An existence result for linear partial differential equations with coefficients in an algebra of generalized functions

We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.

     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

Titanosilicates as Supports for an Enzymatic Alcoholysis Reaction

Novel [Cr^III(amp)(bipy)(Cl)] (1) (H₂amp = N-(hydroxyphenyl)salicyldimine; bipy = 2,2-bipyridyl) and [Cr^III(app)(bipy)(Cl)]⁺ (2) (H₂app = N-(hydroxyphenyl)pyridine-2-carboxaldimine; bipy = 2,2-bipyridyl) complexes have been synthesized and characterized by physico-chemical methods. Complexes 1 and 2 have been employed as catalysts in the oxidation of both saturated and unsaturated hydrocarbons using tert-butylhydroperoxide (t-BuOOH). The significance of the results with respect to oxo-functionalization of C-H bonds both in unsaturated and saturated hydrocarbons is noted.     

Spectroscopic Study of the Complexation of DDQ with 1,10-Diaza-18-crown-6 in Chloroform Solution

The formation of charge transfer complexes with 1:1 and 2:1 stoichiometries (acceptor-to-donor) between DDQ and 1,10-diaza-18-crown-6 in chloroform solution was investigated spectrophotometrically. The stepwise formation constants of the resulting complexes were evaluated from the non-linear least-squaresfitting of the absorbance-mole ratio data. The enthalpies and entropiesof the complexation reactions were determined from the temperature dependence of the stepwise formation constants. The resulting 1:1 and 2:1 complexes were isolated in crystalline form and characterized. The results are consistent with the ionic structure of the resulting charge transfer complexes.     

相转移催化元素硫的歧化反应

本工作将相转移催化(PTC)应用于元素硫歧化反应,大大降低了反应温度,提高了反应速度。该反应被证实与熔态硫在水溶液中的歧化相同,即4S+6OH~-=2S~(2-)+S_2O_3~(2-)+3H_2O。比较了四乙基铵、四丁基铵、十六烷基三甲基铵和三辛基甲基铵四种相转移催化剂及四氯乙烯、二甲苯和四氯乙烷三种溶剂的影响。讨论了本体系相转移催化的证据。为改进以元素硫歧化反应为基础的提取冶金过程提供了依据。     

Free energies of transfer of alkali halides from water to urea-water mixtures at 25°C from EMF measurements

The standard potentials_s E ^o of M/M⁺ (M=Li, Na, K, Rb, and Cs) electrodes in aqueous urea solutions containing 12, 20, 30 and 37% by weight of urea have been determined at 25°C from emf measurements on the cell M(Hg)/MCl (m), solvent/AgCl–Ag, from the activities of metals in amalgams by use of a similar type of cell in water, and from the values of_s E ^o of the Ag/AgCl electrode determined earlier. The standard free energies of transfer of MCl, G _t ^o (MCl), from water to the mixed solvents, computed by use of these values and those for the Ag–AgCl electrode, rise sharply from Li⁺ to Na⁺ but fall from Na⁺ to K⁺ and rather sharply from K⁺ to Cs⁺ with a maximum at Na⁺ in all the solvent compositions. This has been attributed to the superimposition of soft-soft interactions on the electrostatic interactions between the ions and the negative charge centers of the possible hydrogen-bonded solvent complexes in the mixed solvents. Comparison of G _t ^o (i) values for individual ions, obtained by a simultaneous extrapolation procedure, with those in aqueous mixtures of methanol,t-butanol, and dimethyl sulfoxide leads to the conclusion that the solvation of these ions in all these solvents is chiefly dictated by the acid-base type of ion-solvent interactions.     

Structure‐Dependent Photoinduced Electron Transfer in Fullerodendrimers with Light‐Harvesting Oligophenylenevinylene Terminals

Oligophenylenevinylene (OPV)‐terminated phenylenevinylene dendrons G1 – G4 with one, two, four, and eight “side‐arms”, respectively, were prepared and attached to C₆₀ by a 1,3‐dipolar cycloaddition of azomethine ylides generated in situ from dendritic aldehydes and N‐methylglycine. The relative electronic absorption of the OPV moiety increases progressively along the fullerodendrimer family C₆₀G1 – C₆₀G4 , reaching a 99:1 ratio for C₆₀G4 (antenna effect). UV/Vis and near‐IR luminescence and transient absorption spectroscopy was used to elucidate photoinduced energy and electron transfer in C₆₀G1 – C₆₀G4 as a function of OPV moiety size and solvent polarity (toluene, dichloromethane, benzonitrile), taking into account the fact that the free‐energy change for electron transfer is the same along the series owing to the invariability of the donor–acceptor couple. Regardless of solvent, all the fullerodendrimers exhibit ultrafast OPV→C₆₀ singlet energy transfer. In CH₂Cl₂, the OPV→C₆₀ electron transfer from the lowest fullerene singlet level (¹C₆₀*) is slightly exergonic (ΔG_CS≈0.07 eV), but is observed, to an increasing extent, only in the largest systems C₆₀G2 – C₆₀G4 with lower activation barriers for electron transfer. This effect has been related to a decrease of the reorganization energy upon enlargement of the molecular architecture. Structural factors are also at the origin of an unprecedented OPV→C₆₀ electron transfer observed for C₆₀G3 and C₆₀G4 in apolar toluene, whereas in benzonitrile, electron transfer occurs in all cases. Monitoring of the lowest fullerene triplet state by sensitized singlet oxygen luminescence and transient absorption spectroscopy shows that this level is populated through intersystem crossing and is not involved in photoinduced electron transfer.     

Extension of conjugation leading to bathochromic or hypsochromic effects in OPV series

Four OPV series 1-4 (a-d) with a terminal dialkylamino group as electron donor were prepared by Wittig-Horner reactions. To study the influence of the push-pull effect on the long-wavelength absorption, three of the four series contained terminal acceptor groups (CN, CHO, NO(2)). The length of the chromophores strongly affects the intramolecular charge transfer (ICT)-an effect which superimposes upon the extension of the conjugation. Increasing numbers n of repeat units cause an overall bathochromic shift for the purely donor-substituted series 1 a-4 a and the series 1 b-4 b with CN as weak acceptor. The two effects annihilate each other in the series 1 c-4 c with terminal CHO groups, so that the absorption maxima are almost independent of the length of the chromophore. A hypsochromic shift is observed for the series 1 d-4 d, which contains the strong acceptor group NO(2). This anomaly disappears on protonation of the dialkylamino group because the push-pull effect disappears in the ammonium salts. The results can be explained by semiempirical quantum mechanics (AM1, INDO/S). The HOMO-LUMO transition, which is mainly responsible for the ICT, becomes less important in the electron transitions S(0)-->S(1) when the distance between donor and acceptor is increased. The commonly used VB model, which contains an electroneutral and a zwitterionic resonance structure, is contrasted with a MO model with dipole segments at both ends of the OPV chains. The latter model turned out to be more appropriate-at least for donor-acceptor-substituted OPVs with n >/= 2.     

Direct Electrochemistry of Multi‐Copper Oxidases at Carbon Nanotubes Noncovalently Functionalized with Cellulose Derivatives

This study describes the direct electron transfer of multi‐copper oxidases, i.e., laccase (from Trametes versicolor) and bilirubin oxidase (BOD, from Myrothecium verrucaria) at multiwalled carbon nanotubes (MWNTs) noncovalently functionalized with biopolymers of cellulose derivatives, i.e., hydroxyethyl cellulose (HEC), methyl cellulose (MC), and carboxymethyl cellulose (CMC). The functionalization of the MWNTs with the cellulose derivatives is found to substantially solubilize the MWNTs into aqueous media and to avoid their aggregation on electrode surface. Under anaerobic conditions, the redox properties of laccase and BOD are difficult to be defined with cyclic voltammetry at either laccase/MWNT‐modified or BOD/MWNT‐modified electrodes. The direct electron transfer properties of laccase and BOD are thus studied in terms of the bioelectrocatalytic activities of the laccase/MWNT‐modified and BOD/MWNT‐modified electrodes toward the reduction of oxygen and found to be facilitated at the functionalized MWNTs. The possible application of the laccase‐catalyzed O₂ reduction at the laccase/MWNT‐modified electrode is illustrated by constructing a CNT‐based ascorbate/O₂ biofuel cell with the MWNT‐modified electrode as the anode for the oxidation of ascorbate biofuel.