Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.     

Absorbing boundary conditions for reaction-diffusion equations

We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reaction–diffusion equations.     

Numerical simulation of thermally and chemically nonequilibrium flows and heat transfer in underexpanded induction plasmatron jets

The results of numerical simulation are presented for thermally and chemically nonequilibrium air plasma flows in a plasmatron discharge channel and underexpanded dissociated and partially ionized air jets flowing past a cylindrical model with a blunt leading edge and cooled copper surface under the experimental conditions realized in a VGU-4 100 kW induction plasmatron (Institute for Problems in Mechanics of the Russian Academy of Sciences) (see, for example, [1, 2]). The nonequilibrium excitation of the vibrational degrees of freedom of the molecules in the modal approximation and the difference between the electron and translational heavy-particle temperatures are taken into account in the calculations. The calculated data on the heat transfer and pressure at the stagnation point are compared with the results obtained within the framework of the thermally equilibrium model. Comparison with the experimental data obtained in the Institute for Problem in Mechanics of the Russian Academy of Sciences (Laboratory for interaction between plasma and radiation and materials) and kindly provided for comparison purposes gives satisfactory agreement.     

基于椭圆型方程的扭叶片造型方法的研究

本文以偏微分方程造型为基础,提出了一种基于椭圆型方程的扭叶片三维型面直接设计方法,详细推导了叶型曲面函数,给出了型面方程的求解及其前后缘修正。该方法具有设计叶型曲面自然光顺,设计参数少且各参数具有明显的几何意义,叶型曲面调整方便,利于采用非数值优化算法对其进行气动优化等优点。文中给出了设计实例,并通过数值实验分析了所设计叶片型面的流动特性。分析结果表明设计叶片具有良好的气动性能,同时也证明了本文提出的基于椭圆型方程的扭叶片三维型面设计方法的可靠性和实用性。     

Energy decay of solutions to Maxwell's equations with conductivity and polarization

In this paper, Maxwell's equations involving generally nonlinear polarization and field-dependent currents are studied. The main objective is the asymptotic behavior of the solution for t→∞ if no damping term occurs in the equation governing the polarization field.     

Oscillation theorems for differential equations with a nonlinear damping term

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity, and, as a consequence, our results apply to wider classes of nonlinear differential equations. Two illustrative examples are considered.     

带有回报计划的动态客户关系管理模型及实验应用分析

在客户最大化效用及公司最大化CLV的动态环境下。对所提的带有回报计划的动态客户关系管理模型用于某超市的客户数据库中，发现模型的结果对这类客户是适用的。并给出了不同的客户状态空间对应的有效营销组合策略。结果表明：合适的回报计划可以促进客户的购买、提高公司的利润及缓解价格竞争。回报极限应该比客户的平均购买水平偏高，回报率应该与回报极限的改变方向一致。计划的时间范围应定在一年左右比较合适。对于累积购买水平较高的客户一般不邮寄商品信息。在回报计划的初期与末期不用打折。中期对那些购买次数很少的客户可以实行相应的降价策略。     

使用非单调技术的不精确预条件牛顿类方法解非线性方程组

本文提供了预条件不精确牛顿型方法结合非单调技术解光滑的非线性方程组．在合理的条件下证明了算法的整体收敛性．进一步，基于预条件收敛的性质，获得了算法的局部收敛速率，并指出如何选择势序列保证预条件不精确牛顿型的算法局部超线性收敛速率．     

Self-dual Chern–Simons Vortices on Bounded Domains

In this Letter we consider the Abelian Chern–Simons vortices on a bounded simply connected domain. We establish the existence of solutions for the self-duality equations. We prove the uniqueness of solutions when all the vortex points are equal and the domain is star-shaped. We also show the radial symmetry of solutions on balls centered at the vortex point.     

激光诱导间质肿瘤热疗的数值模拟和实验研究

本文在考虑生物组织物性动态变化的情况下建立了激光诱导间质肿瘤热疗(LITT)的物理数学模型,采用MonteCarlo方法数值模拟了LITT中激光能量在生物组织内的传输过程,基于Pennes生物传热方程和Arrhenius方程数值求解了组织内的温度分布和热损伤体积的变化,分析了热物性及血液灌注率的动态变化对LITT过程的影响,并与相应的离体实验结果进行了对比。数值模拟结果表明,组织的热物性及血液灌注率的动态变化对于热损伤体积的变化具有重要的影响。因此在激光诱导间质肿瘤热疗的数值模拟中应该考虑热物性及血液灌注率的动态变化以期为临床治疗方案的制定提供更为准确的依据。