小波变换在多粒子末态相空间分析中的应用

利用小波变换这一数学工具，对于由随机级联α模型模拟产生的多数子末态相空间的几率分布，进行了分析与讨论，得出利用小波变换可直接对末态相空间粒子分布的实验数据进行几率矩、关联矩方面的分析与研究；并且提供了具体的计算方法.     

Wavelet Space Partitioning for Symbolic Time Series Analysis

A crucial step in symbolic time series analysis （STSA） of observed data is symbol sequence generation that relies on partitioning the phase-space of the underlying dynamical system. We present a novel partitioning method, called wavelet-space （WS） partitioning, as an alternative to symbolic false nearest neighbour （SFNN） partitioning. While the WS and SFNN partitioning methods have been demonstrated to yield comparable performance for anomaly detection on laboratory apparatuses, computation of WS partitioning is several orders of magnitude faster than that of the SFNN partitioning.     

Interference in Phase Space

A central problem in quantum mechanics is the calculation of the overlap, that is, the scalar product between two quantum states. In the semiclassical limit (Bohr's correspondence principle) we visualize this quantity as the area of overlap between two bands in phase space. In the case of more than one overlap the contributing amplitudes have to be combined with a phase difference again determined by an area in phase space. In this sense the familiar double-slit interference experiment is generalized to an interference in phase space. We derive this concept by the WKB approximation, illustrate it by the example of Franck-Condon transitions in diatomic molecules, and compare it with and contrast it to Wigner's concept of pseudo-probabilities in phase space.     

基于平稳小波和相空间重构的激光混沌预测

提出了一种激光混沌时间序列预测算法.该算法通过平稳小波分解，将原始数据序列分解为与原序列等长的尺度系数和小波系数，利用坐标延迟理论，重建各级尺度系数和各级小波系数的相空间,再根据混沌吸引子的稳定性和分形性,在相空间中对尺度系数和小波系数进行预测,进而通过平稳小波重构算法,实现了时间序列的非线性预测.该算法对数据可以进行更平滑的处理，比无小波算法预测的时间范围更长.通过仿真试验说明，原始时间数据序列被成功的重建，说明算法能够有效的对非线性动态系统的时间序列进行建模和预测.     

小波相位分析测量成像径向畸变

为了测量光学成像像面各个像素的径向畸变大小,提出将小波变换载频条纹相位分析应用于径向畸变测量。采用正弦载波条纹作为测量模板,把径向畸变转化为径向调制相位。应用条纹相位分析导出径向调制相位和径向畸变的转化关系。采用小波频率估计和相位估计提取变形条纹的相位,由于变形条纹中心点是零畸变,中心点的瞬时频率和相位可以计算参考条纹的基频相位。两种基频相位之差就是与所有像素径向位置畸变分布对应的三维调制相位——称为径向畸变分布。利用校正公式和立方卷积插值算法对彩色畸变图像进行校正,给出详细的理论分析和实验结果。     

小波变换在载频条纹相位分析法中的应用研究

为了克服在非平稳信号分析中傅里叶变换的全局性缺陷,以及窗口傅里叶分析的单一分辨率和伸缩窗口傅里叶分析的尺度不确定性问题,采用伽博解析小波变换技术对空间载频光栅条纹进行相位分析,有效地提取出相对于载频条纹基频的完整相位信息,从本质上解决了上述问题。以三维轮廓术为例,与傅里叶分析进行了对比研究,给出了小波分析应用在空间载频条纹相位分析中详细而完整的理论推导证明、计算机模拟以及实验验证结果。     

小波分析在遥测信号处理中的应用

综述了小波分析的发展现状,通过对比小波变换与短时傅里叶变换之间的差异,指出小波分析是一种多分辨分析方法,特别适合于非平稳信号的分析与处理,并且应用该方法对遥测速变信号进行处理,取得了较好的效果。     

Coulombic Transformation in Momentum Space

We studied the Coulombic transformation of potential in momentum space. The Coulombic transformation is defined as a unitary transformation in momentum space, which is equivalent of the Coulomb–Fourier transformation in coordinate space. The analytic continuation scheme avoids the difficulty which is occurred from the singularity of the Coulomb wave function in momentum space. We adopted the point method to perform the analytic continuation. The validity of the new scheme is checked by comparing with the analytic solution for the Malfliet-Tjon potential. Numerical calculation of the integration was done by separating into four intervals. We demonstrate the high accuracy of our calculation.     

Chaotic Eigenfunctions in Phase Space

We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann–Husimi representations for quantum states as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions which is reminiscent of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on chaotic eigenconstellations, we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions for the constellations which fit quite well the chaotic data. We finally observe that specific dynamical information, e.g., the presence of high peaks (like scars) in Husimi densities, can be recovered from the knowledge of a few long-wavelength Fourier coefficients, which therefore appear as valuable order parameters at the level of individual chaotic eigenfunctions.     

小波分析及其在光谱分析中的应用

近年来,一种被称为小波变换的数学理论和方法成为众多学科关注的焦点,在分析化学领域中,小波分析也逐渐应用于去噪与平滑,数据压缩等方面,本文介绍了小波分析理论并对其光谱分析中的应用进行了综述。     

基于小波变换的红外光谱分析

利用傅里叶变换红外光谱仪,借助OMNI采样器直接、快速、准确地测定了土茯苓及其三种伪品木质部的FTIR谱,采用小波变换分析法对样品进行了详细研究。结果表明：小波变换可以去除噪声和压缩变量,具有运算速度快、分析精度高以及无需去噪后处理等优点, 在红外光谱分析中具有很好的应用前景。     

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.     

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

We propose a new two-fold integration transformation in p-q phase space ∫∫_-∞^∞(dp dq/π)e^2i(p-x)(q-y)f(p,q)≡G( x,y), which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.     

冰晶石的温致相变及熔盐微结构的定量解析

本工作制备了NaF-AlF₃二元系中分子比CR=3的冰晶石晶体,构建了一系列铝氟团簇结构模型,运用显微共焦Raman光谱检测技术与第一性原理理论计算相结合,观察和研究了冰晶石从单斜-立方-六方晶系的温致相变过程,并对熔盐实验拉曼光谱进行散射截面校正、分峰解谱,分析了NaF-AlF₃二元体系中AlF₄^-(622-628 cm^-1)、AlF₅^2-(555-560 cm^-1)、AlF₆^3-(510～515 cm^-1)等阴离子团簇的Raman特征峰位置,定量解析了冰晶石熔盐微结构中的多种阴离子团簇,其摩尔百分含量分别为AlF₄^-(2.7%)、AlF₅^2-(25.8%)、AlF₆^3-(40.4%)、F^-(3...     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

Multiplicity of Phase Transitions and Mean-Field Criticality on Highly Non-Amenable Graphs

We consider independent percolation, Ising and Potts models, and the contact process, on infinite, locally finite, connected graphs. It is shown that on graphs with edge-isoperimetric Cheeger constant sufficiently large, in terms of the degrees of the vertices of the graph, each of the models exhibits more than one critical point, separating qualitatively distinct regimes. For unimodular transitive graphs of this type, the critical behaviour in independent percolation, the Ising model and the contact process are shown to be mean-field type. For Potts models on unimodular transitive graphs, we prove the monotonicity in the temperature of the property that the free Gibbs measure is extremal in the set of automorphism invariant Gibbs measures, and show that the corresponding critical temperature is positive if and only if the threshold for uniqueness of the infinite cluster in independent bond percolation on the graph is less than 1. We establish conditions which imply the finite-island property for independent percolation at large densities, and use those to show that for a large class of graphs the q-state Potts model has a low temperature regime in which the free Gibbs measure decomposes as the uniform mixture of the q ordered phases. In the case of non-amenable transitive planar graphs with one end, we show that the q-state Potts model has a critical point separating a regime of high temperatures in which the free Gibbs measure is extremal in the set of automorphism-invariant Gibbs measures from a regime of low temperatures in which the free Gibbs measure decomposes as the uniform mixture of the q ordered phases. Received: 27 March 2000 / Accepted: 7 December 2000     

Wavelet Transformation and Wigner-Husimi Distribution Function

We find that the optical wavelet transformation can be used to study the Husimi distribution function in phase space theory of quantum optics. We prove that the Husimi distribution function of a quantum state |ψ〉 is just the modulus square of the wavelet transform of with ψ(x) being the mother wavelet up to a Gaussian function. Thus a convenient approach for calculating various Husimi distribution functions of miscellaneous quantum states is presented.     

Phase Measurement in Interacting Fock Space

In this paper we discuss probability operator measure and phase measurement in one mode interacting Fock space.     

Dirac Oscillator in Noncommutative Phase Space

We study the Dirac oscillators in a noncommutative phase space. The results show that the energy gap of Dirac oscillator was changed by noncommutative effect. In addition, we obtain the non-relativistic limit of the energy spectrum.