragonal space group P4 n2 with the lattice parameters a = 12.398(6), c = 18.721(6) Å; Z = 2; D_x = 4.128 g · cm^?3. The structure was solved on a twinned crystal from 1029 observed reflections and refined to an index R of 7.6%. The calculations were done by means of a modified ORFLS-programme by Eitel and Bärnighausen. The heteropolyanion [α-FeO₄W₁₂O₃₆]^5? has the well known α-Keggin structure. The average distance of the four central oxygen atoms to the Fe^III position (0, 0, 0) is 1.84 Å. The angles ? O? Fe? O are 112.3° (4X) and 103.9 (2X), respectively, which leads to an disphenoidal distortion of the FeO₄ tetrahedron. The powder and single crystal ESR spectra of I show the anisotropy of the Fe^III fine structure transition 1/2 ? ?1/2. The Mößbauer spectra confirm the tetragonal distortion of the central FeO₄ tetrahedron (quadrupole splitting Δ ≈ 0.50 mm · s^?1).     

Assignment of E/Z isomers in Schiff bases of 3-acyltetramic acids with ethylenediamine by 1H and 13C NMR spectroscopy

The reaction of ethylenediamine with an equivalent mixture of diversely substituted 3-acyltetramic acids leads to Z/Z, Z/E, E/Z and E/E isomers. The E/Z isomerisation is slow in the NMR time scale of the ¹H and ¹³C chemical shifts; therefore at room temperature and in deuterochloroform all isomers of the new synthesized asymmetric compounds N,N′-ethylene-(1-ethyl-5,5-dimethyl-1′,5′,5′-trimethyl-3,3′-acetyltetramic acid) a, N,N′-ethylene-(5,5-dimethyl-1′,5′,5′-trimethyl-3,3′-acetyltetramic acid) b and, N,N′-ethylene-(1,5,5-trimethyl-1′,5′,5′-trimethyl-3-acetyl-3′-formyl-tetramic acid) c could be found in the corresponding spectra. To assign the ¹³C NMR signals we used two-dimensional ¹³C-¹H one-bond (HMQC) and ¹³C-¹H multibond (HMBC) correlated spectroscopy and the empirical rule that CO signals involved in hydrogen bonds are shifted to a lower field. The relative stability of isomers depending on substitution pattern could be estimated from the composition of the equilibria. b crystallizes as Z/Z isomer from ethanolic solution. The X-ray structural analysis of b has shown two CH-O hydrogen bonds. Received: 31 May 1996 / Revised: 26 June 1996 / Accepted: 1 July 1996     

The Coordination Chemistry of Iron with the 1,4‐Bis(2‐pyridyl‐methyl)piperazine Ligand

The behaviour of Fe^II and Fe^III ions in combination with the potential ligand 1,4‐bis(2‐pyridyl‐methyl)piperazine (BPMP) under anhydrous conditions has been investigated. BPMP has been reacted with FeCl₂, FeCl₃ and [Fe(OTf)₂(MeCN)₂]. This led to the isolation of four new complexes, which were fully characterized and structurally investigated by single crystal X‐ray diffraction. It turned out that in the presence of chloride co‐ligands Fe^III favours the tetradentate coordination mode of BPMP with the piperazine unit in a boat configuration, like for instance in [BPMP(Cl)Fe(μ‐O)FeCl₃] or [BPMP‐FeCl₂][FeCl₄], ( 1 ). However, the employment of FeCl₂ leads to the formation of a coordination polymer [BPMP‐FeCl₂]_n, ( 2 ), containing the piperazine ring in a chair configuration binding to two iron centres each. 2 can only be dissolved in very polar solvents like dmf which is capable of breaking up the polymeric structure under formation of [Cl₂(dmf)Fe(μ‐BPMP‐1κ²N,N:2κ²N,N))Fe(dmf)Cl₂]·2 dmf, ( 3 ). In contrast, using [Fe(OTf)₂(MeCN)₂] instead of FeCl₂ as the starting material leads to a mononuclear Fe^II complex with BPMP bound in the desirable tetradentate fashion: [BPMP‐Fe(OTf)₂], ( 4 ). Unlike other complexes with tetradentate N/py ligands the two residual ligands in 4 are bound almost trans to each other with the potential to adopt a cis orientation under oxidising conditions, and it will be interesting to exploit its catalytic properties in future.     

Phase-field modeling of void evolution and swelling in materials under irradiation

Void swelling is an important phenomenon observed in both nuclear fuels and cladding materials in operating nuclear reactors. In this work we develop a phase-field model to simulate void evolution and void volume change in irradiated materials. Important material processes, including the generation of defects such as vacancies and self-interstitials, their diffusion and annihilation, and void nucleation and evolution, have been taken into account in this model. The thermodynamic and kinetic properties, such...