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.     

Synthesis and characterization of carbohydrate-based phospholipids

Novel carbohydrate-based phospholipids containing two saturated C(12) (dilauroyl ribo-phosphocholine) (DLRPC), C(14) (dimyristoyl ribo-phosphocholine) (DMRPC), and C(20) (diarachadonyl ribo-phosphocholine) (DARPC) carboxylic acid chains were synthesized. The physical properties of the supramolecular structures formed by these compounds were compared to those formed by their direct glycerol analogues dilauroyl phosphocholine (DLPC), dimyristoyl phosphocholine (DMPC), and diarachadonyl phosphocholine (DAPC). Modulated differential scanning calorimetry (MDSC) and X-ray diffraction data indicated that with chain lengths < or =14 carbons, the carbohydrate backbone increased the thermal stability of the bilayer below the phase-transition temperature (T(m)) as compared to the glycerol-based lipids. With longer chains (C(20)), the bilayer structure was destabilized as compared to glycerol-based lipids. NMR studies of a DMRPC vesicle dispersion reveal split choline headgroup signals and distinct magnetization transfer effects arising from the "inner" and "outer" surfaces of the bilayer vesicle. Modulated differential scanning calorimetry also demonstrated that glycerol- and carbohydrate-based lipids mix, as evidenced by a single intermediate T(m). In addition, carbohydrate-based lipid/cholesterol mixtures exhibited a decrease in enthalpy with an increase in cholesterol concentration. Unlike glycerol phospholipids, carbohydrate lipids were resistant to enzymatic degradation by phospholipase A(2) (PLA(2)).     

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 first 4,1,10-MC2B10 supraicosahedral metallacarboranes and a route to previously inaccessible 4,1,12-ruthenium arene species

Reduction of 1,12-closo-C2B10H12 or its C,C-dimethyl analogue with sodium in liquid ammonia followed by metallation with {CpCo}2+, {(arene)Ru}2+ or {(dppe)Ni}2+ fragments affords the first examples of 4,1,10-MC2B10 species; thermolysis of these yields the appropriate 4,1,12-MC2B10 isomers, unavailable for (arene)Ru metallacarboranes by similar thermolysis of known 4,1,6-MC2B10 compounds.     

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.     

On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress. This instability is called the Rayleigh-Plateau instabilty. We consider the model developed by Spencer et ...     

Synthesis,Antibacterial, and Antioxidant Evaluation of Novel Series of Condensed Thiazoloquinazoline with Pyrido,Pyrano, and Benzol Moieties as Five- and Six-Membered Heterocycle Derivatives

A novel synthesis of thiazolo[2,3-b]quinazolines 4(a–e), pyrido[2′,3′:4,5]thiazolo[2,3-b]quinazolines {5(a–e), 6(a–e), and 7(a–e)}, pyrano[2′,3′:4,5]thiazolo[2,3-b]quinazolines 8(a–e), and benzo[4,5]thiazolo[2,3-b]quinazoloine9(a–e) derivatives starting from 2-(Bis-methylsulfanyl-methylene)-5,5-dimethyl-cyclohexane-1,3-dione 2 as efficient α,α dioxoketen dithioacetal is reported and the synthetic approaches of these types of compounds will provide an innovative molecular framework to the designing of new active heterocyclic compounds. In our study, we also present optimization of the synthetic method along with a biological evaluation of these newly synthesized compounds as antioxidants and antibacterial agents against the bacterial strains, like S. aureus, E. coli, and P. aeruginosa. Among all the evaluated compounds, it was found that some showed significant antioxidant activity at 10 μg/mL while the others exhibited better antibacterial activity at 100 μg/mL. The results of this study showed that compound 6(c) possessed remarkable antibacterial activity, whereas compound 9(c) exhibited the highest efficacy as an antioxidant. The structures of the new synthetic compounds were elucidated by elemental analysis, IR, ¹H-NMR, and ¹³C-NMR.