连续时间遗传算法模型及其强收敛性分析

本文在隐马尔可夫链的框架下利用隐马尔可夫链{Xt:t∈[0,∞)}的观测链的概率分布提出一个连续化遗传算法模型，并给出其一个强收敛结果，讨论了其离散骨架的性质。     

不同马赫数Navier-Stokes方程计算方法的研究

为了在低马赫数到高马赫数范围内求解可压缩Navier-Stokes方程,给出了基于预处理算法的PLU-SGS方法.将高分辨率AUSMPW格式与三阶MUSCL格式融合,将其扩展到三阶精度,并采用特征边界条件.为了验证该方法的有效性,通过求解曲线坐标系可压缩Navier-Stokes方程,对几个典型流动问题进行了数值计算.计算结果与文献计算结果或实验数据比较表明,该方法对不同马赫数Navier-Stokes方程的计算,具有较高的计算精度和收敛速度以及良好的稳定性.     

Single and Multi-Interval Legendre τ-Methods in Time for Parabolic Equations

In this paper, we take the parabolic equation with periodic boundary conditions as a model to present a spectral method with the Fourier approximation in spatial and single/multi-interval Legendre Petrov–Galerkin method in time. For the single interval spectral method in time, we obtain the optimal error estimate in L ²-norm. For the multi-interval spectral method in time, the L ²-optimal error estimate is valid in spatial. Numerical results show the efficiency of the methods.     

Exact Buffer Overflow Calculations for Queues via Martingales

Let _n be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean _n and the Laplace transform e^-sn is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results.     

Asymptotic Bound on the Characteristic Function of Signed Linear Serial Rank Statistics

This work establishes an asymptotic bound on the characteristic function of signed linear serial rank statistics. The result is obtained under rather general conditions including the important case of van der Waerden scores. It generalizes the result of Seoh (1983, Ph.D. Thesis, Department of Mathematics, Indiana University) and constitutes an essential step to the elaboration of Berry-Esséen's bounds and the establishment of Edgeworth expansions. These statistics constitute a natural tool for testing the hypothesis of white noise with a symmetrical (unspecified) distribution in comparison to other alternative hypothesis of serial dependence.     

Parallelization of a Two-Phase Metaheuristic for Routing Problems with Time Windows

This paper describes the parallelization of a two-phase metaheuristic for the vehicle routing problem with time windows and a central depot (VRPTW). The underlying objective function combines the minimization of the number of vehicles in the first search phase of the metaheuristic with the minimization of the total travel distance in the second search phase. The parallelization of the metaheuristic follows a type 3 parallelization strategy (cf. Crainic and Toulouse (2001). In F. Glover and G. Kochenberger (eds.). State-of-the-Art Handbook in Metaheuristics. Norwell, MA: Kluwer Academic Publishers), i.e. several concurrent searches of the solution space are carried out with a differently configured metaheuristic. The concurrently executed processes cooperate through the exchange of solutions. The parallelized two-phase metaheuristic was subjected to a comparative test on the basis of 358 problems from the literature with sizes varying from 100 to 1000 customers. The derived results seem to justify the proposed parallelization concept.     

On Short Time Asymptotic Behavior of Some Symmetric Diffusions on General State Spaces

For conservative symmetric diffusions on a general state space (X,m), the short time asymptotic behavior of tlog _X 1 _A T _t 1 _B dm is investigated, where T _t is the associated semigroup and A and B are measurable subsets of X. It is proved that the superior limit is dominated by the inferior limit up to some absolute constant. When ₂ of the associated Dirichlet form is lower bounded, it is shown that the limit exists for any A and B, and is described by the intrinsic metric between them. Applications to infinite-dimensional spaces and fractals are given.     

Backward Euler discretization of fully nonlinear parabolic problems

This paper is concerned with the time discretization of nonlinear evolution equations. We work in an abstract Banach space setting of analytic semigroups that covers fully nonlinear parabolic initial-boundary value problems with smooth coefficients. We prove convergence of variable stepsize backward Euler discretizations under various smoothness assumptions on the exact solution. We further show that the geometric properties near a hyperbolic equilibrium are well captured by the discretization. A numerical example is given.

     

Large time behavior of small solutions to subcritical derivative nonlinear Schrödinger equations

We consider the derivative nonlinear Schrödinger equations

where the coefficient satisfies the time growth condition

is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type

where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when

     

首达渗流中关于lim{(N_(on))/n}(n→∞)的一个结果

在二维首达渗流中,设边上通过时间的分布为F（x）,首达时a_（on）的轨道（route）的最短长度为N_（on）,人们猜测存在.本文对F（0）<1/2的情形,就一类特殊的分布证明此猜想成立.