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51.
Wavelet transform is a versatile time‐frequency analysis technique, which allows localization of useful signals in time or space and separates them from noise. The detector output from any analytical instrument is mathematically equivalent to a digital image. Signals obtained in chemical separations that vary in time (e.g., high‐performance liquid chromatography) or space (e.g., planar chromatography) are amenable to wavelet analysis. This article gives an overview of wavelet analysis, and graphically explains all the relevant concepts. Continuous wavelet transform and discrete wavelet transform concepts are pictorially explained along with their chromatographic applications. An example is shown for qualitative peak overlap detection in a noisy chromatogram using continuous wavelet transform. The concept of signal decomposition, denoising, and then signal reconstruction is graphically discussed for discrete wavelet transform. All the digital filters in chromatographic instruments used today potentially broaden and distort narrow peaks. Finally, a low signal‐to‐noise ratio chromatogram is denoised using the procedure. Significant gains (>tenfold) in signal‐to‐noise ratio are shown with wavelet analysis. Peaks that were not initially visible were recovered with good accuracy. Since discrete wavelet transform denoising analysis applies to any detector used in separation science, researchers should strongly consider using wavelets for their research. 相似文献
52.
1.CompleteLanglandsParametersandL-PacketsInthissectionwereviewsomebasicfactsfrom[1].Wedenotethesetsofrealnumbers,complexnumbersandintegersbyR,CandZ,respectively.SupposethatGisaconnectedcomplexreductivealgebraicgroup.WehaveanextendedgrouPGrforG,andvGrisanE-groupforGr.WedenotethesetofLanglandsparametersandthesetofgeometricparametersforvGrbYp(vG')andX(VG'),respectively.ThereisanaturalmapfromP(VG')toX(vG').ItinducesabijectionfromequivalenceclassesofLanglandsparameterstogeometricparamet… 相似文献
53.
54.
In the last paper, the geometry of the Sz.-Nagy-Foia
model for contraction operators on Hilbert spaces was used to advantage in several problems of multivariate analysis. The lifting of intertwining operators, one of the basic results from the Sz.-Nagy-Foia
theory, is now recognized as the most adequate operatorial form of the deep classical results of the extrapolation theory. The labeling of the exact intertwining dilations given by [1]Acta Sci. Math. (Szeged) 40 9–32] and the recursive methods used there open a broad perspective for using the Sz.-Nagy-Foia
model in multivariate filtering theory. In this paper, using the notion of correlated action (see [5 and 6] Rev. Roumaine Math. Pures Appl. 23, No. 9 1393–1423]) as a time domain, a linear filtering problem is formulated and its solution in terms of the coefficients of the analytic function which factorizes the spectral distribution of the known data and the coefficients of an analytic function which describes the cross correlations is given. In some special cases it is shown that the filter coefficients can be determined using recursive methods from the intertwining dilation theory, of the autocorrelation function of the known data and an intertwining operator, interpreted as the initial estimator given by the prior statistics. 相似文献
55.
The objective is to derive the probability distribution of the frequency of occurrence of a subsequence within a nucleotide
sequence under the hypothesis that the four nucleotides occur at random and with equal probability.
We also consider the Compound Poisson approximation for the same distribution. The exact probability distribution can be obtained
by the finite Markov chain imbedding technique introduced by Fu and Koutras (1994), however we can manage the case as well
if the probabilities are not all equal. The compound Poisson approximation by Stein-Chen's method can be used to develop an
approximate probability distribution with proper setting of the definition of the sets of dependence. Such structure gives
a bound on the total variation distance, which tends to get relatively larger as the frequency goes up.
AMS 2000 Subject Classification: Primary: 60E05; Secondary: 60J10 相似文献
56.
在C~n中有界凸Reinhardt域上讨论了一类介于凸映射类与星形映射类之间的“完全准凸映射类”.特别地,在C~n中的多圆柱上给出了完全准凸映射的分解定理,得到了多圆柱上判别凸映射的一个改进的充分条件. 相似文献
57.
I. Kurkova 《Journal of statistical physics》2003,111(1-2):35-56
We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution
N
i=1
i
i
/N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D
0
0+D
1
1, with random weights D
0, D
1, while for the second one it is
0. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N. 相似文献
58.
We present the implementation into the MOLPRO package of a model for the interaction of a central system with its surrounding environment. The properties of a target system enclosed by a noncovalently bound environment or solvent are modeled as those of a system embedded into the effective pseudopotential arising from the exact electrostatic Coulomb potential and the approximated exchange-repulsion potential. For the latter we use the charge-density overlap model, which relates the exchange-repulsion interaction energy between two species with the overlap of their ground-state electron charge densities. The solutions of the modified Hartree-Fock equations for the target system are obtained self-consistently. This way the exchange-induction effects arising from the converged electron-charge density of the embedded system are implicitly included. Inclusion of the correlation effects is provided by the use of post-Hartree-Fock and density-functional techniques available in the MOLPRO package. The computational and conceptual advantages provided by this approach are shown in the calculation of the dipole polarizabilities of halide and chalcogenide anions in different environments. 相似文献
59.
60.
Alvaro Bustinduy 《Proceedings of the American Mathematical Society》2003,131(12):3767-3775
We prove that a complete polynomial vector field on has at most one zero, and analyze the possible cases of those with exactly one which is not of Poincaré-Dulac type. We also obtain the possible nonzero first jet singularities of the foliation at infinity and the nongenericity of completeness. Connections with the Jacobian Conjecture are established.