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1.
The central problem in the theory of stellar nucleosynthesis (and in reaction theory of controlled thermonuclear fusion as well) is the determination of thermonuclear reaction rates. Continuing our preceding paper on closed-form evaluation of nonresonant reaction rate integral (HAUBOLD and JOHN 1978) now we consider a general thermonuclear reaction rate integral involving the full BREIT -WIGNER resonance cross section. Discerning between two cases – energy-independent partial widths and energy-dependent partial width – we evaluate the arising parameter-dependent integrals in closed form by means of MEIJER 's G-functions of one and two variables. At next, by using the BUNJAKOVSKIJ -SCHWARZ inequality we derive global upper bounds for thermonuclear reaction rate integrals with arbitrary admissible values of input parameters. Finally, in case of great values of the characteristic parameter COULOMB barrier energy divided by thermal energy we give an asymptotic representation of the general resonant reaction rate integral. 相似文献
2.
This paper deals with the closed-form representation of the non-resonant nuclear reaction rate taking into account electron screening effects for the reacting particles. The basic physical principles concerning nuclear reactions in dense astrophysical plasmas are applied to derive the representation of the screened nuclear reaction rate integral. Taking advantage of the theory of Meijer'sG-function it is shown that both the reaction rate integrals with and without screening corrections can be represented in closed form. Mathematical approximations for the reaction rate integral, till now considered as inevitable in the literature, are avoided and exact computable representations given. 相似文献
3.
In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G-function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes contour integral representation of the G-function is also established. The manifold generality of the G-function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R-function, are considered. The obtained results imply more precisely the known results. 相似文献
4.
Konstantin V. Kholshevnikov Sergei L. Kurdubov 《Celestial Mechanics and Dynamical Astronomy》2004,89(1):83-96
According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us
call them isobars). Isobars can be represented by means of Liapunov power series in small parameter q, up to the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. Liapunov has
proved the existence of the universal convergence domain: the above mentioned series converge for all bodies (satisfying a natural condition that the density ρ decreases from the center to the surface) if |q| < q*. Using Liapunov’s algorithm and symbolic manipulation tools, we have found q*= 0.000370916. Evidently, the convergence radius q* may be much greater in common situations. To comfirm it it is reasonable to consider two limiting and one or two intermediate
cases for the density behaviour: ρ is a constant, the Dirac’s δ-function, linear function of the distance from the center,
etc. And indeed, in the previous paper we find a three orders of magnitude greater value for homogeneous figures. In the present
paper we find that in the opposite case of Huygens-Roche figures (a point-mass surrounded by a weightless atmosphere) the
convergence radius is unexpectedly large and coincides with the well-known biggest possible value q*= 0.541115598 for such a class of figures. To ascertain it we ought to use numerical calculations, so our main result is
demonstrated by means of a computer assisted proof.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
A. G. Tlatov 《Astrophysics and Space Science》2009,323(3):221-224
The parameter G, which is determined from the general number of sunspots groups N
g
according to the daily observations G=∑(1/N
g
)2, is offered. This parameter is calculated for the days when there is at least one sunspots group. It characterizes the minimum
epoch solar activity. Parameter G mounts to the maximum during the epoch close to the minimal activity of sunspots. According to the data of the sequence of
sunspots group in Greenwich–USAF/NOAA observatory format, observation data of Kislovodsk solar station and also daily Wolf
number, the changes of parameter G during 100 years were reconstructed. It is demonstrated in the paper that parameter G’s amplitude in minimal solar activity n is linked with the sunspot cycle’s amplitude W
n+1 or one and half cycles. The 24th activity cycle prediction is calculated, which makes W
24=135(±12). 相似文献
6.
Rabindra Nath Das 《Astrophysics and Space Science》2010,326(1):91-103
In radiative transfer, the intensities of radiation from the bounding faces of a scattering atmosphere of finite optical thickness
can be expressed in terms of Chandrasekhar’s X- and Y-functions. The nonlinear nonhomogeneous coupled integral equations which the X- and Y-functions satisfy in the real plane are meromorphically extended to the complex plane to frame linear nonhomogeneous coupled
singular integral equations. These singular integral equations are then transformed into nonhomogeneous Riemann–Hilbert problems
using Plemelj’s formulae. Solutions of those Riemann–Hilbert problems are obtained using the theory of linear singular integral
equations. New forms of linear nonhomogeneous decoupled expressions are derived for X- and Y-functions in the complex plane and real plane. Solutions of these two expressions are obtained in terms of one known N-function and two new unknown functions N
1- and N
2- in the complex plane for both nonconservative and conservative cases. The N
1- and N
2-functions are expressed in terms of the known N-function using the theory of contour integration. The unknown constants are derived from the solutions of Fredholm integral
equations of the second kind uniquely using the new linear decoupled constraints. The expressions for the H-function for a semi-infinite atmosphere are obtained as a limiting case. 相似文献
7.
Pasquale Sconzo 《Astronomische Nachrichten》1967,290(4):163-170
After reviewing the existing procedures for solving the three-body problem by convergent power series, the author develops two algebraic methods in terms of the independent variable which is either the time t or Levi-Civita's regularizing variable u. These power series solve in Weierstrass' and Painlevé's sense the problem formulated in its greatest generality, since no restrictions at all are made on the order of magnitude of masses and none of the three bodies is restricted to moving along a prescribed conic section. Besides, the reference system used is a tridimensional Cartesian one. In the t-domain, the expressions for the high-order derivatives of the coordinates are computed using repeatedly Leibnitz's rule for derivatives of products of functions. In the u-domain, an extremely simple successive approximation procedure is established by means of a single recursion formula which requires elementary operations to be performed on polynomials of increasing degrees. 相似文献
8.
We have considered a homogeneous atmosphere scattering anisotropically with Dirac -function type time-dependent incidence. We used the method of integral operator developed by Ambartsumian and the theory ofN-solutions developed by Busbridge to find the correspondingH-function (in semi-infinite atmosphere) andX- andY-functions (in finite atmosphere). 相似文献
9.
Kenneth Moe 《Solar physics》1983,88(1-2):9-12
Two methods of integrating limb-darkening data to calculate the spectral irradiance are compared. Near 300 nm Moe and Milone's (1978) quadratic approximation to the limb darkening yields an integral 3% larger on average than the two linear segments of Kohl et al. (1980) when the same data are inserted in both formulas. As one would expect, the difference between the two calculations is directly proportional to Moe and Milone's quadratic coefficient. When Moe and Milone's data are inserted in the formula of Kohl et al., the calculated irradiance is 4% higher than when the data of Kohl et al. are used in the same formula. Possible reasons for this difference are suggested. 相似文献
10.
H.-J. Treder 《Astronomische Nachrichten》1974,295(1):1-8
According to the principle of correspondence (in HEISENBERG 's formulation) each general relativistic theory of gravitation must give a NEWTON ian representation for an isotropic cosmos with the ROBERTSON -WALKER metric. Indeed, the FRIEDMANN equations can be interpreted as the expression for the HAMILTON ian H of a closed NEWTON ian system of the cosmic fundamental particles, written in the rest-system of the center of gravity. In this HAMILTON ian H only the relative-coordinates and the relative-velocities of the particles are present and one can write H without absolute quantities but only with MILNE 's relative-quantities. The time-independence of the HAMILTON ian H = 0 is the FRIEDMANN equation. – This NEWTON ian deduction of the FRIEDMANN equation is more general than the relativistic deduction and than MILNE 's deduction for a NEWTON ian fluid, too. In the general NEWTON ian form H the parameter f M of the active mass can be an arbitrary function of the cosmic time t. The choice f = f(t), M = M(t) defines the divers modifications of relativistic cosmology. – In general relativity fM = const and M = const are resulting from EINSTEIN 's equations and from EINSTEIN 's principle of equivalence. 相似文献
11.
In this work, we first establish a simple procedure to obtain with 11-figure accuracy the values of Chandrasekhar’s H-function for isotropic scattering using a closed-form integral representation and the Gauss-Legendre quadrature. Based on the numerical values of the function produced by this method for various combinations of ? 0, the single scattering albedo, and μ, the cosine of the zenith angle θ of the direction of radiation emergent from or incident upon a semi-infinite scattering-absorbing medium, we propose a rational approximation formula with μ 1/4 and \(\sqrt{1-\varpi_{0}}\) as the independent variables. This allows us to reproduce the correct values of H(? 0,μ) within a relative error of 2.1×10?5 without recourse to any iterative procedure or root-finding process. 相似文献
12.
Shi-ju Kang Bang-rong HuangTing Kang Ji-hua LiangYong-gang Zheng 《Chinese Astronomy and Astrophysics》2012
Based on the log-parabolic spectral energy distribution of electrons, and the homogeneous one-zone synchrotron self-Compton (SSC) model, the multiband spectral energy distribution of the BL Lac object S5 0716+714 is calculated. Compared with Paggi's result which is obtained by means of δ-function approximation, it is found that a certain difference exists between our result and Paggi's. The main reason leading to this difference may be that the δ-function approximation on the synchrotron radiation of a single electron loses a part of electron energy, and therefore affects the result of inverse Compton scattering. Applying this model to the results of the multi-band observations made at three different states of Mark 421: high, medium, and low, the results of theoretical calculations are coincident very well with the observational results under the three different states of the object. An analysis indicates that the observed different states of Mark 421 are probably caused by the variation of the electron distribution in the jet. 相似文献
13.
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
14.
S. R. Das Gupta 《Astrophysics and Space Science》1978,56(1):13-20
The transfer equations for non-coherent scattering arising from interlocking of principal lines without redistribution is exactly solved in a very simple way by Laplace tranform and Wiener-Hopf technique which are easily applied by the use of the new representation ofH-functions obtained recently by the author (1977). The emergent intensity in therth line is expressed in terms of anH-function and a Cauchy type integral admitting of closed form evaluation. 相似文献
15.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1981,74(1):211-234
In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofF will be established for anyx
i
; withn, N positive integers 1 and |
i
| fori=1, 2,...n. Moreover, the recurrence formulae satisfied by these coefficients will also be established. Illustrative analytical examples and a full recursive computational algorithm, with its numerical results, are included. The applications of the recurrence formulae are also illustrated by their stencils. As a by-product of the analyses is an integral which we may call a complete elliptic integral of thenth kind, in which the known complete elliptic integrals (1st, 2nd and 3rd kinds) are special cases of it. 相似文献
16.
Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary
problems. Their solution via differential equations implies making hypotheses on the solution itself, namely the specific
intensity I (τ; n) of the radiation field. On the contrary, integral methods require making hypotheses on the source function S(τ). It seems of course more reasonable to make hypotheses on the latter because one can expect that the run of S(τ) with depth is smoother than that of I (τ; n). In previous works we assumed a piecewise parabolic approximation for the source function, which warrants the continuity
of S(τ) and its first derivative at each depth point. Here we impose the continuity of the second derivative S′′(τ). In other words, we adopt a cubic spline representation to the source function, which highly stabilizes the numerical
processes. 相似文献
17.
Anisotropic Bianchi-III cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein’s general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Λ are discussed. Without assuming any specific forms for Λ and the metric potentials, we have tried to extract the time variation of G and Λ from the anisotropic model. The extracted G and Λ are in conformity with the present day observations. Basing upon the observational limits, the behavior and range of the effective equation of state parameter are discussed. 相似文献
18.
S. M. El-Shaboury 《Earth, Moon, and Planets》1990,48(3):243-250
In this paper the circular planar restricted problem of three axisymmetric ellipsoids S
i
(i = 1, 2, 3), such that their equatorial planes coincide with the orbital plane of the three centres of masses, be considered. The equations of motion of infinitesimal body S
3
be obtained in the polar coordinates. Using iteration approach we have given an approximation for another integral, which independent of the Jacobian integral, in the case of P-type orbits (near circular orbits surrounding both primaries). 相似文献
19.
H. Havemann 《Astronomische Nachrichten》1981,302(2):103-112
The two great divisions of the Saturn rings, one of them discovered by the spacecraft observations of 1979, can be explained as narrow zones of meteorites. The new informations by soacecraft encounters raise the probability of a real value of the series 2n(3–4–5), pointed out by the author in 1928 as approached by the sequence of Saturn's rings and moons. The Titius-Bode-series of planets and a similar series of Jupiter's moons also profit from this support. The author's attempt to explain these correspondences dynamically (first published in Havemann 1978) starts with the assumption of a thin central disk in the preplanetary nebulas. The chance of the Titius-Bode series concerning the sequence of planets is much raised by the result of spacecraft informations that Saturn contains an iron core comparable with that of the Earth. This supports the author's conjecture that iron cores of planets have first formed without envelopes. 相似文献