The equivalence of von Zeipel mappings and Lie transforms

An order independent method is used to identify the transformation obtained from Von Zeipel's method with that obtained from Lie transforms. The correspondence between the generators is given in explicit form.     

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 Schwabe Cycle Properties in Solar Activity

Properties of the Schwabe cycles in solar activity are investigated by using wavelet transform. We study the main range of the Schwabe cycles of the solar activity recorded by relative sunspot numbers, and find that the main range of the Schwabe cycles is the periodic span from 8-year to 14-year. We make the comparison of 11-year‘s phase between relative sunspot numbers and sunspot group numbers. The results show that there is some difference between two phases for the interval from 1710 to 1810, while the two phases are almost the same for the interval from 1810 to 1990.     

Comparison of simulated longitudinal profiles of hadronic air showers with MASS2 balloon data

The KASKADE and CORSIKA air shower generators are compared to the data collected by MASS2 balloon experiment in 1991. The test of longitudinal profile for proton, helium and muon flux production provide good constraints on these air shower generators. KASKADE and CORSIKA especially with the new simulator UrQMD for low energies are found to fit these data well. This study is limited to a comparison of longitudinal profiles and therefore does not provide constraints on the overall shower development.     

The Near-Nuclear Study of Comet Hale Bopp

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The frequencies of high frequency quasi-periodic oscillations in two different frames in black hole LMXBs

We discuss the modes of the Alfve'n waves in the accretion disk with a toroidal magnetic field in black hole low mass X-ray binaries in a rotating frame.By solving the perturbed general relativistic magnetohydrodynamic equations in the rotating frame,we find two stable modes of the Alfve'n wave which are the same as those in the fiducial observer frame.This gives a feasible way to transform between the two different frames,which validates the possible Alfve'n wave modes in the accreting celestial bodies wit...     

The use of Fourier transform techniques in the analysis of photoelectrically scanned double star images

A technique for the analysis of photoelectrically scanned double star images is described. The method consists of comparing the Fourier transform of the double star profile with that of a single star profile imaged through the same telescope. If the measured profile of the double star image can be considered to be a linear superposition of two profiles, each identical in shape to the measured profile of a nearby single star, a comparison of the Fourier transforms of these profiles enables the parameters of the double star system to be determined. Certain features of the ratio of the moduli of the transforms yield both the separation and the magnitude difference between the components. A comparison of the phases of the transforms enables one to establish which of the two components is the brighter.     

Perturbation method in the theory of nonlinear oscillations

Asymptotic recurrence formulas for treating nonlinear oscillation problems are presented. These formulas are based on a Lie transform similar to that described by Deprit for Hamiltonian systems. It is shown that the basic formulas have essentially the same forms as those obtained by Deprit and by the present author in the Hamiltonian case.     

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.     

Synchronization of Sunspot Numbers and Sunspot Areas

Sunspot activity is usually described by either sunspot numbers or sunspot areas. The smoothed monthly mean sunspot numbers (SNs) and the smoothed monthly mean areas (SAs) in the time interval from November 1874 to September 2007 are used to analyze their phase synchronization. Both the linear method (fast Fourier transform) and some nonlinear approaches (continuous wavelet transform, cross-wavelet transform, wavelet coherence, cross-recurrence plot, and line of synchronization) are utilized to show the phase relation between the two series. There is a high level of phase synchronization between SNs and SAs, but the phase synchronization is detected only in their low-frequency components, corresponding to time scales of about 7 to 12 years. Their high-frequency components show a noisy behavior with strong phase mixing. Coherent phase variables should exist only for a frequency band with periodicities around the dominating 11-year cycle for SNs and SAs. There are some small phase differences between them. SNs lag SAs during most of the considered time interval, and they are in general more asynchronous around the minimum and maximum times of a cycle than at the ascending and descending phases.     

Time transformations in the extended phase-space

Time transformations involving momenta in addition to the coordinates are studied from the points of view of stabilization and regularization of the equations of motion. The generalization of Sundman's transformation by using the potential function to transform the time is further generalized by using the Lagrangian function for the same purpose. The possibility of the stabilization of the equations of motion is investigated similarly to Stiefel's and Baumgarte's recent results but instead of a factorial, an additive control function is introduced in all equations of motion. The relation between the original and new independent variables is integrated by a modification of Ebert's theorem and it is shown that the new independent variable is Hamilton's principal function. Numerical examples illustrate the method and seem to indicate that the computation of close approach trajectories benefit especially by the transformations discussed. The Appendix offers an analytic treatment regarding the stabilization of the constant of energy.     

日长亚季节变化的振幅调制与厄尔尼诺现象

利用Ｈｉｌｂｅｒｔ变换解算了１９６２年至１９９６年日长亚季节振荡的包络变化．结果显示,日长亚季节变化的振幅调制不仅具有一线性增长趋势,而且包含一个超前厄尔尼诺变化历程的年际变化．分别研究日长亚季节准５０天包络变化以及准１２０天包络变化后发现,这种超前性来自日长亚季节准５０天的振幅变化,这一结论与大气的研究结果一致．日长亚季节准１２０天的振幅变化在１９７２年附近发生了位相１８０°反转,因此日长亚季节准１２０天的振幅变化自１９７６年以来与厄尔尼诺的历程正好同步,１９７２年以前则截然相反．众所周知,日长变化在亚季尺度上具有显著的易变性,然而上述的非线性调制现象不仅表明了日长亚季节变化的内在规律性,而且证实了地球自转运动在不同时间尺度上存在极明显的非线性相互作用．同时也表明,日长变化作为全球风系变化的一个有价值的信息指标,将逐渐成为研究气候系统全球状态的有效手段之一．     

Processing Method Effects on Solar Diameter Measurements: Use of Data Gathered by the Solar Disk Sextant

To determine the apparent diameter of the Sun, it is first necessary to measure the shape of the intensity profile of the solar limb with an imaging optical system (hereafter denoted as a solar-limb profile). The inflection point of the limb profile is usually used as a reference for calculating the diameter. Because this point may be difficult to determine in the presence of noise, it is necessary to define an appropriate filtering process that eliminates noise while preserving the position of the inflection point. In this paper we study two filtering techniques, one based on the compact wavelet transform and the other on the finite Fourier transform definition, that meet these requirements. The application of these two techniques to data gathered by the Solar Disk Sextant experiment shows that the solar radius increased from 1992 to 1996 by about 197 mas. However, a previous analysis of the same data and our present analysis provide a difference in the measured radii of about 92 mas. We show that this difference is entirely traced to the filtering process.     

Dense Z-Pinches

The basic underlying physics of the Z-pinch is reviewed; the Bennett relation, the snowplough model, particle orbits, heat losses to electrodes, equilibrium profiles, radiative collapse, and finally stability in many regimes. Recent experimental results from Imperial College using the MAGPIE and IMP generators on fibre Z-pinches are presented, together with X-ray results from wire arrays from SATURN and PBFA-Z at Sandia National Laboratory.     

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.     

Fragmentation of Cosmic Objects in the Course of Their Evolution and the Possible Role of Hubble Expansion in this Process

A series of phenomenological similarities between activity phenomena in the microscopic world and in the world of galaxies is examined. Proceeding from the high metallicity of quasars, it is shown that the relative amount of light elements, primarily hydrogen, increases during the evolution of the universe. Evidence supporting an analogous enrichment of the world of galaxies by dwarf galaxies is presented. A variant is proposed in which cD galaxies are the generators of the clusters of galaxies in which they are located, while all the galaxies of a given cluster are products of the activity of a central supergiant galaxy. An analogous mechanism is apparently responsible for the formation of systems of globular clusters. A physical connection between activity phenomena and cosmic expansion is sought.     

Scalar field cosmology in $$ gravity via Noether symmetry

This paper investigates the existence of Noether symmetries of isotropic universe model in \(f(R,T)\) gravity admitting minimal coupling of matter and scalar fields. The scalar field incorporates two dark energy models such as quintessence and phantom models. We determine symmetry generators and corresponding conserved quantities for two particular \(f(R,T)\) models. We also evaluate exact solutions and investigate their physical behavior via different cosmological parameters. For the first model, the graphical behavior of these parameters indicate consistency with recent observations representing accelerated expansion of the universe. For the second model, these parameters identify a transition form accelerated to decelerated expansion of the universe. The potential function is found to be constant for the first model while it becomes \(V(\phi )\approx \phi ^{2}\) for the second model. We conclude that the Noether symmetry generators and corresponding conserved quantities appear in all cases.     

Timeline analysis and wavelet multiscale analysis of the AKARI All-Sky Survey at 90 μm

We present a careful analysis of the point-source detection limit of the AKARI All-Sky Survey in the WIDE-S 90-μm band near the North Ecliptic Pole (NEP). Timeline analysis is used to detect IRAS ( Infrared Astronomy Satellite ) sources and then a conversion factor is derived to transform the peak timeline signal to the interpolated 90-μm flux of a source. Combined with a robust noise measurement, the point-source flux detection limit at signal-to-noise ratio  (S/N) > 5  for a single detector row is  1.1 ± 0.1 Jy  which corresponds to a point-source detection limit of the survey of ∼0.4 Jy.
Wavelet transform offers a multiscale representation of the Time Series Data ( tsd ). We calculate the continuous wavelet transform of the tsd and then search for significant wavelet coefficients considered as potential source detections. To discriminate real sources from spurious or moving objects, only sources with confirmation are selected. In our multiscale analysis, IRAS sources selected above 4σ can be identified as the only real sources at the Point Source Scales. We also investigate the correlation between the non- IRAS sources detected in timeline analysis and cirrus emission using wavelet transform and contour plots of wavelet power spectrum. It is shown that the non- IRAS sources are most likely to be caused by excessive noise over a large range of spatial scales rather than real extended structures such as cirrus clouds.     

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。