五对角线矩阵的逆特征值问题

研究了由两个或三个有序的特征值和特征向量来构造规范五对角线矩阵的逆特征值问题,并给出了问题的解的表达式和一些具体的数值例子.     

关于周期对称三对角矩阵的广义特征值反问题

在给定部分特征值、部分特征向量及附加条件下提出了一类反问题,并给出了此问题解存在性的证明及求解的算法.     

考虑晶体应力情况下的单块非平面环形腔分析

简要分析了单块非平面环形腔单频激光器的基本原理,并采用琼斯矩阵计算了单块单向行波非平面环形腔内的本征偏振态。深入分析了磁场强度、输出面偏振反射系数、入射角、非平面角及腔内其它参量对各本征偏振态的损耗及两本征偏振态间损耗差的影响,并且指出如何选择各参量以降低本征偏振态的损耗且增大两本征偏振态间的损耗差。最后还通过计算晶体应力在两个本征偏振态方向引起的相位差,讨论了应力作用方向以及应力双折射系数对腔内本征偏振态的损耗和两本征偏振态间损耗差的影响。     

对称矩阵的两特征值问题

介绍了对称矩阵的两特征值问题,并给出了计算公式.     

也谈不规范的斯特姆-刘维本征值问题

讨论了端点有集中载荷时弹性杆的纵振动问题．比较了现有的两种解法,分析了相关本征值问题的正交性问题．     

Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods

In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements, Q ₁^rot and EQ ₁^rot. Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations. This project is supported in part by the National Natural Science Foundation of China (10471103) and is subsidized by the National Basic Research Program of China under the grant 2005CB321701.     

Eigenvalue analysis for a crack in a power-law material

A nonlinear eigenvalue problem related to determining the stress and strain fields near the tip of a transverse crack in a power-law material is studied. The eigenvalues are found by a perturbation method based on representations of an eigenvalue, the corresponding eigenfunction, and the material nonlinearity parameter in the form of series expansions in powers of a small parameter equal to the difference between the eigenvalues in the linear and nonlinear problems. The resulting eigenvalues are compared with the accurate numerical solution of the nonlinear eigenvalue problem.     

Banach空间中非线性Sturm-Liouville问题的解

利用M(o)nch不动点定理,在更广泛的的条件下,证明了Banach空间中Sturm-Liouville问题解的存在性.     

二阶微分系统奇异正定超线性周期边值问题的多重正解

主要研究了二阶微分系统具有奇异正定超线性周期边值问题多重正解的存在性问题,利用Leray-Schauder抉择定理和锥不动点定理给出了奇异正定超线性周期边值问题-(p(t)x′)′+q1(t)x=f1(t,x,y),t∈I=[0,1]-(p(t)y′)′+q2(t)y=f2(t,x,y)x(0)=x(1),x[1](0)=x[1](1)y(0)=y(1),y[1](0)=y[1](1)(1.1)的多重正解的存在性,其中非线性项fi(t,x,y)(i=1,2)在x=∞,y=∞点处超线性,在(x,y)=(0,0)处具有奇性.这里定义x[1](t)=p(t)x′(t),y[1](t)=p(t)y′(t)为准导数,其中系数p(t),qi(t)(i=1,2)是定义在[0,1]上的可测函数,且p(t)>0,qi(t)>0(i=1,2),a.e[0,1],fi(t,x,y)∈C(I×R×R,R+),R+=(0,+∞).     

A sort-Jacobi algorithm for semisimple lie algebras

A structure preserving sort-Jacobi algorithm for computing eigenvalues or singular values is presented. It applies to an arbitrary semisimple Lie algebra on its (−1)-eigenspace of the Cartan involution. Local quadratic convergence for arbitrary cyclic schemes is shown for the regular case. The proposed method is independent of the representation of the underlying Lie algebra and generalizes well-known normal form problems such as e.g. the symmetric, Hermitian, skew-symmetric, symmetric and skew-symmetric R-Hamiltonian eigenvalue problem and the singular value decomposition.