重根特征灵敏度分析

本文建立了一种确定具有重特征值系统之特征灵敏度的新方法。所提出的方法以Ｍｏｏｒｅ─Ｐｅｎｒｏｓｅ广义逆技术为基础。对于重根结构系统的特征导数计算，它是一项有效的技术。     

极坐标系中的B样条有限元法解波导本征值问题

本文提出了用极坐标系中的Ｂ样条有限元法解波导本征值问题，该方法有两个突出优点：（１）避免某些含曲线边界的波导截面的剖分误差；（２）改善尖角波导的计算精度，本文首先建立了极坐标系中Ｂ样条有限元方程，然后通过对圆形，扇形，双脊加圆形和心形波导本征值问题的实际计算，表明方法的有效性和实有价值。     

弹性圆柱壳的稳定性优化设计

研究任意轴对称边界条件下和受均布法向载荷作用圆柱壳的稳定性优化设计问题，即极大化屈曲临界载荷。利用能量原理分析轴对称变厚度圆柱壳的分支点屈曲，将求解屈曲临界载荷变成求解广义特征值方程，使圆柱壳稳定性优化设计成为极大化最小特征值问题。实际算例验证了本方法的有效性。研究结果可用于圆柱壳的加肋优化设计。     

Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition

This paper provides algorithms for adding and subtracting eigenspaces, thus allowing for incremental updating and downdating of data models. Importantly, and unlike previous work, we keep an accurate track of the mean of the data, which allows our methods to be used in classification applications. The result of adding eigenspaces, each made from a set of data, is an approximation to that which would obtain were the sets of data taken together. Subtracting eigenspaces yields a result approximating that which would obtain were a subset of data used. Using our algorithms, it is possible to perform ‘arithmetic’ on eigenspaces without reference to the original data. Eigenspaces can be constructed using either eigenvalue decomposition (EVD) or singular value decomposition (SVD). We provide addition operators for both methods, but subtraction for EVD only, arguing there is no closed-form solution for SVD. The methods and discussion surrounding SVD provide the principle novelty in this paper. We illustrate the use of our algorithms in three generic applications, including the dynamic construction of Gaussian mixture models.     

基于可信度的双门限DMM协作频谱感知算法

针对已有的双门限特征值频谱感知算法存在忽略本地感知用户可靠性差异及融合判决方式开销大的缺点,提出了一种基于可信度的双门限DMM协作频谱感知算法(DT-CDMM),用于进一步提升协作感知性能。所提算法在最大最小特征值差(DMM)算法的基础上,建立了基于特征极限分布的双门限DMM算法作为本地感知,采用触发式的软、硬判决相结合的判决机制来减少系统开销,以本地感知性能与可信度加权的方式得到全局判决结果,并对硬判决进行自适应补偿。仿真结果表明, 较已有的双门限特征值算法以及双门限能量检测算法,DT-CDMM算法在噪声不确定的环境下提升了多用户协作检测的概率。     

New Upper Matrix Bounds with Power Form for the Solution of the Continuous Coupled Algebraic Riccati Matrix Equation

In this paper, using the structure and coefficient matrix of the continuous coupled algebraic Riccati matrix equation (CCARE), we firstly construct positive definite matrices with power form. Then, applying the variant of the CCARE and inequalities of positive definite matrices, utilizing the characteristics of special matrices and eigenvalue inequalities, we propose new upper matrix bounds with power form for the solution of the CCARE, which improve and extend some of the recent results. Finally, we give corresponding numerical examples to illustrate the effectiveness of the derived results.     

最小特征值的迭代非刚体三维射影重建方法

为了从图像序列中重建出非刚体三维射影重建,本文提出了一种最小特征值的迭代非刚体射影重建方法.该方法利用所有的图像点和深度因子组成一个低秩图像矩阵的特性,将投影求解转化为矩阵特征值及特征向量的求解,迭代地求解深度因子,实现非刚体的三维射影重建.该方法能够保证算法能够收敛到全局最优解.模拟实验和真实实验结果表明,本文方法具有收敛性速度快、误差小等优点.     

EIGENVALUE SPECTRA AND MODAL CONTRIBUTIONS FOR COUNTERFLOW REACTOR MODELS

Counterflow reactor models fall into three classes of partial differential equations: hyperbolic, parabolic, and mixed hyperbolic-parabolic. These have been analyzed to determine the behavior of their eigenvalues and their modal contributions. Using an asymptotic analytical technique (WKB theory), hyperbolic p.d.e. systems and mixed p.d.e. systems with characteristics similar to hyperbolic systems were found to have a “defective” internal structure, making them generally undesirable for modeling or control applications requiring low-order models. Parabolic systems, or mixed systems with characteristics similar to parabolic systems, were found to be “well-behaved”. Hence, where it is possible to choose the type of model to apply to a specific reactor, the choice of the parabolic form is strongly suggested to mitigate potential structural problems.     

广义p-Laplacian方程的特征值问题

主要研究广义p-Laplacian方程在Dirichlet边值条件下的特征值问题。对于问题中给定的参数λ,如果存在λ0使Dirichlet边值问题具有非平凡解u0,那么称这个λ为Dirichtet边值问题的特征值,对应的解u为Dirichlet边值问题的特征函数。应用构造性方法给出了Dirichlet边值问题谱特性及对应的特征函数具体形式。