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.     

Fluorescence lifetimes in BO2 (A2Πu)

Fluorescence lifetimes and fluorescence quenching rates are reported for several vibronic levels in the A²Π_u electronic manifold of BO₂. The relationship of these results to earlier Hanle-effect measurements is discussed.     

Very high Q measurements on a fused silica monolithic pendulum for use in enhanced gravity wave detectors

We present for the first time the results of very high Q factor measurements for a 2.8 kg fused silica mass suspended by two fused quartz fibers attached by a novel technique for joining fused silica or quartz. The Q for the pendulum mode at 0.93 Hz was (2.3+/-0. 2)x10(7), the highest value demonstrated to date for a mass of this size. By employing such a new suspension system the sensitivity of the gravitational wave detectors currently under construction can be increased up to 1 order of magnitude.     

Circular logic: nonribosomal peptide-like macrocyclization with a ribosomal peptide catalyst

A protease from ribosomal peptide biosynthesis macrocyclizes diverse substrates, including those resembling nonribosomal peptide and hybrid polyketide-peptide products. The proposed mechanism is analogous to thioesterase-catalyzed chemistry, but the substrates are amide bonds rather than thioesters.     

On the reversibility of anode supported proton conducting solid oxide cells

Reversible proton conducting solid oxide cells (SOCs) off a highly efficient route to matching supply from intermittent, renewable resources, with power demand by consumers. The cells would store excess electrical energy as chemical fuel during times of peak production, and operate in reverse during times of peak demand. In this study we examine the operation of anode supported proton conducting SOCs in electrolysis mode. The required overpotential for a given current density decreases with increasing humidity at the anode and increasing temperature. All of the V-I curves show distinct curvature. The electrode polarization resistance increases and electrolyte ohmic resistance decreases with increasing current density. This is accompanied by a deviation below the theoretical rate of hydrogen production. We interpret these changes as resulting from deviation away from pure proton conduction in the cell with increasing polarization.     

Reverse micelle synthesis of perovskite oxide nanoparticles

La_0.6Sr_0.4Co_xFe_1−xO_3−δ (LSCF), La_0.6Sr_0.4Cu_0.2Fe_0.8O_3−δ, Ba_0.5Sr_0.4Co_0.8Fe_0.2O_3−δ and LaFeO_3−δ nanoparticles were synthesized by a reverse micelle procedure. Controlling the size of the micelles through the water:oil phase ratio enabled synthesis of phase pure perovskite particles with average sizes from 14 nm to 50 nm. Small amounts of an impurity phase, likely cobalt oxide, were detected in the XRD spectrum of high cobalt content samples of LSCF (x = 0.8). La_0.6Sr_0.4Co_0.2Fe_0.8O_3−δ nanoparticles were utilized to coat the surface of a dense thin-film La_0.6Sr_0.4Co_0.2Fe_0.8O_3−δ solid oxide fuel cell cathode. The polarization resistance of the nanoparticle coated electrode, measured at open circuit in air at 973 K, was 20% lower than an equivalent un-coated electrode.