Compensated Compactness, Paracommutators, and Hardy Spaces

LetB₁: ⁿ× ^N₁→ ^m₁,B₂: ⁿ× ^N₂→ ^m₂andQ: ^m₂→ ^m₁be bilinear forms which are related as follows: ifμandνsatisfyB₁(ξ, μ)=0 andB₂(ξ, ν)=0 for someξ≠0, thenμ^τQν=0. Supposep⁻¹+q⁻¹=1. Coifman, Lions, Meyer and Semmes proved that, ifuL^p( ⁿ) andvL^q( ⁿ), and the first order systemsB₁(D, u)=0,B₂(D, v)=0 hold, thenu^τQvbelongs to the Hardy spaceH¹( ⁿ), provided that both (i)p=q=2, and (ii) the ranks of the linear mapsB_j(ξ, ·) : ^N_j→ ^m₁are constant. We apply the theory of paracommutators to show that this result remains valid when only one of the hypotheses (i), (ii) is postulated. The removal of the constant-rank condition whenp=q=2 involves the use of a deep result of Lojasiewicz from singularity theory.     

Cycloaldol approach to the isobenzofuran core of eunicellin diterpenes

[reaction: see text] A novel cycloaldol approach to the isobenzofuran core common to many of the eunicellin diterpenes is described. The cycloaldol precursor was prepared by aldol addition of (S)-(+)-carvone and methacrolein followed by etherification to a glycolate ester. Chemoselective enolization of the glycolate ester led to the cycloaldol adduct in high yield and diastereoselectivity. An oxidative rearrangement-allylic diazene rearrangement sequence established the requisite cis ring fusion.     

Study of various substrates for peroxidase-coupled peroxide oxidations

It would appear from this study that the sodium sulfonates of 2, 4-dichloro- and 2, 4-dibromophenol when employed in the presence of 4-AAP produce useful and sensitive, colorimetric, cosubstrate systems. What may prove to be of equal importance is the relatively high initial rate of the coupling reactions, as it has been suggested (29, 30) that this might help alleviate interference by competitive proton donors.As long as the general structure of the phenols is maintained, increased aromaticity tends to add stability to the chromogen. This is, of course, an asset when performing equilibrium analysis.The use of MBTH, in the presence of either aromatic amines or alcohols, appears to have little obvious merit. Apart from the continual increase in absorbance of the blank, that is, a spontaneous coupling of the cosubstrates, as well as the comparatively high blank absorbance, this material does not seem to be as sensitive as some of the other reactions studied.     

The synthesis and characterisation of 4,1,2-MC2B10 metallacarboranes

Reduction of the tethered carborane 1,2-(CH2)3-1,2-closo-C2B10H10 followed by treatment with CoCl2/NaCp, [(p-cymene)RuCl2]2(p-cymene=C6H4MeiPr-1,4), (PMe2Ph)2PtCl2 or (dppe)NiCl2(dppe=Ph2PCH2CH2PPh2) affords reasonable yields of the new 13-vertex metallacarboranes 1,2-(CH2)3-4-Cp-4,1,2-closo-CoC2B10H10 (1), 1,2-(CH2)3-4-(p-cymene)-4,1,2-closo-RuC2B10H10 (2), 1,2-(CH2)3-4,4-(PMe2Ph)2-4,1,2-closo-PtC2B10H10 (3) and 1,2-(CH2)3-4,4-(dppe)-4,1,2-closo-NiC2B10H10 (4), respectively. All compounds were characterised spectroscopically and crystallographically. The cobalt and ruthenium species 1 and 2 have Cs symmetry in both solution and the solid state, having henicosahedral cage structures featuring a trapezoidal C1C2B9B5 face. The platinum and nickel compounds 3 and 4 have asymmetric docosahedral cage structures in the crystal (the more so for 4 than for 3) although both appear, by 11B and 31P NMR spectroscopy, to have Cs symmetry in solution. Low-temperature experiments on the more soluble platinacarborane could not freeze out the diamond-trapezium-diamond fluctional process that we assume is operating in solution, and we therefore conclude that this process has a relatively low activation barrier, probably <35 kJ mol-1.     

Comparison of Methionine α,γ‐Lyase and Homocysteine α,γ‐Lyase for Electrochemical Determination of Homocysteine

Recently, a novel enzymatic method was developed for determination of homocysteine. This method utilizes the electrochemical hydrogen sulfide sensor along with methionine α,γ‐lyase to accomplish the fast, accurate, sensitive and selective measurements. As a continuation of this work, another enzyme, homocysteine α,γ‐lyase, was used and the parallel experiments of using both enzymes were carried out against the effect of pH, sensitivity, linearity, and interferences, in an intended comparison between these two enzymes. The excellent linearity of amperometric currents against homocysteine concentrations, high sensitivities and low detection limits for both enzymes reconfirmed that the electrochemical method is superior over other analytical means. The high enzymatic activity of methionine α,γ‐lyase surpassing homocysteine α,γ‐lyase endowed the former higher sensitivity, lower detection limit and faster response than the latter, suggesting methionine α,γ‐lyase a better candidate for homocysteine measurement by electrochemical method. The differences between these two enzymes on the trends of response time and sensitivity at different pH environments, reactivity toward several forms of homocysteine as well as on the interference from several agents were also addressed and discussed.     

Random Copolymers of 1,5-Dioxepan-2-one

ABSTRACT

Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as r_VL=0.5 and r_DXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition.

Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO.     

Single kerr-schild metrics: A double view

Real-vacuum single Kerr-Schild (ISKS) metrics are discussed and new results proved. It is shown that if the Weyl tensor of such a metric has a twist-free expanding principal null direction, then it belongs to the Schwarzschild family of metrics — there are no Petrov type-II Robinson-Trautman metrics of Kerr-Schild type. If such a metric has twist then it belongs either to the Kerr family or else its Weyl tensor is of Petrov type II. The main part of the paper is concerned with complexified versions of Kerr-Schild metrics. The general real ISKS metric is written in double Kerr-Schild (IDKS) form. TheH andl potentials which generate IDKS metrics are determined for the general vacuum ISKS metric and given explicitly for the Schwarzschild and Kerr families of metrics.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

Secondary ion yields produced by keV atomic and polyatomic ion impacts on a self-assembled monolayer surface

A suite of keV polyatomic or 'cluster' projectiles was used to bombard unoxidized and oxidized self-assembled monolayer surfaces. Negative secondary ion yields, collected at the limit of single ion impacts, were measured and compared for both molecular and fragment ions. In contrast to targets that are orders of magnitude thicker than the penetration range of the primary ions, secondary ion yields from polyatomic projectile impacts on self-assembled monolayers show little to no enhancement when compared with monatomic projectiles at the same velocity. This unusual trend is most likely due to the structural arrangement and bonding characteristics of the monolayer molecules with the Au(111). Copyright 1999 John Wiley & Sons, Ltd.     

Properties and performance of BaxSr1−xCo0.8Fe0.2O3−δ materials for oxygen transport membranes

The present paper discusses the oxygen transport properties, oxygen stoichiometry, phase stability, and chemical and mechanical stability of the perovskites (BSCF) and (SCF) for air separation applications. The low oxygen conductive brownmillerite phase in SCF is characterized using in-situ neutron diffraction, thermographic analysis and temperature programmed desorption but this phase is not present for BSCF under the conditions studied. Although both materials show oxygen fluxes well above 10 ml/cm²·min at T=1,273 K and pO₂=1 bar for self-supporting, 200 μm-thick membranes, BSCF is preferred as a membrane material due to its phase stability. However, BSCF’s long-term stable performance remains to be confirmed. The deviation from ideal oxygen stoichiometry for both materials is high: δ>0.6. The thermal expansion coefficients of BSCF and SCF are 24×10⁻⁶ and 30×10⁻⁶ K⁻¹, respectively, as determined from neutron diffraction data. The phenomenon of kinetic demixing has been observed at pO₂<10⁻⁵ bar, resulting in roughening of the surface and enrichment with alkaline earth metals. Stress–strain curves were determined and indicated creep behavior that induces undesired ductility at T=1,073 K for SCF. Remedies for mechanical and chemical instabilities are discussed.