带雪崩项半导体方程稳态解的存在性

考虑带雪崩项半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态弱解的存在性．     

半导体漂移 扩散方程稳态解的存在性

考虑半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态解的存在性.     

半导体漂移-扩散方程速度饱和情形的稳态解

考虑半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态解的存在性。     

双调和型抛物方程的Schauder估计

该文给出了双调和型抛物方程初值问题解的Schauder估计,并且在适当的空间中证明了解的存在性与惟一性．类似于二阶情形,首先通过Fourier变换得到一个形式解,然后再利用位势理论和逼近方法得到解的正则性、唯一性及存在性．该方法简单而易懂．     

关于非单调算子的变分问题

该文应用有限维逼近的方法讨论了一类非单调算子的变分不等方程，并在所谓的（Ｆ）条件下将锐角原理推广到变分问题之中，从而得到了很一般的解的存在性．     

线性流形上反埃尔米特广义汉密尔顿矩阵的最小二乘问题与最佳逼近问题

利用反埃尔米特广义汉密尔顿矩阵的表示定理,得到了线性流形上反埃尔米特广义汉密尔顿矩阵反问题的最小二乘解的一般表达式,建立了线性矩阵方程在线性流形上可解的充分必要条件．对于任意给定的n阶复矩阵,证明了相关最佳逼近问题解的存在性与惟一性,并推得了最佳逼近解的表达式．     

关于等温气流的逼近解的收敛性

该文研究等温气流整体解的存在性．我们用补偿列紧理论证明了逼近解的强收敛性．我们不仅对弱熵,而且对强熵也建立了交换关系式．在证明中我们不需要强熵的Ｈ－１紧性．     

三维Wigner-Poisson方程组的Cauchy问题

考虑三维 Ｗｉｇｎｅｒ－Ｐｏｉｓｓｏｎ方程组的 Ｃａｕｃｈｙ问题，将 ＷＰ问题转化为等价的 Ｓｃｈｒｏｄｉｎｇｅｒ－Ｐｏｉｓｓｏｎ问题．采用有限区域序列上的解的逼近方法，通过对逼近解建立与区域无关的先验估计，证明了 Ｃａｕｃｈｙ问题解的存在性、唯一性和逼近解的收敛性     

Banach空间中的多值拟变分包含

引入和研究了Banach空间中的多值拟变分包含问题．借助预解算子技巧,建立了某些解的存在性定理及解的迭代逼近．文中所给出的结果改进和推广了许多人的最新结果．     

Couette-Taylor流的谱Galerkin逼近

利用谱方法对轴对称的旋转圆柱间的Couette-Taulor流进行数值模拟．首先给出Navier-Stokes方程流函数形式,利用Couette流把边界条件齐次化．其次给出Stokes算子的特征函数的解析表达式,证明其正交性,并对特征值进行估计．最后利用Stokes算子的特征函数作为逼近子空间的基函数,给出谱Galerkin逼近方程的表达式．证明了Navier-Stokes方程非奇异解的谱Galerkin逼近的存在性、唯一性和收敛性,给出了解谱Galerkin逼近的误差估计,并展示了数值计算结果．     

Local networks for computer communications: A. WEST and P. JANSON (Eds.) Proceedings of the IFIP Working Group 6.4, International Workshop on Local Networks,Zürich,Switzerland, August 27–29, 1980, North-Holland,Amsterdam, 1981, xiii + 470 pages,Dfl.125.00

In this paper we present two lower bounds for the p-median problem, the problem of locating p facilities (medians) on a network. These bounds are based on two separate lagrangean relaxations of a zero-one formulation of the problem with subgradient optimisation being used to maximise these bounds. Penalty tests based on these lower bounds and a heuristically determined upper bound to the problem are developed and shown to result in a large reduction in problem size. The incorporation of the lower bounds and the penalty tests into a tree search procedure is described and computational results are given for problems with an arbitrary number of medians and having up to 200 vertices. A comparison is also made between these algorithms and the dual-based algorithm of Erlenkotter.     

Time optimal sampled-data controls for the heat equation

In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls.The study of such a time optimal sampled-data control problem is not easy, because it may have infinitely many optimal controls. We find connections among this problem, a minimal norm sampled-data control problem and a minimization problem, and obtain some properties on these problems. Based on these, we not only build up error estimates for optimal time and optimal controls between the time optimal sampled-data control problem and the time optimal distributed control problem, in terms of the sampling period, but we also prove that such estimates are optimal in some sense.     

On variational perturbations of control problems: Minimum-time problem and minimum-effort problem

In order to obtain numerical solutions for an abstract optimal control problem, one approximates the abstract operations in a computationally feasible manner. After having found an approximate optimal solution, the question is whether a sequence of these approximate optimal solutions converges to an optimal solution of the original problem. In this work, we are concerned with this type of convergence on the time-optimal control problem for a class of linear systems with distributed parameters and on the minimum-effort problem.     

Bin covering algorithms in the second stage of the lot to order matching problem

We formulate the problem of effectively assigning semiconductor fabrication wafer lots to customer orders of various sizes, or the lot-to-order matching problem, as an integer programming problem. Our goal in this paper is to develop an efficient, practical method for solving this problem for various performance measures. Because of its complexity we decompose the problem into a knapsack problem coupled with a generalized bin-covering problem, and solve these subproblems sequentially using heuristic methods. We restrict our attention to solution methods for the less-common second subproblem, and analyze the performance of several heuristics using a data set representative of real situations in a semiconductor back-end. Based on this analysis, we show that these heuristics perform significantly better than current industrial practice in the context of the overall problem.     

Two-edge connected subgraphs with bounded rings: Polyhedral results and Branch-and-Cut

We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that the shortest cycle (a “ring”) to which each edge belongs, does not exceed a given length K. We identify a class of inequalities, called cycle inequalities, valid for the problem and show that these inequalities together with the so-called cut inequalities yield an integer programming formulation of the problem in the space of the natural design variables. We then study the polytope associated with that problem and describe further classes of valid inequalities. We give necessary and sufficient conditions for these inequalities to be facet defining. We study the separation problem associated with these inequalities. In particular, we show that the cycle inequalities can be separated in polynomial time when K≤4. We develop a Branch-and-Cut algorithm based on these results and present extensive computational results.     

二维椭圆型方程反问题中优化算法的比较

近年来，决定椭圆型方程系数反问题在地磁、地球物理、冶金和生物等实际问题上有着广泛的应用．本文讨论了二维的决定椭圆型方程系数反问题的数值求解方法．由误差平方和最小原则，这个反问题可化为一个变分问题，并进一步离散化为一个最优化问题，其目标函数依赖于要决定的方程系数．本文着重考察非线性共轭梯度法在此最优化问题数值计算中的表现，并与拟牛顿法作为对比．为了提高算法的效率我们适当选择加快收敛速度的预处理矩阵．同时还考察了线搜索方法的不同对优化算法的影响．数值实验的结果表明，非线性共轭梯度法在这类大规模优化问题中相对于拟牛顿法更有效．     

On the first eigenvalue of the Dirichlet-to-Neumann operator on forms

We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Dirichlet-to-Neumann (or Steklov) problem on functions. We derive a number of upper and lower bounds for the first eigenvalue in several contexts: many of these estimates will be sharp, and for some of them we characterize equality. We also relate these new eigenvalues with those of other operators, like the Hodge Laplacian or the biharmonic Steklov operator.     

Application of the hypodifferential descent method to the problem of constructing an optimal control

In this paper the problem of optimal control of a nonlinear ODE system with given boundary conditions and the integral restriction on control is considered. With the help of the theory of exact penalty functions the original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. The necessary minimum conditions in terms of hypodifferentials are found. A class of problems for which these conditions are also sufficient is distinguished. On the basis of these conditions the hypodifferential descent method is applied to the considered problem. Under some additional assumptions the hypodifferential descent method converges in a certain sense.     

Detection of multilayered media in the acoustic waveguide

This work is concerned with the inverse problem for ocean acoustics modeled by a multilayered waveguide with a finite depth. We provide explicit formulae to locate the layers, including the seabed, and reconstruct the speed of sound and the densities in each layer from measurements collected on the surface of the waveguide. We proceed in two steps. First, we use Gaussian type excitations on the upper surface of the waveguide and then from the corresponding scattered fields, collected on the same surface, we recover the boundary spectral data of the related 1D spectral problem. Second, from these spectral data, we reconstruct the values of the normal derivatives of the singular solutions, of the original waveguide problem, on that upper surface. Finally, we derive formulae to reconstruct the layers from these values based on the asymptotic expansion of these singular solutions in terms of the source points.     

On two-coefficient identification in elliptic variational inequalities

Abstract

This paper is concerned with elliptic variational inequalities that depend on two parameters. First, we investigate the dependence of the solution of the forward problem on these parameters and prove a Lipschitz estimate. Then, we study the inverse problem of identification of these two parameters and formulate two optimization approaches to this parameter identification problem. We extend the output least-squares approach, provide an existence result and establish a convergence result for finite-dimensional approximation. Further, we investigate the modified output least-squares approach which is based on energy functionals. This latter approach can be related to vector approximation.