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.     

Delamination of layered double hydroxides in polar monomers: new LDH-acrylate nanocomposites

The layered double hydroxide Mg2Al(OH)6(C12H25SO4) was delaminated to give high levels of inclusion in acrylate monomers; subsequent polymerisation of the monomers containing the LDH dispersion gave polyacrylates with the inorganic component still in the delaminated form.     

Light-directed radial combinatorial chemistry: orthogonal safety-catch protecting groups for the synthesis of small molecule microarrays

We describe the development of photolabile protecting groups based on the 3,4,5-trimethoxyphenacyl group (TMP). Orthogonal safety-catches were created by introducing an acid-activatible dimethyl ketal (AA-TMP) and an oxidatively activatible 1,3-dithiane (OA-TMP) into the photolabile TMP group. We demonstrate the application of these protecting groups in light-directed synthesis of small molecule microarrays with diversity elements radially attached to a hydroxyproline scaffold.     

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)).     

Synthesis of titanium(IV) guanidinate complexes and the formation of titanium carbonitride via low-pressure chemical vapor deposition

The mono(guanidinato) complex [Ti(NMe2)2Cl{i-PrNC[N(SiMe3)2]N-i-Pr}] (1) was prepared by reaction of [Ti(NMe2)2Cl2] with 1 or 2 equiv of the lithium guanidinate salt [Li{i-PrNC[N(SiMe3)2]N-i-Pr}]. Compound 1 has been characterized by X-ray crystallography. Treatment of TiCl4 with 2 equiv of [Li{i-PrNC[N(SiMe3)2]N-i-Pr}] resulted in the formation of dark red crystals. X-ray crystallography showed that these crystals consist of a 70:30 mixture of two bis(guanidinato) complexes, namely, [TiCl2{i-PrNC[N(SiMe3)2]N-i-Pr}{i-PrNC(N=CMe2)N-i-Pr}] (2) and [TiCl2{i-PrNC[N(SiMe3)2]N-i-Pr}{i-PrNC[N(H)-i-Pr]N-i-Pr}] (3). Both compounds 2 and 3 possess a transformed guanidinate ligand. Low-pressure chemical vapor deposition of either compound 1 or [TiCl2{i-PrNC(NMe2)N-i-Pr}] (4) at 600 degrees C results in thin films of titanium carbonitride.     

Structural and Spectroscopic Characterization of Iron(III) Dioxoporphodimethene Complexes and Their Autoreduction to an Iron(II) Complex in Pyridine

Three iron complexes of the meso-dioxo derivative of octaethylporphryin (trans-H(2)OEPO(2)) were characterized by X-ray diffraction. Green ClFe(III)(trans-OEPO(2)).1.5C(6)H(6) crystallizes in the monoclinic space group P2(1)/c with a = 13.766(3) ?, b = 19.075(3) ?, c = 15.217(3) ?, beta = 99.87(2) degrees at 123 K with Z = 4. Refinement of 2712 reflections with F > 6.0sigma(F) and 223 parameters yielded R = 0.0624, R(w) = 0.0596. The iron complex contains a domed dioxoporphodimethene macrocyclic ligand. The observation of a five-coordinate iron(III) ion with an axial Fe-Cl distance of 2.232(2) ? and in-plane Fe-N distances averaging 2.082 ? is consistent with its high-spin (S = (5)/(2)) character. This monomer is readily converted to the green {Fe(III)(trans-OEPO(2))}(2)O using aqueous hydroxide. {Fe(III)(trans-OEPO(2))}(2)O crystallizes in the monoclinic space group C2/c with a = 23.541(8) ?, b = 15.392(5) ?, c = 18.686(8) ?, and beta = 90.09(3) degrees at 294 K with Z = 8. Refinement of 3472 reflections with F > 6.0sigma(F) and 393 parameters yielded R = 0.0484, R(w) = 0.0527. The complex possesses a crystallographically imposed 2-fold symmetry axis that passes through the oxo ligand. The dioxoporphodimethene ligands within the molecule are roof-shaped and fold away from each other. The axial Fe-O distance is 1.749(1) ? with longer in-plane Fe-N distances (average 2.077 ?). The Fe-O-Fe angle of 165.4(2) degrees deviates significantly from linearity and is more acute than related porphyrin complexes. Pyridine solutions of either the iron(III) monomer or &mgr;-oxo dimer autoreduce over a period of days to give (py)(2)Fe(II)(trans-OEPO(2)). This red compound crystallizes in the space group P2(1) with a = 19.177(4) ?, b = 20.039(4) ?, c = 10.547(2) ?, and beta = 100.36(3) degrees at 130 K with Z = 2. Refinement of 5090 reflections with one restraint and 984 parameters yielded R1 = 0.0684, wR2 = 0.1763. The complex crystallizes with two distinct molecules in the asymmetric unit; each molecule contains a different degree of disorder with respect to the trans meso oxygen atoms (50/50, 71/29). Each independent molecule exhibits severe ruffling of the macrocycle. The six coordinate iron(II) center is diamagnetic. The axial Fe-N(pyridine) distances average 1.98 ?, and the in-plane Fe-N(pyrrole) distances average 1.95 ?. A common trend observed for the dioxoporphodimethene macrocycle in all of these structures is an elongation toward the trans oxidized meso carbons. These complexes were originally prepared as cis and trans isomeric mixtures that can be enriched in the trans isomer by fractional crystallization. This is evident in their distinctive (1)H NMR spectra. In addition, these compounds are characterized by electron impact mass spectrometry and UV-visible, ESR, and infrared spectroscopies.     

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.     

Regioselective coupling of pentafluorophenyl substituted alkynes: mechanistic insight into the zirconocene coupling of alkynes and a facile route to conjugated polymers bearing electron-withdrawing pentafluorophenyl substituents

The reaction of Cp(2)ZrCl(2) with 2 equiv of BuLi at -78 degrees C, followed by the addition of an unsymmetrical tetra- or pentafluorophenyl substituted alkyne R(1)C[triple bond]CAr(f) (R(1), Ar(f) = (CH(2))(4)Me, p-C(6)F(4)H; Me, p-C(6)F(4)H; Ph, C(6)F(5)), resulted in regioselective couplings of these alkynes to zirconacyclopentadienes in which the Ar(f) substituents preferentially adopt the 3,4-positions (beta beta) of the zirconacyclopentadiene ring. With Cp(2)Zr(py)(Me(3)SiC[triple bond]CSiMe(3)) as the zirconocene reagent, the couplings could be carried out at room temperature; however, at higher temperatures significant quantities of the 2,4-fluoroaryl substituted (alpha beta) isomers were also formed. None of the conditions employed produced the 2,5-fluoroaryl substituted (alpha alpha) isomers. These fluoroaryl-substituted zirconacyclopentadienes were readily converted to butadienes via reactions with acids. The zirconacyclopentadiene Cp(2)ZrC(4)-2,5-Ph(2)-3,4-(C(6)F(5))(2), which resulted from the coupling of PhC[triple bond]C(C(6)F(5)), was converted to the corresponding thiophene by reaction with S(2)Cl(2), and to an arene by reaction with MeO(2)CC[triple bond]CCO(2)Me/CuCl. Mechanistic studies on zirconocene couplings of (p-CF(3)C(6)H(4))C[triple bond]C(p-MeC(6)H(4)) indicate that the observed regioselectivities are determined by an electronic factor that controls the orientation of at least one of the two alkynes as they are coupled. Additionally, these studies suggest an unsymmetrical transition state for the zirconocene coupling of alkynes, and this is supported by DFT calculations. The reaction of [(C(6)F(5))C[triple bond]CCH(2)](2)CH(2) with Cp(2)Zr(py)(Me(3)SiC[triple bond]CSiMe(3)) resulted in a zirconacyclopentadiene in which the pentafluorophenyl substituents have been forced into the 2,5-positions (alpha alpha). Zirconocene coupling of the diyne (C(6)F(5))C[triple bond]C-1,4-C(6)H(4)-C[triple bond]C(C(6)F(5)) provided a route to conjugated polymers bearing electron-withdrawing pentafluorophenyl groups.     

Cs+ -selective membrane electrodes based on ethylene glycol-functionalized polymeric microspheres

A new strategy for improving the robustness of membrane-based ion-selective electrodes (ISEs) is introduced based on the incorporation of microsphere-immobilized ionophores into plasticized polymer membranes. As a model system, a Cs⁺-selective electrode was developed by doping ethylene glycol-functionalized cross-linked polystyrene microspheres (P-EG) into a plasticized poly(vinyl chloride) (PVC) matrix containing sodium tetrakis-[3,5-bis(trifluoromethyl)phenyl] borate (TFPB) as the ion exchanger. Electrodes were evaluated with respect to Cs⁺ in terms of sensitivity, selectivity, and dynamic response. ISEs containing P-EG and TFPB that were plasticized with 2-nitrophenyl octyl ether (NPOE) yielded a linear range from 10⁻¹ to 10⁻⁵ M Cs⁺, a slope of 55.4 mV/decade, and a lower detection limit (log a_Cs) of −5.3. In addition, these membranes also demonstrated superior selectivity over Li⁺, Na⁺, and alkaline earth metal ion interferents when compared to analogous membranes plasticized with bis(2-ethylhexyl) sebacate (DOS) or membranes containing a lipophilic, mobile ethylene glycol derivative (ethylene glycol monooctadecyl ether (U-EG)) as ionophore.