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.     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

An Efficient and Simple Entry to N-Substituted beta-Enamino Acid Derivatives from 2-Alkyl-2-oxazolines and 2-Alkyl-2-thiazolines

Reaction of azaenolates of 2-alkyl-oxa(thia)zolines 6 with imidoyl chlorides 7 as electrophiles to furnish masked N-substituted beta-enamino acid derivatives 1-2 in 70-90% yield is described. Alternative routes are discussed. Compounds 1-2 generally appear in one tautomeric form, imino or enamino, depending on the nature of the imidoyl chloride. The configuration of the enamino moiety (Z) and the conformation (s-cis) of compounds 1-2 obtained were established by an NMR study and unequivocally set by nuclear Overhauser effect difference experiments. An X-ray structure of compound 1e is also reported, showing a strong intramolecular NH.N hydrogen bond. Ab initio calculations (HF/3-21G and HF/3-21+G) have been carried out on several representative examples (1e, 1p, and 1l) in an attempt to support and provide the correct geometry of these derivatives. Structural considerations among the possible isomers of compounds 1 are discussed. From these studies it was concluded that the theoretical calculations agree with the experimental results. In addition, a very simple one-pot procedure for the preparation of masked N-substituted alpha-alkylated beta-enamino acid derivatives 2 from 6, 7, and different alkyl halides (R(3)Y) is described.     

Polarization of the Electrical Double Layer. Time Evolution after Application of an Electric Field

Electrophoresis is one of the electrokinetic phenomena most widely investigated, both from a fundamental point of view and as a research tool in academia and industry. However, the dependence between electrophoretic mobility and zeta potential is, in a general case, far from simple, because of the many physical processes involved. In this work, we first describe qualitatively and (in some cases) quantitatively the time behavior of the dipole moment induced in the electrical double layer by an applied electric field. Further, a simple relationship is deduced between the dipole moment and the electrophoretic mobility. Through the analysis of the time dependence of the former, it is possible to resolve the different contributions to the stationary values of the mobility. Three characteristic relaxation times are distinguished in the time evolution of the dipole moment: tau(H) (the time needed for hydrodynamic flows to be established), tau(MW) (time for ionic electromigration to develop), and tau(VD) (after this time, diffusion flows are established in the system, and the double layer polarization is complete). This means that different mechanisms are operating on the double layer for different times after the application of the field, and that computing the mobility at such different times is equivalent to calculating the steady-state electrophoretic mobility under different approximations. A comparison is shown between estimated and computed mobility values as functions of time and of zeta potential, confirming the validity of the asymptotic calculations. Copyright 2000 Academic Press.     

Application of partial least-squares regression to the resolution of highly correlated spectra. Simultaneous spectrofluorimetric determination of Al(3+), Ga(3+) and In(3+)

The simultaneous spectrofluorimetric determination of mixtures of aluminium, gallium and indium as their 8-hydroxyquinoline complexes following extraction into chloroform is studied. The high collinearity of the spectra hindered their resolution by multiple linear regression (MLR) methodology; therefore, experimental data were processed by partial least-squares regression (PLSR) methodology. A previous step in the study of three-dimensional fluorescence spectrum is possible to select the best information to quantify this system with high collinearity. Finally the optimal conditions for quantitation, the best data preprocessing procedure and the most suitable spectral mode for calibration were established. Using an external set allowed the three analytes to be determined simultaineously at concentrations below 1 mug ml(-1) with errors less than 10% for aluminium and indium, and 15% for gallium.     

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.     

Infrared Study of Solid Dispersions of β-Cyclodextrin with Naphthalene Derivitaves

The inclusion complexes of β-cyclodextrin (β-CD) with naphthalene and some of its derivatives in the solid state have been studied by infrared spectroscopy. Digital subtraction, deconvolution and curve fitting have been used to investigate the interactions between the naphthalene derivatives andβ-CD. Several preparation methods for the solid dispersions have been tested, using FTIR as an effective tool to evaluate the interactions at the molecular level. The effects of temperature and humidity on the spectra have been also analyzed. A carbonyl moiety in the guest molecule can increase the stability of the complex by establishing specific interactions with the hydroxyl groups of the CD cavity rims. The stability of the complexes is higher for 2-naphthylacetate than that for 1-naphthyl acetate, andso is the degree of association of its carbonyl groups. On the other hand, 2-acetylnaphthaleneforms very stable inclusioncomplexes although its carbonyl groups appear to be significantly less associated.