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71.
Abstract In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jinand Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weaklyparabolic, has a linearly hyperbolic convection part, and is endowed with a generalized eotropy inequality. Itagrees with the solution of the Boltzmann equation up to the Burnett order via the Chapman-Enskog expansion. We develop a one-dimensional non-oscillatory numerical scheme based on the relaxed Burnett system forthe Boltzmann equation. We compare numerical results for stationary shocks based on this relaxation scheme,and those obtained by the DSMC (Direct Simulation Monte Carlo), by the Navier-Stokes equations and bythe extended thermodynamics with thirteen moments (the Grad equations). Our numerical experiments showthat the relaxed Burnett gives more accurate approximations to the shock profiles of the Boltzmann equationobtained by the DSMC, for a range of Mach numbers for hypersonic flows, th 相似文献
72.
强混合样本下回归加权估计的一致渐近正态性 总被引:5,自引:0,他引:5
在强混合样本下,讨论固定设计回归模型的加权函数估计的一致渐近正态性,给出一致渐近正态性的收敛速度,这个速度接近n-1/6. 相似文献
73.
This paper studied the cost allocation for the unfunded liability in a defined benefit pension scheme incorporating the stochastic phenomenon of its returns. In the recent literature represented by Cairns and Parker [Insurance: Mathematics and Economics 21 (1997) 43], Haberman [Insurance: Mathematics and Economics 11 (1992) 179; Insurance: Mathematics and Economics 13 (1993) 45; Insurance: Mathematics and Economics 14 (1994) 219; Insurance: Mathematics and Economics 14 (1997) 127], Owadally and Haberman [North American Actuarial Journal 3 (1999) 105], the fund level is modeled based on the plan dynamics and the returns are generated through several stochastic processes to reflect the current realistic economic perspective to see how the contribution changed as the cost allocation period increased. In this study, we generalize the previous constant value assumption in cost amortization by modeling the returns and valuation rates simultaneously. Taylor series expansion is employed to approximate the unconditional and conditional moments of the plan contribution and fund level. Hence the stability of the plan contribution and the fund size under different allocation periods could be estimated, which provide valuable information adding to the previous works. 相似文献
74.
使用“对称性匹配簇-组态相互作用”方法,对Li2分子三重态的第一激发态、LiH分子的基态、单重态的第一和第二激发态的几何构型与谐振频率进行了优化计算.利用“群操作求和”方法分别对这4个态进行单点能扫描计算,并拟合出了相应各态的Murrell-Sorbie势能函数.使用多种方法对Li2H分子的基态结构进行优化,并用优选出的密度泛函(B3P86)方法对该分子进行了进一步的频率计算.结果发现Li2H分子的基态稳态结构为C2v构型,在此基础上用多体项展式理论导出了它的解析势能函数,其等值势能图准确再现了Li2H分子的结构特征和离解能.首次报导了该分子对称伸缩振动等值势能图中存在的两个对称鞍点,对应于反应LiH Li→Li2H,活化能大约为18.7×4.184 KJ/mol. 相似文献
75.
We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani(9) and Bobylev, Cercignani and one of the authors.(11) 相似文献
76.
本文讨论了一类Rosenbrock方法求解比例延迟微分方程,y′(t)=λy(t) μy(qt),λ,μ∈C,0 相似文献
77.
We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability
pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0≤ n0≤ m). Numerical studies back up the asymptotic analysis.
AMS subject classification: 60K25,34E10
Supported in part by NSF grants DMS-99-71656 and DMS-02-02815 相似文献
78.
在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示.在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程.当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简. 相似文献
79.
本文研究了未知分布的逼近问题,利用随机加权法,给出了有Edgeworth展式的一类(未知)分布的模拟分布,证明了在一定条件下,模拟分布与未知分布的逼近精度达到O(n^-1√lnlnn),称之为随机加权逼近的重对数律。 相似文献
80.
The purpose of this paper is two-fold. First, we introduce a new asymptotic expansion in the exponent for the compound binomial
approximation of the generalized Poisson binomial distribution. The dependence of its accuracy on the symmetry and shifting
of distributions is investigated. Second, for compound binomial and compound Poisson distributions, we present new smoothness
estimates, some of which contain explicit constants. Finally, the ideas used in this paper enable us to prove new precise
bounds in the compound Poisson approximation.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 1, pp. 67–110, January–March, 2006. 相似文献