有限时滞微分系统依照双测度的实际稳定性

本文对具有有限时滞的泛函微分方程建立了关于依照两种测度的实际稳定性的Razumikhin型判定定理，其中未采用通常的辅助函数，且可运用多个含有状态变量x的部分变元的Lyapunov函数，得出部分变远实际稳定性的判定定理，从而改进了已有的结果。     

Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions

In this paper we consider an initial boundary value problem for a reaction-diffusion equation under nonlinear and nonlocal Robin type boundary condition. Assuming the existence of an ordered pair of upper and lower solutions we establish a generalized quasilinearization method for the problem under consideration whose characteristic feature consists in the construction of monotone sequences converging to the unique solution within the interval of upper and lower solutions, and whose convergence rate is quadratic. Thus this method provides an efficient iteration technique that produces not only improved approximations due to the monotonicity of its iterates, but yields also a measure of the convergence rate.     

The Markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half-axis

In this paper necessary and sufficient conditions of null-controllability and approximate null-controllability are obtained for the wave equation on a half-axis. Controls solving these problems are found explicitly. Moreover, bang-bang controls solving the approximate null-controllability problem are constructed with the aid of solutions of a frequency extinguishing problem in the restricted band (−a,a) for this equation and the Markov power moment problem.     

Global and uniform convergence of subspace correction methods for some convex optimization problems

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.

     

纳米MOSFET迁移率解析模型

从玻尔兹曼方程出发，重新计算了纳米MOSFET沟道内的载流子所服从的分布函数，特别是考虑了纳米MOSFET横向电场和纵向电场之间的相互作用，并且以得到的非平衡状态下的分布函数为基础，考虑载流子寿命和速度的统计分布，给出了纳米MOSFET载流子迁移率的解析表达式.通过与数值模拟结果进行比较和分析，该迁移率解析模型形式简洁、物理概念清晰，且具有相当精度. 关键词： 玻尔兹曼方程 纳米MOSFET 迁移率 沟道有效电场     

8 mm回旋行波管和返波管的三折螺旋波纹波导色散分析

 三折螺旋波纹波导使TE11模和TE21模相互耦合，其色散曲线能够在宽频带内与电子回旋共振，因此需要对色散方程进行研究。提出了适合工程实用的行波模式和返波模式的色散方程，并对方程中的耦合系数进行了简化，误差在1%左右。利用CST软件的VBA语言对螺旋波纹波导进行建模和计算，根据模拟得到的传输特性曲线的特点，提出一种模拟方法，将模拟与理论计算得到的色散曲线作对比，误差在5%左右。     

Numerical analysis of the spiral Couette flow of a rarefied gas between coaxial cylinders

An implicit quasi-monotone second-order accurate method is proposed for analyzing the spiral Couette flow of a rarefied gas between coaxial cylinders. The basic advantages of the method over the conventional method of stationry iterations are that the former is conservative with respect to the collision integral, has a simple software implementation for any types of boundary conditions, and applies to a wide range of Knudsen numbers.     

饮酒驾车模型

据统计,我国每天困饮酒过量而产生的车祸竟达交通事故伤亡总人数的50%-60%,酒后驾车的问题已经引起了社会各界的高度重视.为此本文建立了酒后血液中酒精含量的房室数学模型,从而为司机饮酒驾车提供合理的忠告和建议.     

Σ-原子能级的理论计算与分析

通过对Σ-原子的理论分析,数值求解了相应的Dirac方程,得到 了一组Σ-原子的能级值,与实验数据相当吻合;其结果连同K-原子的情况支持了Batty 光学模型势在奇异原子中应用的正确性,进而表明核子间的强相互作用力为吸引力.     

鞅方法在一类破产问题中的应用

本文从鞅条件出发 ,推导出了总理赔过程分别为复合 Poisson过程与复合二项过程 ,利率强度波动为带跳的 Poisson过程情形下的调节方程 ,并由此得到了一些有趣的结果。