Stokes算子的特征值问题

本文用球坐标，利用Ｂｅｓｓｅｌ函数和Ｌｅｇｅｎｄｅｒ多项式给出特征函数表达式，并用一族级数的零点来表示特征值。     

FACILITATED TRANSPORT OF CARBON DIOXIDE: A REVIEW

The effect of reversible chemical reaction upon the diffusion of carbon dioxide in thin liquid film membranes is reviewed. Particular emphasis is placed upon the hydration reaction of CO₂ and catalysis thereof. Theoretical analysis is developed for equilibrium, near-equilibrium and near-diffusion regimes. The important effects of weak acid buffers, proteins and amines upon CO₂ transport are also discussed, as well as the significance of diffusion potentials, particularly in the case of protein systems. Results of experimental investigations of facilitated CO₂ transport are reviewed, as well as general aspects of CO₂ transport in biological systems and absorbers.     

Linear eigenvalue code for edge plasma in full tokamak X-point geometry

A new code is presented for solving linear eigenvalue problems from fluid models of the edge plasma of tokamaks. The 2DX code solves linearized fluid equations in a 2D cross-section of the plasma, with toroidal mode number resolving the third dimension. Geometry capabilities include both closed and open field lines, allowing solution of X-point problems as well as a variety of other toroidal and cylindrical systems. The code generates a pair of sparse matrices forming a generalized eigenvalue problem which is then solved using a standard sparse eigensolver package. Use of a specialized equation parser permits a high degree of flexibility in both equations and coordinate systems. Both analytic and full geometry benchmark cases are presented.     

求实对称矩阵特征向量与特征值的新方法

为了避免现有特征向量与特征值求解方法的复杂运算,本文给出了两种新解法——最优化法与自组织网络法。它们都采用参数随机逼近策略,便于并行计算或网络实现,最后经实验证明了新法的有效性。     

Eigenvalue and eigenfunction analysis arising from degenerate scale problem of BIE in plane elasticity

A new boundary integral equation (BIE) of plane elasticity is suggested with the use of a novel kernel. The relevant homogenous equation is also suggested. The equation is studied in a discrete form, or it is reduced to an algebraic equation. From the condition that the value of a determinant vanishes, the degenerate scale (or the eigenvalue) and the non-trivial solution (or the eigenfunction) are obtained approximately. Except for the notch with symmetric configuration for two axes, computed results prove that there are two degenerate scales in general. The dependence of the eigenvalue and eigenfunction with respect to the translation or the rotation of notch is investigated. It is found that the eigenvalues are invariant with respect to the translation and the rotation of notch. However, the eigenfunctions are changed when the notch has a rotation. Several numerical examples that include a rectangular notch, a half-ring-shaped notch and a complicated notch configuration are presented with the computed eigenvalues and eigenfunctions.     

Identification of global modeshape from a few nodal eigenvectors using simple free-form deformation

A new method, different from common eigenvalue extraction methods, was proposed by Li and Kikuchi (in 8th ARC conference, 2002). It consists of explicit finite-element method and eigenvalue-extraction method in time domain. Even though the new method performs well in extracting eigenvalues, it is difficult to identify global modeshape of the given structure due to large size of time history data. Only some eigenvectors of a few nodal points can be extracted. In this paper, we apply computer animation technique to identify the global modeshape from a few nodal eigenvectors. Free-form deformation (FFD) technique is simply modified—simple FFD—and applied to the identification of global modeshapes. The basic concepts that consist of simple FFD algorithm are Delaunay triangulation and barycentric coordinate. Some numerical examples show good performance for the identification of global modeshape of a given structure.     

基于MAS的供应链可靠性综合评估模型

为了保证供应链的正常运作,构建了一种基于MAS的供应链可靠性综合评估模型。模型上最底层的节点Agent利用遗传投影寻踪法计算节点可靠度,中间层的子系统Agent利用特征值赋权法计算子系统可靠度,最上层的系统Agent负责供应链整体可靠性评估。应用实例表明,该模型可以从局部到整体对供应链可靠性进行全面评估。     

谷物害虫图像识别中特征值提取技术的研究

本文阐述了在仓储物害虫分类识别研究中利用计算机数字图像处理技术，对谷物害虫图像的一阶灰度值直方图和图像的目标区域，自动提4取静态仓储物害虫图像的数理统计特征、纹理特征和几何形状特征的主要技术和方法。试验结果表明，该方法可以为谷物害虫的计算机自动模式识别(快速分类)提供稳定的特征参数值，有效地提高了识别率。该方法为仓储物害虫的快速鉴定和分类研究开辟了新的途径。     

Exponential stability of variable coefficients Rayleigh beams under boundary feedback controls: a Riesz basis approach

In this paper, we study the boundary stabilizing feedback control problem of Rayleigh beams that have non-homogeneous spatial parameters. We show that no matter how non-homogeneous the Rayleigh beam is, as long as it has positive mass density, stiffness and mass moment of inertia, it can always be exponentially stabilized when the control parameters are properly chosen. The main steps are a detail asymptotic analysis of the spectrum of the system and the proving of that the generalized eigenfunctions of the feedback control system form a Riesz basis in the state Hilbert space. As a by-product, a conjecture in Guo (J. Optim. Theory Appl. 112(3) (2002) 529) is answered.