核磁共振成像一维空间编码教学实验

利用梯度磁场实现检测信号的空间编码,是核磁共振成像(MRI)的关键技术.本文采用ccc系列样品将二维问题简化为一维,使用超小型教学用核磁共振成像仪进行了一维空间编码实验研究,并对实验过程及实验结果进行了计算模拟和分析.     

泛函梯度数值计算的一种新方法—正交试验法

本文研究并揭示了L_(2~a)(2~(2~a-1))型正交表行(列)间的递推规律,提出了一种泛函梯度数值计算的新方法——正交试验法,该方法在计算速度和精度上优于直接梯度法;在通用性及节省内存方面优于伴随算子法。     

H‐self‐adjoint matrices. Application to radiosity

In computer graphics, in the radiosity context, a linear system Φx=b must be solved and there exists a diagonal positive matrix H such that H Φ is symmetric. In this article, we extend this property to complex matrices: we are interested in matrices which lead to Hermitian matrices under premultiplication by a Hermitian positive‐definite matrix H. We shall prove that these matrices are self‐adjoint with respect to a particular innerproduct defined on ?ⁿ. As a result, like Hermitian matrices, they have real eigenvalues and they are diagonalizable. We shall also show how to extend the Courant–Fisher theorem to this class of matrices. Finally, we shall give a new preconditioning matrix which really improves the convergence speed of the conjugate gradient method used for solving the radiosity problem. Copyright © 2002 John Wiley & Sons, Ltd.     

Modulation of Particle Concentrations in the Interference Laser Radiation Field

Spatial redistribution of microparticles in a suspension on exposure to the interference laser field depending on the parameters of the particles and the field characteristics has been analyzed theoretically. Results of experimental investigations are presented that illustrate the capture of an ensemble of polymeric small spheres and also of the lymphocytes of human blood and other microparticles in a liquid in the interference radiation bands of the He–Ne laser.     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

抽吸和压力梯度在层流边界层转捩过程中的作用

用空间模式的二次稳定性理论研究了抽吸和压力梯度对边界层三维亚谐扰动流动稳定性的影响．数值结果表明，固体边界上的抽吸有明显的层流控制作用，逆压梯度则有较强的不稳定作用．     

Determination of the boiling point distribution of sulfur compounds in light cycle oil using GC with a flame photometric detector and pyrolyzer

A method has been developed to determine the boiling point distribution of sulfur compounds in light cycle oils (LCO'S). The method chosen for this analysis was GC with a flame photometric detector (FPD) and pyrolyzer. Tests were carried out to evaluate the recovery efficiency, repeatability, and accuracy of the method. Repeatabilities within 2% were obtained. The recovery of benzothiophenes and dibenzothiophenes was close to 100%; this was important because these are the major sulfur components in LCO's. No hydrocarbon or solvent interferences were observed with the use of the pyrolyzer, even for a 95% solvent level. Comparison with results from other techniques showed that the method accurately determined the levels of sulfur compounds in the LCO boiling point range.     

Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

精确搜索下的非线性共轭梯度法

该文提出一种无约束优化非线性共轭梯度法，证明了精确线性 搜索下的全局收敛性。当目标函数为一致凸函数时，证明了算法具有线性收敛速度。数值实验表明算法对于求解实际问题是有效的。