Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

Extraction of humic acids from a natural matrix by alkaline pyrophosphate. Evaluation of the molecular weight of fractions obtained by ultrafiltration

 Fractions of humic acids, resolved by ultrafiltration of extracts from a sample of peat treated with alkaline pyrophosphate solution, have been submitted to high-performance size-exclusion chromatography, with the aim of determining the molecular weight distributions. Anomalous peaks, located at retention volumes higher than those corresponding to the main signal, are present in the elution profiles relative to the lightest fractions. These peaks are more intense when using a refractive index detector rather than a UV detector. Elemental analysis data for the lightest fractions suggested that the spurious peaks are due to the presence of inorganic material. The hypothesis that pyrophosphate interacts with humic acids in the course of the extraction has been confirmed by colorimetric determination of the phosphorus content in the different fractions. As a consequence, the extraction procedure has been modified by using 0.1 mol/L NaOH as extractant. The average molecular weights of the various fractions, following NaOH extraction, result in substantial agreement with those obtained following pyrophosphate solution extraction (if the ‘pyrophosphate peaks’ present in the chromatographic profile are discarded in the calculations). Received: 18 November 1996 / Revised: 18 February 1997 / Accepted: 23 February 1997     

Reagents and synthetic methods 55. New methods for the preparation of t-butyldimethylsilyl triflate and trimethylsilyl triflate.

An expeditious synthesis of t-butyldimethylsilyl triflate is described from triflic acid and t-butyldimethylsilane. Reaction between trichloromethyltrimethylsilane and triflic acid is also reported.     

Why is the partial molar volume of CO2 so small when dissolved in a room temperature ionic liquid? Structure and dynamics of CO2 dissolved in [Bmim+] [PF6(-)

When supercritical CO2 is dissolved in an ionic liquid, its partial molar volume is much smaller than that observed in most other solvents. In this article we explore in atomistic detail and explain in an intuitive way the peculiar volumetric behavior experimentally observed when supercritical CO2 is dissolved in 1-butyl-3-methylimidazolium hexafluorophosphate ([Bmim+] [PF6(-)]). We also provide physical insight into the structure and dynamics occurring across the boundary of the CO2 ionic liquid interface. We find that the liquid structure of [Bmim+] [PF6(-)] in the presence of CO2 is nearly identical to that in the neat ionic liquid (IL) even at fairly large mole fractions of CO2. Our simulations indicate, in agreement with experiments, that partial miscibilities of one fluid into the other are very unsymmetrical, CO2 being highly soluble in the ionic liquid phase while the ionic liquid is highly insoluble in the CO2 phase. We interpret our results in terms of the size and shape of spontaneously forming cavities in the ionic liquid phase, and we propose that CO2 occupies extremely well-defined locations in the IL. Even though our accurate prediction of cavity sizes in the neat IL indicates that these cavities are small compared with the van der Waals radius of a single carbon or oxygen atom, CO2 appears to occupy a space that was for the most part a priori "empty".     

A goldstone mode in the Kawasaki-Ising model

The hydrodynamic regime of superfluids is dominated by a Goldstone mode corresponding to a spontaneously brokenU(1) symmetry. In this article we map the Kawasaki-Ising model for a classical lattice gas into a quantum model for a superfluid and establish a connection between the normal density fluctuations of the first and the Goldstone mode of the second. The fact that the quantum model we obtain describes a superfluid derives from an inequality by Penrose and Onsager which gives a lower bound to the Bose-Einstein condensate density. Mathematically, the Goldstone mode can be described by means of a quantum extension of the local algebra of the Ising model. The classification of its irreducible representations requires an additionalU(1) phase factor and the correspondingU(1) gauge symmetry is spontaneously broken for all finite values of the temperature and of the density.     

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.     

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.     

New Factorial Designs to Evaluate Chemisorption of Divalent Metals on Aminated Silicas

Adsorption processes of Cu(II), Co(II), and Hg(II) on two aminated silica gel surfaces with immobilized ethylenediamine and diethylenediamine groups were studied by a new 2(3) full factorial design. Two metal quantity levels, temperatures of 25 and 50 degrees C, and silica amounts of 100 and 200 mg were employed. Our study indicates that higher factorial design levels increase adsorption for all metals evaluated, with the exception of the mass parameter. Adsorption is also significantly affected by important antagonistic and synergistic effects involving all factors. Both functionalized silica gel surfaces present higher interactions and good perspectives in preconcentration studies for mercury. The factorial design results are also discussed in terms of some solvation properties for each of the metals studied. Copyright 2001 Academic Press.