Multistep methods of numerical integration using back-corrections

A new class of linear multistep methods is proposed for the solution of the equations of motion of certain dynamical systems encountered in celestial mechanics and astrodynamics. These methods are distinguished from the classical predictor-corrector methods in that they permit back-corrections of the solution to be made. As the integration advances in time, the numerical solution is corrected or improved at certain points in the past. The enhanced numerical stability of these methods allows the meaningful application of high-order algorithms. Consequently, stepsizes larger than those attainable with the classical methods may be adopted and thus greater over-all efficiency may be realized. The application of these methods to the problem of determining the orbit of an artificial satellite is accomplished and the results are compared with those obtained using classical methods.     

Two multiderivate multistep (MDMS) integrators

A preliminary survey of multiderivative multistep integrators is carried out. It is found that all of them are much more accurate than the classical linear multistep methods, but most of them have poor stability. After parameter adjustment, two of them (called MDMS I and MDMS II by us) are competitive with or superior to the classical methods in some aspects, such as accuracy and stability. MDMS I behaves especially well in all the cases which have been studied.     

ePSF拟合法与Gaussian拟合法的比较

为了解决哈勃空间望远镜的图像欠采样问题,美国学者Anderson和King提出了精确测量星像位置和通量的有效点扩散函数(ePSF—effective point-spread function)拟合法。然而,他们却不加比较地将其应用于地面CCD图像中星像的位置高精度测量。因此,我们试图将ePSF拟合法与经典的高斯函数(Gaussian)拟合法作比较研究。调用CFITSIO库生成模拟的背景图像,并应用不同参数条件下的星像轮廓模型产生非欠采样的星像。最后,分别采用ePSF拟合法与Gaussian拟合法对这些星像进行拟合,并对它们的拟合精度进行比较。实验结果表明,在非欠采样的图像中这两种算法对星像位置的测量几乎是等精度的。     

Studies in the application of recurrence relations to special perturbation methods

The numerical integration of the differential equations describing dynamical systems has been shown in previous papers of this series to be most effectively accomplished by an explicit Taylor series method.In this paper we show that one explicit Taylor series method, developed earlier in this series and which appears to possess a high degree of versatility, yields considerable gains in efficiency over classical single-step and multi-step methods. (In this context efficiency is a measure of the time taken to carry out a calculation of a specific accuracy).For a given accuracy criterion governing the local truncation error (LTE) it is found that the Taylor series method is generallytwice as fast as the classical multi-step method and up totwenty times faster than the classical single-step method.     

Orbit determination by four observations

An elliptic orbit is determined from two short-arc pairs of observations at different oppositions by the angular momentum integral. Other methods for initial orbit determination than the classical do exist.     

Expansion of the planetary disturbing function

Some methods are described for the expansion of the disturbing function in planetary theory. One method uses the classical binomial expansion theorem or a successive approximation process derived from it. Another method is a direct application of the Laplace series expansions. For both methods it is proposed to first prepare the series to be manipulated by a scaling operation. These methods can be applied either in a literal or in a numerical form, or any combination of both, but they are especially designed for use on a large scale digital computer with standard Poisson series programs. No usage is made of Newcomb operators or derivatives of Laplace coefficients.     

Wavelet Analysis Algorithm for Synthetic Pulsar Time

The pulsar time defined by a single pulsar is affected by several noises and in order to weaken their effects and acquire a much more stable time scale we define a synthetic pulsar time from many single pulsar times. Synthesis of the two pulsars, PSR B1855 + 09 and PSR B1937 + 21 is implemented by two methods: the classical weighting algorithm and the wavelet decomposition algorithm. The results are compared. The classical weighting algorithm is unable to take into consideration the different degrees of stability at different frequencies while the wavelet algorithm can, and thereby get better results.     

The periodicity of solar activity cycles

On the basis of published Wolf Numbers and Schove Row, solar activity cycles in the interval of 11 to hundreds of years have been investigated. In this case the method of investigation of pulsating stars showing the Blazhko effect was applied. The elements of cycles and O-C were calculated and compared with results of solar activity parameters determined by classical methods.     

Comparison of neural network and McNish and Lincoln methods for the prediction of the smoothed sunspot index

In this paper we propose a comparison between two methods for the problem of long-term prediction of the smoothed sunspot index. These two methods are first the classical method of McNish and Lincoln (as improved by Stewart and Ostrow), and second a neural network method. The results of these two methods are compared in two periods, during the ascending and the declining phases of the current cycle 22 (1986–1996). The predictions with neural networks are much better than with the McNish and Lincoln method for the atypical ascending phase of cycle 22. During the second period the predictions are very similar, and in agreement with observations, when the McNish and Lincoln method is based on the data of declining phases of the cycles.     

Significance of periodogram peaks and a pulsation mode analysis of the Beta Cephei star V403 Car

We discuss some commonly used methods for determining the significance of peaks in the periodograms of time series. We review methods for constructing the classical significance tests, their corresponding false alarm probability functions and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We discuss the concepts of independent frequencies and oversampling in periodogram analysis. We then compare the results of new Monte Carlo simulations for evenly spaced time series with results obtained previously by other authors, and present the results of Monte Carlo simulations for a specific unevenly spaced time series obtained for V403 Car.     

Estimates of Chandler's Component of Polar Motion as Derived from Various Data Sets

Data sets consisting of several combinations of classical and modern techniques (Doppler and laser ranging to artificial sattellites) have been analysed by autoregressive (AR), sinusoidal and autoregressive moving averag (ARMA) methods in order to obtain estimates of the frequency and quality factor of the Chandler component of polar motion. The ARMA method shows advantages over the other methods and the results obtained do not furnish evidence of temporal variation in these polar motion parameters. The disadvantages associated with smoothing the data sets and the difficulties as sociated with short time intervals for the data are cleary demonstrated. There is a great need for regular and long observational series obtained by the modern techniques.     

Behaviour of a new type of Runge–Kutta methods when integrating satellite orbits

Recently, González, Martín and Farto have developed new numerical methods (RKGM methods) of Runge–Kutta type and fixed step size for the numerical integration of perturbed oscillators. Moreover, it seems natural to study the behaviour of these new methods for the accurate integration of orbital problems after the application of linearizing transformation, such us KS or BF due to the fact that in these variables, the structure of the problem is of the form of perturbed oscillators, for which the methods constructed are indicated. In this paper, we check the efficiency of these new methods when integrating the satellite problem. The RKGM methods show a very good behaviour when they compete with other, classical and special, methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Population i pulsating stars

On the basis of our age estimations of Population I pulsating stars in our Galaxy (Tsvetkov, 1986a), the mean ages of 6 open star clusters containing 21 Delta Scuti-variables and of 8 star clusters and associations containing 13 classical cepheids, have been evaluated. These mean cluster age estimations weighted according to the probabilities for different evolutionary phases of the pulsating stars, are obtained in the evolutionary track systems of Iben (1967) and Paczyski (1970); the cluster ages are larger in the former system. Our results are compared with those obtained from various methods by other authors. Clusters with classical cepheids and with Delta Scuti-stars have ages, respectively, in the ranges 10⁷–10⁸ years and 10⁶–10⁹ years. It is shown that the use of simple period-age(-colour) relations for Population I pulsating stars gives sufficiently accurate cluster age estimations. By use of our period-age relations for classical cepheids (Tsvetkov, 1986a), the mean ages of 56 other star clusters and associations in our Galaxy, the Magellanic Clouds, and M 31 galaxy have been estimated in both systems of tracks. The results are generally in agreement with those obtained from various methods by other authors. The use of Population I pulsating stars in star clusters and associations is one of the simplest and most easily applied methods for determining cluster ages; but there are some limitations in its application.     

On the dynamics in the asteroids belt. Part I : General theory

The classical problem of the dynamics in the asteroids belt is revisited in the light of recently developed perturbation methods. We consider the spatial problem of three bodies both in the circular and in the elliptic case, looking for families of periodic or quasi periodic orbits. Some criteria for deciding the stability of these families are also indicated.     

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。     

Derivation of physical parameters of chromospheric structures assuming a constant and a varying source function

H profiles of a rosette region consisting of several bright and dark mottles were obtained with the Multichannel Subtractive Double Pass (MSDP) spectrograph mounted on the 50 cm 'Tourelle' refractor of the Pic du Midi Observatory. These profiles have been analysed in terms of the classical cloud model which assumes a constant source function and holds only for optically thin structures. A new technique is also described which enables the determination of various physical parameters of chromospheric features taking into account the variation of the source function with the optical depth. This method can be applied, in contrast to the classical cloud model, to all lines whether optically thin or optically thick and gives a good fit to the entire profile from the core to the wings. A comparison of the results given by the two different methods is also performed.     

Interstellar Extinction and the Intrinsic Colors of Classical Cepheids in the Galaxy, the LMC, and the SMC

New methods are applied to samples of classical cepheids in the galaxy, the Large Magellanic Cloud, and the Small Magellanic Cloud to determine the interstellar extinction law for the classical cepheids, R _B:R _V:R _I:R _J:R _H:R _K= 4.190:3.190:1.884:0.851:0.501:0.303, the color excesses for classical cepheids in the galaxy, E(B-V)=-0.382-0.168logP+0.766(V-I), and the color excesses for classical cepheids in the LMC and SMC, E(B-V)=-0.374-0.166logP+0.766(V-I). The dependence of the intrinsic color (B-V)₀ on the metallicity of classical cepheids is discussed. The intrinsic color (V-I)₀ is found to be absolutely independent of the metallicity of classical cepheids. A high precision formula is obtained for calculating the intrinsic colors of classical cepheids in the galaxy: (<B>-<V>)₀=0.365(±0.011)+0.328(±0.012)logP.     

Multichannel Blind Deconvolution As A Tool For Solar Image Restoration

A principle of restoration methods based on multichannel blind deconvolution (MBD) is introduced. The methods assume that for every un-degraded unobservable image several degraded observed images are available. It is better conditioned than classical single channel approach. The first algorithm represents a generalization of iterative deconvolution scheme introduced for single images. The second MBD algorithm is based on so-called subspace technique. The subspace method is not iterative and this possibly implies an implementation that can be computationally more efficient. Both methods are presented in applications to artificial image data (computer-generated multichannel degraded data) with known ideal image to get a comparison with restored one. Performance in a real situation on solar photosphere images is shown.     

Detection of superimposed periodic signals using wavelets

In this paper we present a wavelet-based algorithm that is able to detect superimposed periodic signals in data with low signal-to-noise ratio. In this context, the results given by classical period determination methods depend strongly on the intrinsic characteristics of each periodic signal, like amplitude or profile. It is then difficult to detect the different periods present in the data set. The results given by the wavelet-based method for period determination we present here are independent of the characteristics of the signals.     

Numerical image processing applied to the solar corona

Numerical data processing is applied to the high-resolution images-of the solar corona obtained with the 20 cm coronagraph of the Pic du Midi observatory. Two complementary methods are proposed to solve some classical difficulties usually met in the morphological analysis of the solar corona, namely the brightness gradient in the inner and medium corona, the low contrast of numerous emissive regions and the superimposition along the line of sight of different structures. The methods which are described in this paper may help to resolve the complex coronal active regions into fine structures which is now necessary to interpret all observed corona data.