共查询到20条相似文献,搜索用时 15 毫秒
1.
Rémi Soufflet 《Bulletin of the Brazilian Mathematical Society》2002,33(1):125-146
The aim of this paper is to study the asymptotic expansion of real functions which are finite compositions of globally subanalytic
maps with the exponential function and the logarithmic function. This is done thanks to a preparation theorem in the spirit
of those that exist for analytic functions (Weierstrass) or subanalytic functions (Parusinśki). The main consequence is that
logarithmic-exponential functions admit convergent asymptotic expansion in the scale of real power functions. We also deduce
a partial answer to a conjecture of van den Dries and Miller.
Received: 19 March 2002 相似文献
2.
Asymptotic expansions in the two limitsx → + ∞ andx → 0+ are obtained for the Mehler-Fock transform
相似文献
3.
The asymptotic expansions for the distribution functions of Pickands-type estimators in extreme statistics are obtained. In
addition, several useful results on regular variation and intermediate order statistics are presented.
Project supported by the National Natural Science Foundation of China (Grant No. 19601007) and Doctoral Program Foundation
of Higher Education of China. 相似文献
4.
Asymptotic expansions of posterior expectations,distributions and densities for stochastic processes
Martin Crowder 《Annals of the Institute of Statistical Mathematics》1988,40(2):297-309
Asymptotic expansions are derived for Bayesian posterior expectations, distribution functions and density functions. The observations constitute a general stochastic process in discrete or continuous time. 相似文献
5.
Marilena?Munteanu 《Bulletin of the Brazilian Mathematical Society》2007,38(1):39-50
In this paper we propose a technique of approximation for the generalized Riemann-Stieltjes integral and we found an analogue
for Newton-Cotes formulas in the case n = 2 and n = 3.
*Beneficiary of a Socrates fellowship at the Department of Mathematics, University of Study of Cagliari, Via Ospedale, n.
72, Cagliari, 09124, Italy, in the period February – July 2002. 相似文献
6.
We describe high-precision computations of the Pearcey integral Pe(x,y) for real x and y by means of Hadamard expansions. Numerical results for (x,y) situated in different regions of the x,y-plane are given to illustrate the levels of precision that can be achieved. Particular emphasis is given to computation in the neighbourhood of the two cusped curves associated with Pe(x,y) across which there is either a coalescence of saddles or a Stokes phenomenon. 相似文献
7.
Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter 下载免费PDF全文
Chelo Ferreir Jose L. Lopez Ester Perez Sinusia 《Journal of Applied Analysis & Computation》2018,8(3):965-981
In previous papers [6-8,10], we derived convergent and asymptotic expansions of solutions of second order linear differential equations with a large parameter. In those papers we generalized and developed special cases not considered in Olver"s theory [Olver, 1974]. In this paper we go one step forward and consider linear differential equations of the third order: $y"+a\Lambda^2 y"+b\Lambda^3y=f(x)y"+g(x)y$, with $a,b\in\mathbb{C}$ fixed, $f"$ and $g$ continuous, and $\Lambda$ a large positive parameter. We propose two different techniques to handle the problem: (i) a generalization of Olver"s method and (ii) the transformation of the differential problem into a fixed point problem from which we construct an asymptotic sequence of functions that converges to the unique solution of the problem. Moreover, we show that this second technique may also be applied to nonlinear differential equations with a large parameter. As an application of the theory, we obtain new convergent and asymptotic expansions of the Pearcey integral $P(x,y)$ for large $|x|$. 相似文献
8.
We derive asymptotic formulae for two‐dimensional and three‐dimensional steady state voltage potentials associated with thin conductivity imperfections having no uniform thickness. These formulae recover highly conducting inclusions and those with interfacial resistance. Our calculations are rigorous and based on layer potential techniques. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
9.
10.
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
11.
张领海 《应用数学学报(英文版)》1994,10(4):377-386
ASYMPTOTICPROPERTYFORTHESOLUTIONTOTHEGENERALIZEDKORTEWEG-DEVRIESEQUATIONZHANGLINGHAI(张领海)(DeportmentofMathematics,theOhioStat... 相似文献
12.
J. L. López 《Constructive Approximation》2001,17(4):535-559
Symmetric standard elliptic integrals are considered when two or more parameters are larger than the others. The distributional approach is used to derive seven expansions of these integrals in inverse powers of the asymptotic parameters. Some of these expansions also involve logarithmic terms in the asymptotic variables. These expansions are uniformly convergent when the asymptotic parameters are greater than the remaining ones. The coefficients of six of these expansions involve hypergeometric functions with less parameters than the original integrals. The coefficients of the seventh expansion again involve elliptic integrals, but with less parameters than the original integrals. The convergence speed of any of these expansions increases for an increasing difference between the asymptotic variables and the remaining ones. All the expansions are accompanied by an error bound at any order of the approximation. January 31, 2000. Date revised: May 18, 2000. Date accepted: August 4, 2000. 相似文献
13.
Alessandro Savo 《Geometriae Dedicata》1998,73(2):181-214
We give a recursive algorithm for the computation of the complete asymptotic series, for small time, of the amount of heat inside a domain with smooth boundary in a Riemannian manifold; we consider arbitrary smooth initial data, and we impose Dirichlet condition on the boundary. When the Ricci curvature of the domain and the mean curvature of its boundary are both nonnegative, we also give sharp upper and lower bounds of the heat content which hold for all values of time. These estimates extend to convex sets of the Euclidean space having arbitrary boundary. 相似文献
14.
Asymptotic expansions for currents caused by small interface changes of an electromagnetic inclusion
Habib Zribi 《Applicable analysis》2013,92(1):172-190
We consider solutions to the Helmholtz equation in two dimensions. The aim of this article is to advance the development of high-order asymptotic expansions for boundary perturbations of currents caused by small perturbations of the shape of an inhomogeneity with 𝒞2-boundary. The work represents a natural completion of Ammari et al. [H. Ammari, H. Kang, M. Lim, and H. Zribi, Conductivity interface problems. Part I: Small perturbations of an interface, Trans. Am. Math. Soc. 363 (2010), pp. 2901–2922], where the solution for the Helmholtz equation is represented by a system and the proof of our asymptotic expansion is radically different from Ammari et al. (2010). Our derivation is rigorous and is based on the field expansion method. Its proof relies on layer potential techniques. It plays a key role in developing effective algorithms to determine certain properties of the shape of an inhomogeneity based on boundary measurements. 相似文献
15.
Chelo Ferreira José L. López Ester Pérez Sinusía 《Studies in Applied Mathematics》2023,150(1):254-276
We consider the highly oscillatory integral for large positive values of w, , K and p positive integers with , and an entire function. The standard saddle point method is complicated and we use here a simplified version of this method introduced by López et al. We derive an asymptotic approximation of this integral when for general values of K and p in terms of elementary functions, and determine the Stokes lines. For , the asymptotic behavior of this integral may be classified in four different regions according to the even/odd character of the couple of parameters K and p; the special case requires a separate analysis. As an important application, we consider the family of canonical catastrophe integrals for large values of one of its variables, say , and bounded values of the remaining ones. This family of integrals may be written in the form for appropriate values of the parameters w, θ and the function . Then, we derive an asymptotic approximation of the family of canonical catastrophe integrals for large . The approximations are accompanied by several numerical experiments. The asymptotic formulas presented here fill up a gap in the NIST Handbook of Mathematical Functions by Olver et al. 相似文献
16.
讨论了广义中立型延迟系统理论的渐近稳定性,给出了广义中立型系统渐近稳定的一些充分条件。 相似文献
17.
The symbolic calculus developed by Francis Hirsch (in several papers, between 1972 and 1976) is an already classical theory that introduces and studies the operators f(A) associated to a non-negative linear operator A on a Banach space and to the Stieltjes transform f of a Radon measure . It is required that the operator A has a dense domain and that the measure , as well as the value f()), are real and non-negative. These three conditions are essential in the proof of the main results, but they are very restrictive, since important cases are excluded, as the fractional powers A of complex exponent , or of base A non-densely defined. In this paper we present a reconstruction of the Hirsch theory, without using those hypothesis. 相似文献
18.
In this paper the Parseval theorem for Laplace and Stieltjestransforms which was proved by Yurekli (1989, IMA J. Appl. Math.,42, 241249) for conventional functions is proved forgeneralized functions. The theorem yields some corollaries similarto the corollaries in Yurekli (1989). 相似文献
19.
Asymptotic expansions are given for the distributions of latent roots of matrices in three multivariate situations. The distribution of the roots of the matrix S1(S1 + S2)?1, where S1 is and S2 is Wm(n2, Σ), is studied in detail and asymptotic series for the distribution are obtained which are valid for some or all of the roots of the noncentrality matrix Ω large. These expansions are obtained using partial-differential equations satisfied by the distribution. Asymptotic series are also obtained for the distributions of the roots of n?1S, where S in Wm(n, Σ), for large n, and S1S2?1, where S1 is Wm(n1, Σ) and S2 is Wm(n2, Σ), for large n1 + n2. 相似文献
20.
The Barnes double gamma function G(z) is considered for large argument z. A new integral representation is obtained for log G(z). An asymptotic expansion in decreasing powers of z and uniformly valid for |Arg z|<π is derived from this integral. The expansion is accompanied by an error bound at any order of the approximation. Numerical experiments show that this bound is very accurate for real z. The accuracy of the error bound decreases for increasing Arg z. 相似文献
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