On the long‐time stability of the Crank–Nicolson scheme for the 2D Navier–Stokes equations

In this article we study the stability for all positive time of the Crank–Nicolson scheme for the two‐dimensional Navier–Stokes equations. More precisely, we consider the Crank–Nicolson time discretization together with a general spatial discretization, and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the numerical scheme is stable, provided a CFL‐type condition is satisfied. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

On error operators related to the arbitrary functions principle

The error on a real quantity Y due to the graduation of the measuring instrument may be asymptotically represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator does not depend on the probability law of Y as soon as this law possesses a continuous density. This feature is related to the “arbitrary functions principle” (Poincaré, Hopf). We give extensions of this property to Rd and to the Wiener space for some approximations of the Brownian motion. This gives new approximations of the Ornstein-Uhlenbeck gradient. These results apply to the discretization of some stochastic differential equations encountered in mechanics.     

一类广义的Kdv方程的显式差分解

本文考察一类具耗散的广义KdV方程组■ (gradφ(■))_x ■_(xxx)-α■_(xx) γ■ =■(x,t,■)的周期初值问题的显式差分格式．利用有界延拓法证明了该差分格式的收敛性与稳定性,并给出了算法和数值例子．     

Rheology of polystyrene solutions around the coil overlapping concentration: A phenomenological description of stresses in simple shear flow

Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τ_RZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τ_L > τ_RZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ₁) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ²)^?1/2, where γ is the magnitude of shear. Contributions to η and Ψ₁ from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τ_st = τ + (τ_RZ ? τ)/(1 + 0.35τ_RZ γ˙) instead of τ_RZ. Here, γ˙ is the rate of shear, and τ is the τ_RZ value at the infinite dilution limit. η and Ψ₁ at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol^?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002     

A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations北大核心CSCD

针对三维非稳态对流扩散反应方程,构造了一种高精度紧致有限差分格式,对空间的离散采用四阶紧致差分方法,对时间的离散采用Taylor级数展开和余项修正技术,所提格式在时间上的精度为二阶、在空间上的精度为四阶。利用Fourier稳定性分析法证明了该格式是无条件稳定的。最后给出数值算例验证了理论结果。     

On the population monotonicity of independent set games

An independent set game is a cooperative game dealing with profit sharing in the maximum independent set problem. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for independent set games admitting population monotonic allocation schemes. Moreover, our characterization can be verified efficiently.     

带五次项的非线性Schrödinger方程的守恒差分格式

本文研究带有五次项的非线性Schrödinger方程初边值问题的有限差分法,其中方程中二阶偏导数项的系数、五次项的系数及初值满足下面的条件（1.6）.针对此问题,我们研究了一个守恒差分格式,在条件（1.6）下,差分解的$L^{\infty}$模先验估计被得到.在此基础上,我们得到了差分解最优$L^2$模的误差估计.     

汽车制造商分时租赁模式采用及产品线策略研究

考虑自有平台和第三方平台两种分时租赁方式,将汽车质量划分为性能质量和环境质量,构建销售模式、纯分时租赁模式和混合模式下的产品线策略模型,研究制造商产品线策略与商业模式之间的相互作用。研究发现,同品牌产品间竞争和合并效应是分时租赁模式影响产品线策略的两个关键因素。同品牌产品间竞争的加剧和合并效应的增大都会激励企业选择性能更好的车型而忽略其环境表现。分时租赁模式能同时改进利润与产品环境表现,但存在条件:当消费者价格敏感性较低时,使用成本高且合并效应小是实现同时改进的条件;当消费者价格敏感较高时,使用成本低且合并效应小则是同时改进的条件。     

“限时服务规则”下的复线船闸多目标调度优化

针对现有船舶过闸排队规则的欠缺,基于“限时服务规则”,构建复线船闸多目标双层优化调度模型:上层模型用于获得两个闸室安全区域的船舶排布可行方案;下层模型用于获得不同船舶排布可行方案的优化闸次数。下层模型分两个阶段完成:对符合“限时服务规则”的船舶,构建以闸次最少为目标的0-1规划模型,获得此类船舶安排的闸次;对其余船舶按照“先到先服务规则”,构建以闸次最少、闸室利用率最大为目标的多目标决策模型,获得不同船舶排布可行方案应该安排的频次。以位于江苏省干线航道上的某复线船闸某日24小时内过闸船舶的数据为例,计算结果表明:采用本文优化模型获得的优化方案与“经验编排方式”相比,两座船闸各节约2个闸次,两个船闸的平均闸室利用率分别提高了3.66和4.72个百分点。