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1.
In this paper of the series, the time transform and the explicit exact forms of the time will be established in terms of the sectorial variables j (i) introduced in Paper IV (Sharaf, 1982) to regularize the highly oscillating perturbation force. Simple recurrence formulae are given to facilitate the computations. The formulations are general in the sense that they are valid whatever the types and the number of sectors forming the divisions situation of the elliptic orbit may be. Moreover, the constants of integration for the explicit forms of the time are determined in a way that it gives for these forms its generality during any revolution of the body in its Keplerian orbit.  相似文献   

2.
The possibility of radio emission is considered within a model which produces the beam-plasma system near the pulsar. A longitudinal instability develops near the light cylinder for a particular choice of parameters adopted in the paper. The excited wave strongly oscillates the beam particles perpendicular to its average velocity on one hand, and forms bunches of them on the other hand. Consequently, coherent radiation is expected. The frequency of the emission falls within the radio band, but the intensity turns out to be too low to explain observations. An appreciable enhancement of the beam number density over the Goldreich-Julian value (n bB/2ec) is needed if the mechanism discussed in the present paper is responsible for the pulsar radio emission.  相似文献   

3.
C. K. Ng 《Solar physics》1988,114(1):165-179
Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealised solution suggests that the invariant anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.  相似文献   

4.
Decomposition of the product of functions like exp (– 0/z)S +(z) [S +(z = 0 1 P(x) dx/(x–z)], obtained by Das Gupta (1978) and relevant to the solution of equations of radiative transfer or of transfer problems in finite media by Wiener-Hopf technique, is reviewed and transformed to quite simple integral forms amenable to easy numerical evaluations. The same forms are then shown to be directly obtainable in one step under a slightly stronger condition consistent with practical cases.  相似文献   

5.
This paper discusses the methods used to analyse and interpret X-ray filtergrams obtained by solar soft X-ray telescopes such as the S-056 Skylab instrument. First, an appropriate definition of the line-of-sight emission measure L(T) is developed, and it is shown how the X-ray data may be analysed to obtain an approximation to L(T). The accuracy of this approximation is severely limited by the mathematical ill-conditioning of the problem, and additional constraints on the solutions must be imposed through the use of a specific model of the coronal region under study. Such a model is also required for the proper interpretation of the results in terms of coronal plasma processes. Examples of such models are provided and the forms of L(T) derived from them compared with other, semi-empirical forms.The filter ratio method (a simplified form of analysis in which the region under study is assumed isothermal) is discussed. It is shown that in the presence of line-of-sight temperature gradients, the values of effective temperature and emission measure yielded by this method cannot be directly related to the physical state of the plasma and so are of little utility in the study of coronal processes.Now at: Institute for Plasma Research, Stanford University, Via Crespi, Stanford, Calif. 94305, U.S.A.  相似文献   

6.
Kopal's new iterative method for analysing partially eclipsing binary light curves in the frequency domain has been put into a form suitable for applications, and explicit forms for basic expressions developed. To facilitate the computations in practice, the required newS m -functions, which are expressed in terms ofJ , 0 -integrals, have been extensively tabulated by making use of hypergeometric series. The automated method has been tested successfully on the light curves of Persei (Algol). Short information on the system and the revised sets of elements including a new determination of the limb-darkening coefficient in the ultraviolet have been presented.  相似文献   

7.
The area preserving mapping x = x + a(y – y 3), y = y – a(x – x3), for 0.3 a 2.0 has been studied to locate approximately the x-axis points bounding almost stable regions. For each value of a, these are fixed points with variational trace just greater than 2.0. Transition to chaos can occur rapidly as a increases (with n/k fixed).  相似文献   

8.
New expressions for the fractional loss of light l 0 have been derived in the simple forms of rapidly converging expansions to the series of Chebyshev polynomials, Jacobi polynomials, and Kopal'sJ-integrals. In these expansions, which are a supplement to those given by Kopal (1977b), variablesk andh occur in different products that simplify the numerical computation. The treatment follows the new definition of l 0 which has been recently developed by Kopal (1977a).  相似文献   

9.
The asymptotic properties of a turbulent disk dynamo at large dimensionless numbersR andR characterizing the helicity and the differential rotation are analysed. Three types of generations in the dependence of the relations betweenR andR are found: 2-dynamo and two types of -dynamo. For each of these types the rates of growth are obtained and the forms of solution are pointed out. Boundaries of the disk dynamo approximation are given.  相似文献   

10.
The aim of the present paper will be to make use of the expressions, established in Paper XI, for the fractional loss of light l 0 of arbitrarily limb-darkened stars in the form of Hankel transforms of zero order, in order to evaluate the explicit forms of the l 0's for different types of eclipses (Section 2), as well as of the momentsA 2mof the respective light curves (Section 3)-in a closed form; or in terms of expansions that converge under all circumstances envisaged. Particular attention will be directed to a connection between these expansions and other functions already available in tabular form; or to alternative forms amenable to automatic computation.  相似文献   

11.
Ai-Hua  Zhou  Guang-Li  Huang  Xin-Dong  Wang 《Solar physics》1999,189(2):345-356
Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity –/BNand absorptivity – B/Nfor e-mode, effective temperature T effand frequency of peak brightness p. The expressions are designed for the range 2 to 7 of electron energy spectral index and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=/B). Their statistical error is, respectively, ±18% and ±29% for –/BNand – B/Nfor 10/B100, ±128% and and ±170% for 2/B10.  相似文献   

12.
The diagramV - log(1 +z e ) as function of (, ) is considered for the quasars. HereV is the apparent visual magnitude,z e is the emission line redshift, and are the equatorial coordinates. Two opposite extreme spots NE and SE are observed on the sky, where the inclination of the straight line fitting the dependenceV - log(1 +z e ) is maximum and minimum. The coordinates of the centres of these extreme spots are ( NE, NE) = (282°, +42°) and ( SE, SE) = (70°, -38°) with errors 5°. A hypothesis of the Superattractor (SA) is proposed to explain such an effect. Two independent tests of this hypothesis are realized. First, the dependence or the frequency a of the absorbers in QSO spectra on (, ) is investigated. A region of the larger a is found. The coordinates of its centre are (, ) = (82°, - 10°) with error 5°. Second, the cases ofz a >z e are plotted in the Mercatorial projection (, ). The most of the casesz -z e > 0.02 are concentrated within the circle with radiusR = 34° and centre (, ) = (50°, - 15°). The both anomalous regions overlap the Southern extreme spot around SE. The SA direction is (, ) = (67°, -21°) with errors about 12°. The redshift of SA isz SA = 1.7 ± 0.3 that corresponds to the distancer SA = (3100 ± 300)h –1 Mpc for the Hubble constantH 0 = 75h kms–1 Mpc–1. The SA mass isM SA ~ 1018-1020 M . The orientation of the normal to the quasiperiodical large-scale sheet structure on the sky occurs near SA.  相似文献   

13.
The variation of radio luminosity with redshift and its effect on the analysis of the angular size-redshift ( –z) relation for a bright radio source sample (s 178 10Jy) has been investigated. By assuming a power law dependence of luminosity on redshift of the formP (1 +z), it was found that 4.4 (with correlation coefficientr 0.99) for at leastz 0.3. Correction for such a strongP – (1 +z) correlation when considering the –z data for the sample led to a steeper –z slope. This could be explained by assuming linear size evolution of the formD (1 +z)–n withn = 2.8 – 3.3 consistent with both theoretical results and those obtained for more homogeneous source samples.  相似文献   

14.
A new method has been developed by Kopal (1977c, Paper XII) to make use of expressions for the fractional loss of light 0 l of the arbitrarily limb-darkened stars in the form of Hankel transforms of zero-order, in order to evaluate the explicit forms of the 0 l s for different types of eclipse, as well as of the momentsA 2m of the respective light curves in a closed form. The automated method has been tested successfully on the light curves of RT Persei. Also, a photometric curve fit of RT Persei is investigated by application of numerical quadratures to determine the theoretical light curve appropriate for the Roche model. Finally a comparative discussion is given of various methods of light curve analaysis.On leave from Department of Physics, University of Ferdowsi, Mashad, Iran.  相似文献   

15.
A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(p + 22), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(p +42). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.  相似文献   

16.
We have developed a new model of evolutionary synthesis of stellar population, from a working cyclical approximation to a general solution for the mass and time dependence of the birth function of stars. The general solution enables us to introduce a functionG(t): the ratio of gas injected into a defined region to that which forms stars in the same time interval, at timet. This function, by relating directly the output of dying stars with the formation of the next generation, allows us to make analytical approximations (in the absence of more accurate numerical information) to the macroscopic evolution of stellar populations in a well-defined zone of a galaxy.The model has been initially applied to 4 zones of the dwarf elliptical M32 (NGC 221) where, usingU, B, V from the literature, and our own photometric maps inJ andK, we obtained the following results: (a) Star formation in the most recent 108 years is lower by a factor 3–4 in a zone 68 arc sec (200 pc) from the nucleus than in the nuclear zone. (b) The metallicity appears to be a little lower in a zone diametrically away from the parent galaxy M31 than in a zone towards M31 at the same galactocentric distance (c) TheM/L ratio is a factor 2 higher at 200 pc from the nucleus towards M31, than in the nuclear zone. (d) A high concentration of mass is evident in the nuclear zone. (e) The estimated age of all the zones is of the same order,1.5×1010 yr.  相似文献   

17.
The magnetic field in solar active regions forms a highly structured pattern without an apparent length scale. We study this pattern in detail for a plage and its surroundings observed with the Swedish Solar Observatory on La Palma. The magnetogram has a resolution of about 1/3, after image optimisation. We analysed the geometric properties of isolated patches of magnetic flux. Patches with a linear size up to 3 appear to be statistically self-similar, with a fractal dimension ofD f = 1.54 ± 0.05 for the relation between area and linear size. This value agrees very well with the dimensionD f = 1.56 which is found in percolation theory for clusters of tracers placed randomly on a lattice with a tracer density below a critical threshold. The distribution of observed cluster areas also agrees with that of clusters on such a random lattice. The correspondence between properties of observations and of clusters on randomly filled lattices suggests that- well after emergence - the magnetic flux on the Sun is randomly distributed at least up to sizes of about 3 and possibly larger.  相似文献   

18.
In the previously published Parts I and II of the paper, the author has constructed a formal long-periodic solution for the case of 11 resonance in the restricted problem of three bodies to 0(m 3/2), wherem is the small mass parameter of the system. The time-dependencet(, ,m), where is the mean synodic longitude and is related to the Jacobi constant, has been expressed by ahyperelliptic integral. It is shown here that with the approximationm=0 in the integrand, the functiont(, , 0) can be expanded in a series involving standardelliptic functions. Then the problem of inversion can be formally solved, yielding the function (t, , 0).Similarly, the normalized period (,m) of the motion can be approximated by theHagihara hyperelliptic integral (, 0), corresponding tom=0. This integral is also expanded into elliptic functions. Asymptotic forms for (, 0) are derived for 0 and for 1, corresponding to the extreme members of thetadpole branch of the family of orbits.  相似文献   

19.
According to the classical theory of equilibrium figures surfaces of equal density, potential and pressure concur (let call them isobars). Isobars may be represented by means of Liapunov power series in small parameter q, up to the first approximation coincident with centrifugal to gravitational force ratio on the equator. A. M. Liapunov has proved the existence of the universal convergence radius q : above mentioned series converge for all bodies if q < q . Using Liapunov's algorithm and symbolic calculus tools we have calculated q = 0.000370916. Evidently, convergence radius q 0 may be much greater in non-pathological situations. We plan to examine several simplest cases. In the present paper, we find q 0 for homogeneous liquid. The convergence radius turns out to be unexpectedly large coinciding with the upper boundary value q 0 = 0.337 for Maclaurin ellipsoids.  相似文献   

20.
This paper is the text of a course offered at Cortina d'Ampezzo (NATO Advanced Study Institute-Long time prediction in dynamics 1975). The integral invariants were introduced by H. Poincaré and E. Cartan. This mathematical notion is very tractable by the use of exterior algebra of different forms. Work at the University of Besançon introduces again this theory, in Celestial Mechanics. This paper has two parts: mathematical tools, then an application to then-body problem where, by the use of the 11th local integral, I found some new equations and developed them for the collinear triple collision of three bodies.  相似文献   

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