Multivoice Littlewood-Paley-Meyer wavelets and diagonal dominated pseudodifferential operators

Given a pseudodifferential operator (p) satisfying certain growth and smoothness conditions in momentum space, we construct a wavelet basis ofL ²( ^d ) in which the corresponding matrix is diagonal dominated with arbitrarily small prefactor.     

The adiabatic approximation for quantum spin systems with a spectral gap

Summary We estimate the accuracy of the adiabatic approximation in predicting the time evolution of local observables for an XY quantum magnet with a slowly variable external magnetic field. The system evolves according to the natural Hamiltonian dynamics and the spectral gap produced by the magnetic field is assumed to be large with respect to the term inducing quantum fluctutions. The proof is based on a finite order truncation of a time dependent cluster expansion in inverse powers of the time scale . In the analytic case, we show that the accuracy of this truncated expansion is of order for any >1. If the time dependent perturbation is suddenly switched on at time zero and switched off at time , the accuracy of the adiabatic approximation is proven to be of orderO( ^–1.     

Determination of coplanar and non-coplanar polychlorinated biphenyls in human serum by gas chromatography with mass spectrometric detection: electron impact or electron-capture negative ionization?

A time- and cost-saving method for the congener-specific analysis of polychlorinated biphenyls (PCBs) in human serum has been developed and validated. After two fast extraction and clean-up steps, analyses were performed using gas chromatography coupled with mass spectrometry with single ion monitoring (GC/SIM-MS), either in electron impact (EI) or electron-capture negative ionization (ECNI) mode. For the determination of dioxin-like congeners, an improvement in EI-MS sensitivity is desirable and use of NI is thus preferred. The procedure was validated for 12 dioxin-like congeners by analyzing spiked samples on three different days and using (13)C(12)-labelled analogues as internal standards. When using an NCI source, the limit of quantification was assessed at 0.01 microg/L, except for PCBs #77 and #81, which cannot be reliably detected below 0.05 microg/L. For the lower chlorinated non-dioxin-like congeners, NI offers less selectivity because of limited fragmentation. Electron impact ionization and electron-capture negative ionization mode can therefore be considered to be complementary for the determination of PCB congeners in the general population.     

The First VOPO4·2H2O Intercalation Compound Synthesized through a Solid-State Reaction at Room Temperature

This communication reports the first intercalation into VOPO₄·2H₂O performed through a solid-state reaction at room temperature. Ethyleneurea, EU (2-imidazolidone) was intercalated into the oxovanadium phosphate by grinding in a mortar stoichiometric amounts of both reagents at room temperature for 30 min. C, H and N elemental analyses of the obtained intercalation compound gave the formula VOPO₄·(EU)·H₂O. The profile of the absorption bands due to the VOPO₄ lattice vibration around 1000 cm⁻¹ was retained after reaction, providing evidence that an intercalation compound and not merely a salt of V-P-O species was produced. For α-VOPO₄·2H₂O, the interlayer distance is 0.75 nm, whereas for the EU inter-calation compound it is 0.95 nm. The obtained SEM micrographs show that the microstructure of VOPO₄·2H₂O is changed after reaction, with a total exfoliation of the oxovanadium matrix.     

Electronic and Steric Influence of Axial and Equatorial Ligands in Vitamin B12 Model Complexes Derived from Cobaloxime: Electrochemical and 59Co-NMR Studies

In four series of strictly related organocobalt complexes, derived from cobaloximes by replacement of the O…H…O with O…-BF₂…O and/or (CH₂)₃ groups, the trends of ⁵⁹Co-NMR shielding and electrochemical data are discussed. A largely parallel behaviour of the plots of E_1/2(I) values for the first Co(III)/Co(II) electron transfer vs. the ₅₉Co chemical shifts reflects the similar sensitivity of the two parameters to a change in electron affinity of the central metal ion due to a variation of the organic group R. E_1/2(II) values for the second Co(II)/CO(I) electron transfer are less sensitive to the change of R, but the trend of the plot vs. δ(₅₉Co) is still parallel in the four series. Consistent deviations from a roughly linear dependence of E_1/2(I) on pK_a of the hydrocarbon acid corresponding to R, on Taft constant s?_* and on ⁵⁹Co shielding are noticed for the isopropyl derivatives and attributed to a steric effect. This was confirmed in a series of R? Co(DMG)pyridine complexes in which ⁵⁹Co shielding decreases steadily with increasing steric parameter E_s (Taft) of the alkyl group. There is experimental evidence from X-ray data that δ(⁵⁹Co) decreases with an increase of the Co? C bond length, illustrating steric hindrance in alkyl coordination to be responsible for the decreased shielding of the ⁵⁹Co nucleus. The relative displacements of the graphic displays for the different series reflect the effect of changes in electron affinity of the redox center, due to the equatorial ligand, which, in turn, is caused by variations in the electron-withdrawing power due to the introduction of the BF₂ group and by the change from ?2 to ?1 valence of the (CH₂)₃-capped ligands.     

Catalytic oxidation of thiols to disulfides using iodine and CeCl3·7H2O in graphite

A very simple procedure for the efficient oxidation of thiols to disulfides catalyzed by I₂/CeCl₃·7H₂O in graphite and ethyl acetate as the solvent, in an open system at room temperature is described. The reaction proceeds cleanly under mild conditions and was performed with aromatic, aliphatic, and heterocyclic thiols.     

Sterols with Cyclopropane-Containing Side Chains: Synthesis and Acid Isomerization

To test the eventual involvement of sterols with a cyclopropane containing side chain in bio-methylation processes, 24,25-methanocholest-5-en-3β-ol ( 5 ) and 24,25-methano-26-methylcholest-5-en-3β-ol ( 6 ) were synthesized. Together with the naturally occurring cyclopropane petrosterol ( 1 ), they were submitted to acid isomerization to provide chemical models for some of their potential metabolites.     

Synthetic tanning agents. Characterization,control of synthesis and assessment of correlations between product composition and taning properties by reversed-phase high performance liquid chromatography

Summary Gradient elution RP-HPLC has been applied to the separation of the constituents of synthetic tanning agents. Information obtained from the chromatographic results was used to assess the possibility of optimizing the conditions of synthesis, to find out the number of species formed and to make a start at correlating the composition of the tanning agents and their properties.     

In situ disorder-order transformation in synthetic gallosilicate zeolites with the NAT topology

Here, we report that synthetic gallosilicate molecular sieves with the NAT topology and Si/Ga ratios close to but slightly higher than 1.50 undergo an in situ transformation under their crystallization conditions. The materials have been studied ex situ by using powder X-ray diffraction, elemental and thermal analyses, and multinuclear MAS NMR. The transformation is characterized by a change in the distribution of Si and Ga of the NAT framework, from a quite (but not completely) disordered phase to a very highly (but not completely) ordered one, accompanied by a change from tetragonal to orthorhombic symmetry. During most of the solution-mediated transformation, no noticeable signs of fresh precipitation, phase segregation, or changes in the chemical composition are detected. Intermediate materials show variations in the degree of Si-Ga ordering and orthorhombic distortion and are not physical mixtures of the disordered and ordered phases. Ab initio calculations strongly suggest a preferential siting of Si in the tetrahedral sites involved in a smaller number of 4-rings in the NAT topology (i.e., the low multiplicity site). The cost of violations of Loewenstein's rule has also been calculated. For this topology and chemical composition the preferential siting and Loewenstein's rule drive together the system to the ordered configuration. A Monte Carlo sampling procedure affords a reasonable model for the initial, mainly disordered state, which fits well within the experimental disorder-order series.