共查询到20条相似文献,搜索用时 31 毫秒
1.
P. P. Gorvat V. Yu. Lazur L. P. Presnyakov D. B. Uskov 《Theoretical and Mathematical Physics》1992,91(1):373-384
The eikonal approximation in the distorted wave formalism is modified for application to three-particle scattering with rearrangement in the region in which neither the Born nor the adiabatic approximation is valid. The long-range effects due to Coulomb interaction between the particles in both the entrance and exit reaction channels are investigated. The leading asymptotic term (in the large impact parameter) of the eikonal charge exchange amplitude is calculated for transitions betweens states of atoms. It is shown that the general expression for the amplitude correctly describes both limiting casesvv
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0.State University, Uzhgorod; P. N. Lebedev Physics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 66–82, April, 1992. 相似文献
2.
Toshikazu Kimura 《The Journal of the Operational Research Society》1991,42(7):595-603
This paper deals with refining Cosmetatos's approximation for the mean waiting time in an M/D/s queue. Although his approximation performs quite well in heavy traffic, it overestimates the true value when the number of servers is large or the traffic is light. We first focus on a normalized quantity that is a ratio of the mean waiting times for the M/D/s and M/M/s queues. Using some asymptotic properties of the quantity, we modify Cosmetatos's approximation to obtain better accuracy both for large s and in light traffic. To see the quality of our approximation, we compare it with the exact value and some previous approximations. Extensive numerical tests indicate that the relative percentage error is less than 1% for almost all cases with s ≤ 20 and at most 5% for other cases. 相似文献
3.
Chelo Ferreira 《Journal of Mathematical Analysis and Applications》2004,298(1):210-224
The Hurwitz-Lerch zeta function Φ(z,s,a) is considered for large and small values of a∈C, and for large values of z∈C, with |Arg(a)|<π, z∉[1,∞) and s∈C. This function is originally defined as a power series in z, convergent for |z|<1, s∈C and 1−a∉N. An integral representation is obtained for Φ(z,s,a) which define the analytical continuation of the Hurwitz-Lerch zeta function to the cut complex z-plane C?[1,∞). From this integral we derive three complete asymptotic expansions for either large or small a and large z. These expansions are accompanied by error bounds at any order of the approximation. Numerical experiments show that these bounds are very accurate for real values of the asymptotic variables. 相似文献
4.
We construct a relativistic potential quark model of D, Ds, B, and Bs mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy
quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination
of the perturbative one-gluon exchange potential VCoul(r) and the long-range Lorentz-scalar and Lorentz-vector linear potentials Sl.r.(r) and Vl.r.(r). In the semiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the
mean radii of D, Ds, B, and Bs mesons, which ensure a high accuracy of calculations even for states with the radial quantum number nr ∼ 1. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters:
the strong-coupling constant αs and the coefficient λ of mixing of the long-range scalar and vector potentials Sl.r.(r) and Vl.r.(r).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 371–397, June, 2008. 相似文献
5.
A. A. Belolipetskii A. M. Ter-Krikorov 《Computational Mathematics and Mathematical Physics》2016,56(11):1859-1871
The functional equation f(x,ε) = 0 containing a small parameter ε and admitting regular and singular degeneracy as ε → 0 is considered. By the methods of small parameter, a function x n 0(ε) satisfying this equation within a residual error of O(ε n+1) is found. A modified Newton’s sequence starting from the element x n 0(ε) is constructed. The existence of the limit of Newton’s sequence is based on the NK theorem proven in this work (a new variant of the proof of the Kantorovich theorem substantiating the convergence of Newton’s iterative sequence). The deviation of the limit of Newton’s sequence from the initial approximation x n 0(ε) has the order of O(ε n+1), which proves the asymptotic character of the approximation x n 0(ε). The method proposed is implemented in constructing an asymptotic approximation of a system of ordinary differential equations on a finite or infinite time interval with a small parameter multiplying the derivatives, but it can be applied to a wider class of functional equations with a small parameters. 相似文献
6.
Marcin Kulczycki 《Regular and Chaotic Dynamics》2014,19(3):310-317
This paper introduces the notion of a general approximation property, which encompasses many existing types of shadowing. It is proven that there exists a metric space X such that the sets of maps with many types of general approximation properties (including the classic shadowing, the L p -shadowing, limit shadowing, and the s-limit shadowing) are not dense in C(X), S(X), and H(X) (the space of continuous self-maps of X, continuous surjections of X onto itself, and self-homeomorphisms of X) and that there exists a manifold M such that the sets of maps with general approximation properties of nonlocal type (including the average shadowing property and the asymptotic average shadowing property) are not dense in C(M), S(M), and H(M). Furthermore, it is proven that the sets of maps with a wide range of general approximation properties (including the classic shadowing, the L p -shadowing, and the s-limit shadowing) are dense in the space of continuous self-maps of the Cantor set. A condition is given that guarantees transfer of general approximation property from a map on X to the map induced by it on the hyperspace of X. It is also proven that the transfer in the opposite direction always takes place. 相似文献
7.
E. Bolthausen 《Stochastic Processes and their Applications》1984,16(2):199-204
Let ξt, t ? 0, be a d-dimensional Brownian motion. The asymptotic behaviour of the random field ??∫t0?(ξs) ds is investigated, where ? belongs to a Sobolev space of periodic functions. Particularly a central limit theorem and a law of iterated logarithm are proved leading to a so-called universal law of iterated logarithm. 相似文献
8.
M. Hnatich V. M. Khmara V. Yu. Lazur O. K. Reity 《Theoretical and Mathematical Physics》2017,190(3):345-358
Using a modified perturbation theory, we obtain asymptotic expressions for the two-center quasiradial and quasiangular wave functions for large internuclear distances R. We show that in each order of 1/R, corrections to the wave functions are expressed in terms of a finite number of Coulomb functions with a modified charge. We derive simple analytic expressions for the first, second, and third corrections. We develop a consistent scheme for obtaining WKB expansions for solutions of the quasiangular equation in the quantum mechanical two-Coulomb-center problem. In the framework of this scheme, we construct semiclassical two-center wave functions for large distances between fixed positively charged particles (nuclei) for the entire space of motion of a negatively charged particle (electron). The method ensures simple uniform estimates for eigenfunctions at arbitrary large internuclear distances R, including R ≥ 1. In contrast to perturbation theory, the semiclassical approximation is not related to the smallness of the interaction and hence has a wider applicability domain, which permits investigating qualitative laws for the behavior and properties of quantum mechanical systems. 相似文献
9.
Mark W. Coffey 《Journal of Mathematical Analysis and Applications》2006,317(2):603-612
The Stieltjes constants γk(a) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about s=1. We present new asymptotic, summatory, and other exact expressions for these and related constants. 相似文献
10.
We estimate the degree of comonotone polynomial approximation of continuous functions f, on [?1,1], that change monotonicity s??1 times in the interval, when the degree of unconstrained polynomial approximation E n (f)??n ??? , n??1. We ask whether the degree of comonotone approximation is necessarily ??c(??,s)n ??? , n??1, and if not, what can be said. It turns out that for each s??1, there is an exceptional set A s of ????s for which the above estimate cannot be achieved. 相似文献
11.
B. E. Klots 《Mathematical Notes》1975,18(1):640-646
We consider the problem of the asymptotically best linear method of approximation in the metric of Ls[?π, π] of the set \(\tilde W_p^\alpha (1)\) of periodic functions with a bounded in Lp[?π, π] fractional derivative, by functions from \(\tilde W_p^\beta (M)\) ,β >α, for sufficiently large M, and the problem about the best approximation in Ls[?π, π] of the operator of differentiation on \(\tilde W_p^\alpha (1)\) by continuous linear operators whose norm (as operators from Lr[?π, π] into Lq[?π, π])does not exceed M. These problems are reduced to the approximation of an individual element in the space of multipliers, and this allows us to obtain estimates that are exact in the sense of the order. 相似文献
12.
Expansions in terms of Bessel functions are considered of the Kummer function 1
F
1(a; c, z) (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials
in the parameters of the Kummer function and the asymptotic behavior of these polynomials for large degree is given. Tables
are given to show the rate of approximation of the asymptotic estimates. The numerical performance of the expansions is discussed
together with the numerical stability of recurrence relations to compute the polynomials. The asymptotic character of the
expansions is explained for large values of the parameter a of the Kummer function. 相似文献
13.
14.
$ {\rm Let}\ f\ \epsilon\ {C^{1}}[-1,1] $ change its convexity finitely many times in the interval, say s times, at ${\rm at}\ {Y_{s}}\:\ -1\ <\ y_{s}\ <\ \dots\ < y_{1}\ < 1 $ . We estimate the degree of simultaneous approximation of ? and its derivative by polynomials of degree n, which change convexity exactly at the points Y s, and their derivatives. We show that provided n is sufficiently large, depending on the location of the points Y s, the rate of approximation can be estimated by C(s)/n times the second Ditzian-Totik modulus of smoothness of ?′. This should be compared to a recent paper by the authors together with I. A. Shevchuk where ? is merely assumed to be continuous and estimates of coconvex approximation are given by means of the third Ditzian-Totik modulus of smoothness. However, no simultaneous approximation is given there. 相似文献
15.
Daniel Berend 《Journal d'Analyse Mathématique》1988,50(1):123-142
Given measure preserving transformationsT 1,T 2,...,T s of a probability space (X,B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {T_1^n f_1 \cdot T_2^n f_2 } \cdot \cdots \cdot T_s^n f_s $$ wheref 1,f 2,...,f s ?L ∞(X,B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) inL 2-norm is ∫ x f 1 dμ·∫ x f 2 dμ...∫ x f s dμ for anyf 1,f 2...,f s ?L ∞(X,B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups. 相似文献
16.
This paper studies the asymptotic behavior of the steady-state waiting time, W ∞, of the M/G/1 queue with Subexponential processing times for different combinations of traffic intensities and overflow levels. In particular, we provide insights into the regions of large deviations where the so-called heavy-traffic approximation and heavy-tail asymptotic hold. For queues whose service time distribution decays slower than \(e^{-\sqrt{t}}\) we identify a third region of asymptotics where neither the heavy-traffic nor the heavy-tail approximations are valid. These results are obtained by deriving approximations for P(W ∞>x) that are either uniform in the traffic intensity as the tail value goes to infinity or uniform on the positive axis as the traffic intensity converges to one. Our approach makes clear the connection between the asymptotic behavior of the steady-state waiting time distribution and that of an associated random walk. 相似文献
17.
Define the incremental fractional Brownian field Z_H(τ,s)=B_H(s+τ)-B_H(s),where B_H(s) is a standard fractional Brownian motion with Hurst parameter H ∈(0,1).In this paper,we first derive an exact asymptotic of distribution of the maximum M_H(T_u)=sup_τ∈[0,1],s∈[0,xT_u]Z_H(τ,s),which holds uniformly for x ∈[A,B]with A,B two positive constants.We apply the findings to analyse the tail asymptotic and limit theorem of MH(τ) with a random index τ.In the end,we also prove an ahnost sure limit theorem for the maximum M_(1/2)(T) with non-random index T. 相似文献
18.
J.W. Cohen 《Stochastic Processes and their Applications》1973,1(2):107-124
For the GI?G?1 queueing system a number of asymptotic results are reviewed. Discussed are asymptotics related to the time parameter for t → ∞ relaxation times, heavy traffic theory, restricted accessibility with large bounds, approximation by diffusion processes, exponential and regular variation of the tail of the waiting time distribution, limit theorems and extreme value theorems. 相似文献
19.
M. Pitchaimani 《Journal of Applied Mathematics and Computing》2013,41(1-2):133-152
In this paper, we provide an interval of existence of critical mortality rate parameters M r and b and their asymptotic expressions in allometry survival model, in the absence of age-specific mortality data. 相似文献
20.
A Yanushka 《Journal of Combinatorial Theory, Series A》1979,26(2):193-196
If a generalized octagon with parameters (s, t) for t > s has a proper suboctagon with parameters (s1, t1), then st ? s12t1. 相似文献