共查询到20条相似文献，搜索用时 46 毫秒
1.
The Voigt functions, so important in spectroscopy and neutron physics, are represented as generalized hypergeometric functions (G-functions) of two real variables. A system of partial differential equations for the Voigt functions is derived. By applying Hölder's inequality to an integral representation of the Voigt functions apparently not known in the literature until now, lower and upper bounds are obtained. Moreover, from this representation an asymptotic expansion of Voigt functions for large values of one variable is extracted. 相似文献
2.
Stanley W. Shepperd 《Celestial Mechanics and Dynamical Astronomy》1987,42(1-4):91-106
A family of functions involving integrals of universal functions is introduced. These functions have some interesting mathematical properties including the fact that they may be expressed as Gaussian continued fractions. An unique method of performing the integration is demonstrated which indicates why these functions may be important in the variation of Kepler's equation.This work was supported at the Charles Stark Draper Laboratory, Inc. by the National Aeronautics and Space Administration under Contract NAS9-17560. 相似文献
3.
Anisotropic distribution functions for spherical galaxies 总被引：1，自引：1，他引：0
A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric,
densities, which depends only on the two classical integrals of the energy and the magnitude of the angular momentum. It requires
the density to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution
corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the
angular momentum. The products of the density and its radial and transverse velocity dispersions can be also expressed as
a sum of products of functions of the potential and of the radial coordinate. Several examples are given, including some of
new anisotropic distribution functions. This device can be extended further to the related problem of finding two-integral
distribution functions for axisymmetric galaxies. 相似文献
4.
大气角动量(AAM) 变化和地球自转变化密切相关,它们可应用于全球环流模型的检验.根据日本气象厅全球环流模型的输出数据计算出AAM 函数,将AAM 函数的模拟值与它的观测值以及地球自转变化序列相比较,来检验该模型对大气角动量的模拟.限于篇幅,仅给出AAM 函数的季节性分量模拟的结果.对于半年项,轴向AAM 函数的气压项和风项的模拟值都偏高,赤道向AAM 函数的气压项和风项很小,因而未予考虑;对于周年项,轴向AAM函数气压项的模拟值偏低,而赤道向AAM 函数气压项的模拟值偏高,轴向AAM 函数的风项模拟得最好,而赤道向AAM 函数的风项模拟得较差.总之,高精度的天文观测的地球自转系列可以作为全球环流模型检验的一种重要参考依据. 相似文献
5.
《New Astronomy》2022
In this paper, general sufficiently analytical formulae are developed for the arbitrary order generalized relativistic Fermi-Dirac (FD) functions. Analytical assessment of relativistic FD function is very important for various fields of physics especially in the theory of relativistic nondegenerate and degenerate electron gas systems. One of the more appropriate and correct approximations is based on a binomial expansion method and incomplete Gamma functions that have been used in the calculations of the generalized relativistic FD functions. Note that, the established expression in special cases of specific values of parameters becomes the evaluation formulae of other type FD functions. Calculation results of the generalized relativistic FD functions are compared with the other approximations methods and available numerical approaches and demonstrated satisfactory agreement. 相似文献
6.
《Chinese Astronomy and Astrophysics》2022,46(2):65-72
Computational efficiency of the recursion of eccentricity functions is investigated, and a kind of batch recursion method is given. Its computational efficiency is significantly superior to the direct calculation method. Moreover, this kind of batch recursion is forward so that the magnitudes of eccentricity functions experience from small to large change in the recursive process. Hence in this way the high accuracy of the recursion of eccentricity functions can be guaranteed. 相似文献
7.
Demetrios D. Dionysiou 《Astrophysics and Space Science》1981,80(2):477-482
A new approach to the problem of the equilibrium conditions of a self-interacting massive charged particles is presented.As is well-known, the solution of the Laplace or Poisson equation in a finite volume V, with or without charged particles inside, and with prescribed boundary conditions of the bounding surfaces, can be obtained by means of the Green's theorem and Green's functions. This solutions permits the choice of an arbitrary harmonic or potential functions inside the volume V. The generalized concept of the Green functions gives rise to the possibility that we can define these arbitrary harmonic or potential functions in order to generalize the well-known equilibrium conditions. 相似文献
8.
Adopting luminosity functions of various morphological types of galaxies and galaxy populations for different environments characterized by the density, the overall differential and integrated luminosity functions of Hubble mix in different dense regions have been obtained. The calculated overall luminosity functions show a weak dependence on the density. Although there is a satisfactory agreement between the calculated overall luminosity functions and the observed distributions of samples of corresponding densities, the observed data are too uncertain in order to confirm the expected density dependence. 相似文献
9.
Toshiki Aikawa 《Astrophysics and Space Science》1985,109(1):183-189
Weight functions for the non-adiabatic radial pulsations are introduced. It is shown from behavior of these functions that the pulsation periods in classical Cepheids are determined essentially in the adiabatic region of stellar envelopes and, on the other hand, those of low surface-gravity models are strongly affected in the region where the acoustic waves are strongly coupled with the radiation fields. The fact is important for understanding basic difference of the pulsation properties between classical Cepheids and low surfacegravity models.The non-adiabatic weight functions deviate from adiabatic ones in two ways in the stellar envelope layers. In the region where the acoustic waves are tightly coupled with radiation fields, the non-adiabatic weight functions have larger values than the corresponding adiabatic ones. On the contrary, the functions are smaller in the outer isothermal region.These results are discussed from the viewpoint on the propagation of the acoustic waves in radiation nelds. 相似文献
10.
M. Clutton-Brock 《Astrophysics and Space Science》1972,16(1):101-119
A set of bi-orthogonal pairs of functions is derived which is especially suited for the calculation of the gravitational field of flat galaxies. The functions are Hankel tranforms of associated Laguerre functions, or Hankel-Laguerre functions. They can be calculated by means of recurrence relations, which are derived from a generating function.Numerical computations are most efficiently performed using a related set of Chebyshev type functions, which have more economic recurrence relations. The necessary algorithms for efficient calculation of the field are derived using the properties of Hankel-Laguerre functions.This field calculation, can be used for a relatively cheap and simple computer simulation of galaxies. 相似文献
11.
Alireza Rahmati Mir Abbas Jalali 《Monthly notices of the Royal Astronomical Society》2009,393(4):1459-1466
We use the weighted integral form of spherical Bessel functions and introduce a new analytical set of complete and biorthogonal potential–density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to r −(1+ l ) and r −(4+ l ) at large radii, where l is the latitudinal quantum number of spherical harmonics. The lowest order term associated with l = 0 is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modelling of three-dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our functions by expanding the density and potential profiles of some spherical and oblate galaxy models. 相似文献
12.
R. G. Langebartel 《Astrophysics and Space Science》1981,75(2):437-454
The restricted three-body Hamiltonian is partitioned into a two-center type principal part and its accompanying perturbational part. The mathematical analysis, involving the Jacobian elliptic functions, is adapted for the case of figure-eight orbits winding around the two given mass points. For many such orbits the elliptic function modulusk is small and can serve as a small parameter.Fourier expansions in terms of a parameter related tot are obtained for the intermediate orbit functions which provide representations in terms of elementary functions. 相似文献
13.
田谐项摄动是分析法轨道预报中的重要部分,其中包含大量倾角函数及其偏导数的计算.由于具有精度更高、速度更快的优点,倾角函数一般通过递推方法计算.以文献中提出的改进Gooding方法为基础,将其给出的程序稍加改进,在计算2–50阶倾角函数时缩短了约24%的计算时间.考虑到分析法预报过程中轨道平倾角变化很小,以泰勒展开式计算倾角函数,可极大提高计算速度,较大程度地减小分析法预报耗时,且引力场阶次越高,减小幅度越大,取50阶时预报耗时缩短了48%.另一方面,以2阶展开式计算倾角函数时,与改进Gooding法相比,分析法预报星历偏差很小.对于500 km高度的低轨卫星,分别以改进Gooding法和2阶泰勒展开式计算倾角函数,预报3天,当地球引力场阶次不高于50时,二者预报星历偏差RMS (Root Mean Square)低于1 mm,且随着轨道高度的增加,预报星历偏差RMS逐渐减小. 相似文献
14.
A new approach to solve Kepler’s equation based on the use of implicit functions is proposed here. First, new upper and lower bounds are derived for two ranges of mean anomaly. These upper and lower bounds initialize a two-step procedure involving the solution of two implicit functions. These two implicit functions, which are non-rational (polynomial) Bézier functions, can be linear or quadratic, depending on the derivatives of the initial bound values. These are new initial bounds that have been compared and proven more accurate than Serafin’s bounds. The procedure reaches machine error accuracy with no more that one quadratic and one linear iterations, experienced in the “tough range”, where the eccentricity is close to one and the mean anomaly to zero. The proposed method is particularly suitable for space-based applications with limited computational capability. 相似文献
15.
W. Lohmann 《Astronomische Nachrichten》1972,294(3):105-111
The strip functions, circular velocity functions and various characteristic parameters of NGC 659, 1027, 1245, 1502, 1528, 1907, 2420, 6830, 6866, 7062 and IC 1848 are derived. From these functions the relative density distribution in the “mean” cluster defined by the 11 clusters is determined. The corresponding generalized SCHUSTER model is found (n = 3.04). The stars of the mean cluster are somewhat more concentrated to the centre than in the model. 相似文献
16.
Flattened Jaffe models for galaxies 总被引：1，自引：0，他引：1
Jiang Zhenglu 《Monthly notices of the Royal Astronomical Society》2000,319(4):1067-1078
This paper introduces a class of galactic models which extend Jaffe's spherical models to axisymmetric systems, and then studies the properties of their densities and two-integral even distribution functions. The models have finite total mass and finite densities which, at large distances, decay radially like r −4 except on the major axis, and like r −3 on the major axis. The more flattened the galaxy, the stronger is the dependence of the even distribution functions on the angular momenta of its stars. Their distribution functions can be obtained by using the maximum entropy principle or assuming the anisotropy of the models. In particular, some formulae analogous to those of Hunter & Qian are obtained to calculate two-integral odd distribution functions, and they can be applied to obtain the distribution functions under the assumption of anisotropy for the oblate models. 相似文献
17.
TOPEX/POSEIDON is a joint American/French ocean topography experiment. It was launched by an Ariane launch vehicle on August 10, 1992 to study and map ocean circulation. The primary functions of the navigation subsystem of the TOPEX/POSEIDON project are to establish and maintain a pre-designed reference orbit, and to measure, monitor, and predict the satellite ground track continuously. To fulfill these functions, trajectory analysis is required to design and generate all trajectory related products. This paper is concerned with the trajectory functions of TOPEX/POSEIDON navigation. It describes various activities of this support function. 相似文献
18.
Prasenjit Sengupta 《Celestial Mechanics and Dynamical Astronomy》2007,99(1):13-22
This paper presents a method for the truncation of infinite Fourier–Bessel representations for functions requiring a solution
to Kepler’s equation. Use is made of the Lambert W function to solve for the desired index that bounds the remainder terms of the series, within the prescribed tolerance. The
enforcement of a maximum on the number of Bessel functions is also useful in truncating the Bessel functions themselves, resulting
in an analytical representation of the solution to a desired tolerance, without the use of infinite series. 相似文献
19.
Ranjna Bakaya R. R. Rausaria P. K. Koul P. N. Khosa 《Astrophysics and Space Science》1989,151(1):103-113
Evolution of electron energy distributions have been studied by combining small-angle scattering with analytical treatment of large-angle collision using the Monte-Carlo technique. By use of these, the distributions and energy loss have been calculated as functions of column density, the heating functions have been calculated at different depths of the solar atmosphere. From the heating functions, an increase in temperature produced by the electrons at different column densities has been computed. It is found that rise in temperature increases with an increase in incident electron energy. 相似文献
20.
F. Wger 《Astronomische Nachrichten》2010,331(6):662-664
The use of atmospheric transfer functions is common in image reconstruction techniques such as speckle interferometry to calibrate the Fourier amplitudes of the reconstructed images. Thus, an accurate model is needed to ensure proper photometry in the reconstruction. The situation complicates when adaptive optics (AO) are used during data acquisition. I propose a novel technique to derive two‐dimensional transfer functions from data collected using AO simultaneously with the observations. The technique is capable to compute the relevant transfer functions within a short time for the prevailing atmospheric conditions and AO performance during data acquisition (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献