关于正定可对称化线性代数方程组的预对称正则化算法

1引言考虑线性代数方程组A_x=b,A∈R~(n×n)非奇异,x,b∈R~n(1)的求解．当系数矩阵是大型稀疏的正定可对称化矩阵,文[1,2]讨论了一类预对称共轭梯度算法(LRSCG算法是其中之一),这类算法的实质是利用非对称的系数矩阵可对称化的性质,并结合共轭梯度法而构造的一种预处理的共轭梯度法[12,16,17]．但非对称的系数     

价格波动对进出初级产品行业的影响

初级产品生产行业有两大特点：一是其初级投资有较大的不可逆转性，二是其产品价格具有较大的随机性（不确定性）。这两点的同时存在，给进入和退出初级产品行业造成壁垒。     

Sample-path optimization of convex stochastic performance functions

In this paper we propose a method for optimizing convex performance functions in stochastic systems. These functions can include expected performance in static systems and steady-state performance in discrete-event dynamic systems; they may be nonsmooth. The method is closely related to retrospective simulation optimization; it appears to overcome some limitations of stochastic approximation, which is often applied to such problems. We explain the method and give computational results for two classes of problems: tandem production lines with up to 50 machines, and stochastic PERT (Program Evaluation and Review Technique) problems with up to 70 nodes and 110 arcs. Sponsored by the National Science Foundation under grant number CCR-9109345, by the Air Force Systems Command, USAF, under grant numbers F49620-93-1-0068 and F49620-95-1-0222, by the U.S. Army Research Office under grant number DAAL03-92-G-0408, and by the U.S. Army Space and Strategic Defense Command under contract number DASG60-91-C-0144. The U.S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Sponsored by a Wisconsin/Hilldale Research Award, by the U.S. Army Space and Strategic Defense Command under contract number DASG60-91-C-0144, and the Air Force Systems Command, USAF, under grant number F49620-93-1-0068. Sponsored by the National Science Foundation under grant number DDM-9201813.     

1．5GHz锯材超导腔的研制

介绍铌材超导腔的研制进展，重点讨论了国产铌腔的材料改性，以及相应的超导腔性能的改进．叙述了１．５ＧＨｚ铌腔的腔形设计，分析了铌材的射频性能和机械性能，制定了铌腔制作与后处理的特定工艺．最后给出了１．５ＧＨｚ铌材超导腔的低温实验结果．     

Stochastic algorithms with armijo stepsizes for minimization of functions

Stochastic algorithms for optimization problems, where function evaluations are done by Monte Carlo simulations, are presented. At each iteratex _i, they draw a predetermined numbern(i) of sample points from an underlying probability space; based on these sample points, they compute a feasible-descent direction, an Armijo stepsize, and the next iteratex _i+1. For an appropriate optimality function , corresponding to an optimality condition, it is shown that, ifn(i) , then (x _i) 0, whereJ is a set of integers whose upper density is zero. First, convergence is shown for a general algorithm prototype: then, a steepest-descent algorithm for unconstrained problems and a feasible-direction algorithm for problems with inequality constraints are developed. A numerical example is supplied.     

Kinetic limit of a conservative lattice gas dynamics showing long-range correlations

An anisotropic lattice gas dynamics is investigated for which particles on ^d jump to empty nearest neighbor sites with (fast) rate ^–2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the fast-rate direction is rescaled by ^–1. It follows that the density field converges in probability, as 0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (1/r ^d ) with the direction dependence of a quadrupole field.     

Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

Hereditary optimal control problems: Numerical method based upon a padé approximation

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t – ). In our approximation scheme, we first replace the variable with an augmented statey(t) x(t - ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant NCC-2-106.     

Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

On-chip potential gradient detection with a portable capillary electrophoresis system

A portable chip-CE system with potential gradient detection (PGD) was developed and applied to the determinations of alkali metals and alkaloids. The separation efficiency appeared to be satisfactory and nonaqueous capillary electrophoresis (NACE) proved to be applicable to PGD or conductivity detection. The power supplies, separation and detection were built on a device of 3 kg in weight. A branch channel near the end of the separation channel was designed to perform PGD and make the application of relatively high field strength possible. The study is the first report on the application of PGD on the microchip platform. The design of the chip-CE system shows several advantages, such as simplicity, miniaturization and wide applicability.