关于B-凸空间及其上黎斯算子West分解

给出 Ｂａｎａｃｈ空间列｛Ｘｉ｝ｉ＝１∞的 ｌｐ乘积Ｂ－凸的特征刻划, 证明Ｂ－凸空间上的每个黎斯算子可Ｗｅｓｔ分解,即分解成一个紧算子和一个拟幂 零算子的和．     

Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.     

The projection method for computing multidimensional absolutely continuous invariant measures

We present an algorithm for numerically computing an absolutely continuous invariant measure associated with a piecewiseC ² expanding mappingS: on a bounded region R ^N. The method is based on the Galerkin projection principle for solving an operator equation in a Banach space. With the help of the modern notion of functions of bounded variation in multidimension, we prove the convergence of the algorithm.     

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.     

Some remarks on the operator of Foias and Williams

In this paper we study the Foias-Williams operator

where , and is a Hankel operator with symbol . We exhibit a relationship between the similarity of to a contraction and the rate of decay of , the absolute values of the Fourier coefficients of the symbol .

     

Spectrally determined growth is generic

Let be the infinitesimal generator of a -semigroup of operators in a Hilbert space. We consider the class of operators , where is bounded. It is proved that the spectrum of determines the growth of the associated semigroup for ``most" operators (in the sense of Baire category).

     

Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

Evaluation of the limit of performance of an analytical method based on a statistical calculation of its critical concentrations according to ISO standard 11843: Application to routine control of banned veterinary drug residues in food according to European Decision 657/2002/EC

Traceability of the measurement of analytical parameters capable of evaluating the performance of methods is an important concept for the assessment of quality for the routine control, especially for residue monitoring of non-authorized medicinal substances in food from animal origin. The European Decision no. 657/2002/EC recommends to calculate two statistical limits, CCα and CCβ, which allow to evaluate the critical concentrations above which the method reliably distinguish and quantify a substance taking into account the variability of the method and the statistical risk to take a wrong decision. The calculation, which can be derived from the ISO standard no. 11843 is applied on a routine basis. An example displays a very simple way for evaluating the performance of an LC-MSMS method which has been validated a few years ago and is qualified onto a Micromass Quattro LCZ tandem mass spectrometer to monitor and confirm the nitrofuran metabolite residues in food from animal origin. Community Reference Laboratory for Antimicrobial Veterinary Drug Residue Control in Food from Animal Origin     

The effect of capillary column diameter on the performance of thermal conductivity detectors

The concentration sensitivity of a thermal conductivity detector (TCD) depends, among other factors, on the amount of sample mixture in the detector's sensing cell. Since the cell volume has to be appropriately matched with column diameter, it makes the concentration sensitivity of a TCD dependent on column diameter and, therefore, on the speed of gas chromatography. Through reduction of column diameter, higher speed tends to lead to a reduction in the concentration sensitivity of the cell. The factor which the most directly affects the concentration sensitivity of a TCD cell is the heat power conducted through the cell. The higher the power, the greater the sensitivity. The limit of detection of a TCD depends on the concentration-sensitivity of its cell and on the level of statistical errors in the measurement. The errors increase with increasing analysis speed. As the column diameter is reduced, the errors cause additional worsening (on top of the decrease in concentration sensitivity) of the detection limit, dynamic range, and other performance characteristics of the TCD.     

Patterns in the precision of quantitative data from multicomponent gas chromatographic or gas chromatographic-mass spectrometric analysis

The dispersion of the quantitative results in the analysis of volatile compounds from multicomponent mixtures by different fractionation techniques (solid-phase microextraction and direct thermal desorption) followed by GC or GC-MS presents nonrandom patterns related to the existence of different factors in the fractionation process or in the chromatographic separation which affect, to a different extent, the recovery of the sample components. Statistical techniques have been used to show the relative importance of these factors. The improvement in data precision achieved by using volatile compound concentration ratios is discussed.