极移振幅和相位的时—频域统计分析

极移的各种周期变化与地球上的许多现象，如地震等，有某种紧密的联系。研究这些周期变化及其成因是相当重要的。利用新的观点来分析这 一经典问题。首先将复小波变换引入极移的研究之中，了解极移的复小波变换及各种周期变化。提出小波变换对数幅相图的概念，并对小波变换的振幅和相位的变化分别进行了分析。结果表明：极移的模值以及小波变换的模值都有某种周期的变化。小波变换尺度比较小时，可以描述短周期的变化；小波变换尺度大时可以描述较长周期的变化。     

Comparison between Deprit and Dragt-Finn perturbation methods

In this paper, the relationship between the Dragt-Finn transform and the classical Lie transform introduced by Deprit is discussed. The relative performance of the algorithms used for the computations of the transformed functions is compared, and the relation between their generators is given. These generators produce the same transform which insures the construction of the same invariants.     

太阳黑子数的子波分析

本文讨论了子波变换用于信号突变检测的原理，用它分析了１７００－１９９３年间的太阳黑子数的年均值．精确地检测到了太阳活动的突变点，用相邻两个突变点的时间长度求得了不同尺度下太阳黑子变化的周期．结果表明：利用子波变换检测太阳黑子周期与传统方法相比具有独到之处．     

Inversion of synchrotron spectra

The problem of synchrotron radiation spectra is treated from the viewpoint of deconvolving the spectrum of ultrarelativistic source electrons from the observed photon spectrum. It is shown that for homogeneous sources the problem amounts to inversion of a Meijer transform with a modified Bessel finction kernel. A precise analytic inversion is only possible in the complex plane but Meijer transform tables are available for a wide range of functions. More convenient inversion formulae prove possible by use of a Laplace transform approximation or by analysing the spectra in terms of their integral moments. The filtering property of the transform is also established showing that the contribution to the synchrotron spectrum of high frequency components in the electron spectrum declines exponentially with their frequency. Thus, as with other Laplace-like transforms, only a few terms in an electron spectrum expansion can be deconvolved for any plausible noise level in the synchrotron spectrum.     

Relative phase analyses of long-term hemispheric solar flare activity

Wavelet transform methods, including the continuous wavelet transform, cross-wavelet transform and wavelet coherence, have been proposed to investigate the phase synchrony of the monthly mean flare indices in the time interval 1966 January–2007 December in the solar northern and southern hemispheres, respectively. The Schwabe cycle is the only period of statistical significance, and its mean value is 10.7 yr for the monthly mean flare indices in the northern hemisphere but slightly smaller, 10.1 yr, in the southern hemisphere – this should lead to phase asynchrony between the two. Both the cross-wavelet transform and wavelet coherence analyses show asynchronous behaviour with strong phase mixing in the high-frequency components of hemispheric flare activity, and strong synchronous behaviour with coherent phase angles in the low-frequency components, corresponding to the period-scales around the Schwabe cycle. The northern flare activity should lead the southern for the low-frequency components.     

The solution of a time-dependent problem in radiative transfer

The time-dependent equation of radiative transfer for a finite, plane-parallel, non-radiating, and isotropically scattering atmosphere of arbitrary stratification is solved by using the integral equation method. The medium is taken to be inhomogeneous. The Laplace transform is used in the time domain. It is seen that the obtained solutions are reducible to the corresponding ones for steady-state problems by simply changing the Laplace transform parameter to zero.     

Evaluation of the short-term periodicities in the flare index between the years 1966–2002

The short-term periodicities of the flare index are investigated in detail using Fourier and wavelet transforms for the full disc and for the northern and the southern hemispheres of the Sun separately over the epoch of almost 4 cycles (1966–2002). The most pronounced power peaks were found by the Fourier transform to be present at 25.6, 27.0, 30.2, and 33.8 days. The wavelet transform results show that the occurrence of periodicities of flare index power is highly intermittent in time. A comparison of the results of the Fourier transform and the time-period wavelet transform of the flare index time series has clarified the importance of different periodicities, whether they are or are not the harmonics of the basic ones, as well as the temporal location of their occurrence. We found that the modulation of the flare index due to the 27-day solar rotation is more pronounced during the declining portion of solar cycle than during the rising portion.     

Wavelet analysis and applications to some dynamical systems

For about five years the wavelet transform technique has given interesting results in a great number of different fields such as mathematics, quantum mechanics, signal analysis and image processing, cluster analysis... The wavelet transform appears as a new time-frequency method which is particularly well-suited to detect and to localize discontinuities and scaling behaviours in signals. The main properties of the wavelet transform and its improvements over classical analyzing methods are summarized. Some results among the first applications to the dynamical systems are presented: solution of partial differential equations, fractal and turbulence characterization, and asteroid family determination from cluster analysis.     

Wavelet Analysis: the effect of varying basic wavelet parameters

The most commonly used methods to analyse (observed) quasi-periodic signals are standard techniques such as Fourier and wavelet analysis. Whereas a Fourier transform provides information on the dominant frequencies, wavelet analysis has the added advantage of providing the time localisation of the various frequency components. The usefulness and robustness of wavelet analysis is investigated by varying the different parameters which characterise the `mother' wavelet. We examine the effect of varying these parameters on the temporal and frequency resolution and the damping profile, which can be obtained from the wavelet transform. Additionally, the effect of a changing periodicity on the wavelet transform is investigated. Both simple harmonic functions and intensity oscillations observed by TRACE are used to demonstrate the various advantages and disadvantages of the different methods. In general, using the Paul wavelet or a smaller value of the wavelet parameter k provides a better time resolution, whereas the Morlet wavelet or a larger value of k improves the frequency resolution. Overall, our results indicate that great care is needed when using a wavelet analysis and that all the possible factors that could affect the transform should be taken into consideration.     

Image compression by means of wavelet transform - application to solar observations

Images and spectra contain a large amount of data. Therefore the question arises, how this data can be decreased or compressed without losing important detail. The discrete wavelet transform is a tool which can be used to compress data because of its good approximation properties. It is very easy to implement and requires approximately the same amount of calculation as the fast Fourier transform. It has the advantage of giving information both in time and frequency. Since most of the coefficients in the transformed data are very small compared to the maximum values, which means that they do not contribute much to the transform, a large number of them can be neglected. Although some data get lost, the physical results deduced from the data remain the same, as is demonstrated by various examples. By this method it is even possible to compress data containing much noise to high-compression ratios.     

Wavelet analysis of the standard map: Structure and scaling

Wavelet analysis is applied to distributions of points generated by iterating the standard map. The initial condition is chosen so that the points fill the largest chaotic region. When the standard map parameterk=1.3, the distribution of points contains many voids corresponding to islands in the chaotic region. The wavelet transform is dominated by contributions from these islands. Fork=10 the chaos fills phase space and no structure is apparent; the wavelet transform reveals statistical fluctuations in the distribution of points.     

A Multiscale Vision Model to Analyse Field Astronomical Images

We have implemented a multiscale vision model based on the wavelet transform to analyse field astronomical images. The discrete transform is performed by the à trous algorithm. The vision model is based on the notion of significant structures. We identify the pixels of the associated wavelet transform space (WTS) with the objects. For each scale a region labelling is carried out. An interscale connectivity graph is then established. In accordance with some rules that permit false detections to be removed, the objects and their sub-objects are identified. They define respectively trees and sub-trees in the graph. In this way, the identification of the WTS pixels of the tree related to a given object leads to the reconstruction of its image by the conjugate gradient method. The model has been tested successfully on simulated images of stars and galaxies which allow us to show the capabilities of the detection and restoration procedures of the model. Finally, tests on real images show that one can analyse complex structures better than with classical astronomical vision models.     

The Near-Nuclear Study of Comet Hale Bopp

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｍｅｔＨａｌｅ Ｂｏｐｐ(Ｈａｌｅ,1 995 )ｉｓａｎｅｘｔｒｅｍｅｌｙｂｒｉｇｈｔｃｏｍｅｔ.Ｉｔｈａｓｂｅｅｎａｃｔｉｖｅｗｈｅｎｄｉｓｃｏｖ ｅｒｙａｔ 7ＡＵｆｒｏｍｔｈｅＳｕｎ(Ｓｅｋａｎｉｎａ ,1 996 ) .Ｔｈｅｌｏｃａｌｉｚｅｄｅｊｅｃｔｉｏｎｏｆｄｕｓｔａｎｄｇａｓｐｒｏｄｕｃｅｄｃｏｍ ｐｌｅｘｃｏｍａｓｔｒｕｃｔｕｒｅｔｈａｔｃａｎｂｅｕｓｅｄｔｏｓｔｕｄｙｔｈｅｅｊｅｃｔｉｏｎｓｐｅｅｄａｎｄｎｕｃｌｅｕｓｒｏｔａｔｉｏｎｐｅｒｉｏｄ .Ｆｕｒ ｔｈｅｒｍｏｒｅ…     

小波变换及其在天文地球动力学中的应用

小波变换是近几年来国际上流行的一种新的数学分析方法，近年来在天文学和天文地球动力学领域中得到了广泛的应用，文中对连续小波的概况，原理，有关技术及其在天文地球动力学中的应用作了简单而系统的介绍。     

Possible Influence of the 11-year Solar Cycle on Precipitation in Huashan Mountain of China over the Last 300 Years

Taking into account reconstructed precipitation time series in Huashan mountain area of China on the one hand and sunspot numbers observations on the other hand, the authors used here continuous wavelet transform and cross wavelet transform to investigate possible connection between the two sets of indicators. The analysis was performed over the last 300 years: it is found that solar activity influences precipitation in that geographical area of China to some extent, with an excess of 5% statistical significance level red noise over the 11-year solar activity cycle.