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151.
该文研究有限区间上一般自伴边界条件下的Sturm-Liouville方程的逆特征值问题.将Neumann边界条件下Sturm-Liouville方程的Ambarzumyan型定理推广到一般自伴边界条件下情形,证明了如果它的特征值与零势的特征值一样,则Sturm-Liouville方程的势为零. 相似文献
152.
Marek Niezgoda 《Journal of Mathematical Analysis and Applications》2009,354(1):111-9789
In this paper we study translation-invariant maps on a linear space. A method for estimating quantities induced by such maps is presented. Applications for differences of operators, commutators, G-contractive maps and Grüss type inequalities are also given. 相似文献
153.
Qun Gu & Weiguo Gao 《计算数学(英文版)》2015,33(6):557-575
We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accelerated two-grid method, we point out that it is enough to apply an inexact solver to the fine grid problems, which will cut down the computational cost. Different stopping criteria for both methods are developed for keeping the optimality of the resulting solution. Numerical examples are provided to verify our theoretical analyses. 相似文献
154.
线性流形上的矩阵最佳逼近 总被引:7,自引:1,他引:7
戴华 《高校应用数学学报(A辑)》1994,(3):312-320
令S={A∈Rn×m|f1(A)=‖AX1-Z1‖2+‖YT1A-WT1‖2=min},其中X1∈Rm×k1,Z1∈Rn×k1,Y1∈Rn×11和W1∈Rm×11均为给定的矩阵,‖·‖是Frobenius范数。本文考虑如下问题:问题Ⅰ给定X2∈Rm×k2,Z2∈Rn×k2,Y2∈Rn×l2,W2∈Rm×l2,求A∈S,使得f2(A)=‖AX2-Z2‖2+‖YT2A-WT2‖2=min.问题Ⅱ给定A∈Rn×m,求A∈SA,使得‖A-A‖=infA∈SA‖A-A‖,其中SA是问题I的解集合。本文给出问题I解集合SA的通式和问题Ⅱ的解A的表达式,提出了求解问题Ⅰ与Ⅱ的数值方法。许多文献的结果都是本文结果的特例。 相似文献
155.
The susceptible–infected–susceptible (SIS) model is widely adopted in the studies of epidemic dynamics. When it is applied on contact networks, these networks mostly consist of nodes connected by undirected and unweighted edges following certain statistical properties, whereas in this article we consider the threshold and immunization problem for the SIS model on generalized networks that may contain different kinds of nodes and edges which are very possible in the real situation. We proved that an epidemic will become extinct if and only if the spectral radius of the corresponding parameterized adjacent matrix (PAM) is smaller than 1. Based on this result, we can evaluate the efficiency of immune strategies and take several prevailing ones as examples. In addition, we also develop methods that can precisely find the optimal immune strategies for networks with the given PAM. 相似文献
156.
In this paper we prove the internal feedback stabilization of steady-state solutions of semilinear parabolic equations and introduce a controller synthesis methodology based on finite element approximations of the original PDEs. Numerical tests are given for some one- and two-dimensional nonlinear parabolic equations. 相似文献
157.
A group G is called an A-group, where A is a given Abelian group, if it comes equipped with an action of A on G which mimics the way in which Z acts on any group. This action is codified in terms of certain axioms, all but one of which were introduced some years ago by R. C. Lyndon. For every such G and A there exists an A-exponential group G
A
which is the A-completion of G. We prove here that if G is a torsion-free hyperbolic group and if A is a torsion-free Abelian group, then the Lyndon's type completion G
A
of G is G-discriminated by G. This implies various model-theoretic and algorithmic results about G
A
. 相似文献
158.
Rü diger Gö bel Saharon Shelah 《Transactions of the American Mathematical Society》2000,352(11):5357-5379
Let be a subring of the rationals. We want to investigate self splitting -modules (that is . Following Schultz, we call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples of splitters. Are there others? Answering an open problem posed by Schultz, we will show that there are more splitters, in fact we are able to prescribe their endomorphism -algebras with a free -module structure. As a by-product we are able to solve a problem of Salce, showing that all rational cotorsion theories have enough injectives and enough projectives. This is also basic for answering the flat-cover-conjecture.
159.
160.
In this paper, we apply the augmented Lagrangian (AL) approach to steady buoyancy driven flow problems. Two AL preconditioners are developed based on the variable’s order, specifically whether the leading variable is the velocity or the temperature variable. Correspondingly, two non-augmented Lagrangian (NAL) preconditioners are also considered for comparison. An eigenvalue analysis for these two pairs of preconditioners is conducted to predict the rate of convergence for the GMRES solver. The numerical results show that the AL preconditioner pair is insensitive with respect to the mesh size, Rayleigh number, and Prandtl number in terms of GMRES iterations, resulting in a significantly more robust preconditioner pair compared to the NAL pair. Accordingly, the AL pair performs much better than the NAL pair in terms of computational time. For the AL pair, the preconditioner with velocity as the leading variable gives slightly better efficiency than the one with temperature as the leading variable. 相似文献