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81.
Let be the th Neumann eigenvalue of a bounded domain with piecewisely smooth boundary in . In 1992, P. Kröger proved that , where the upper bound is sharp in view of Weyl's asymptotic formula. The aim of this paper is twofold. First, we will improve this estimate by multiplying a factor in terms of to its right-hand side which approaches strictly from below to 1 as tends to infinity. Second, we will generalize Kröger's estimate to the case when is a compact Euclidean submanifold.
82.
《Operations Research Letters》2020,48(4):441-445
With the help of the newly developed technique—second order cone (SOC) constraints to strengthen the SDP relaxation of the extended trust-region subproblem (eTRS), we modify two recent SDP relaxation based branch and bound algorithms for solving eTRS. Numerical experiments on some types of problems show that the new algorithms run faster for finding the global optimal solutions than the SDP relaxation based algorithms. 相似文献
83.
84.
Jia-Yong Wu 《Journal of Mathematical Analysis and Applications》2010,361(1):10-18
Let L=Δ−∇φ⋅∇ be a symmetric diffusion operator with an invariant measure on a complete Riemannian manifold. In this paper we give an upper bound estimate on the first eigenvalue of the diffusion operator L on the complete manifold with the m-dimensional Bakry-Émery Ricci curvature satisfying Ricm,n(L)?−(n−1), and therefore generalize a Cheng's result on the Laplacian (S.-Y. Cheng (1975) [8]) to the case of the diffusion operator. 相似文献
85.
Mohamed Saleh Rogelio Oliva Christian Erik Kampmann Pål I. Davidsen 《European Journal of Operational Research》2010
Formal tools to link system dynamics model’s structure to the system modes of behavior have recently become available. In this paper, we aim to expand the use of these tools to perform the model’s policy analysis in a more structured and formal way than the exhaustive exploratory approaches used to date. We consider how a policy intervention (a parameter change) affects a particular behavior mode by affecting the gains of particular feedback loops as well as how it affects the presence of that mode in the variable of interest. The paper demonstrates the utility of considering both of these aspects since the analysis provides an assessment of the overall impact of a policy on a variable and explains why the impact occurs in terms of structural changes in the model. Particularly in the context of larger models, this method enables a much more efficient search for leverage policies, by ranking the influence of each model parameter without the need for multiple simulation experiments. 相似文献
86.
We derive eigenvalue asymptotics for Sturm-Liouville operators with singular complex-valued potentials from the space , α∈[0,1], and Dirichlet or Neumann-Dirichlet boundary conditions. We also give application of the obtained results to the inverse spectral problem of recovering the potential from these two spectra. 相似文献
87.
In this paper, we generalize the well-known Lyapunov-type inequality for second-order linear differential equations to a class of even-order linear differential equations, the results of this paper are new and generalize some known inequalities in the literatures. 相似文献
88.
In this paper, the computation of eigenvalue bounds for generalized interval eigenvalue problem is considered. Two algorithms based on the properties of continuous functions are developed for evaluating upper and lower eigenvalue bounds of structures with interval parameters. The method can provide the tightest bounds within a given precision. Numerical examples illustrate the effectiveness of the proposed method. 相似文献
89.
Xuecang Zhang 《Applied mathematics and computation》2010,217(5):2266-2276
In this paper, using spectral differentiation matrix and an elimination treatment of boundary conditions, Sturm-Liouville problems (SLPs) are discretized into standard matrix eigenvalue problems. The eigenvalues of the original Sturm-Liouville operator are approximated by the eigenvalues of the corresponding Chebyshev differentiation matrix (CDM). This greatly improves the efficiency of the classical Chebyshev collocation method for SLPs, where a determinant or a generalized matrix eigenvalue problem has to be computed. Furthermore, the state-of-the-art spectral method, which incorporates the barycentric rational interpolation with a conformal map, is used to solve regular SLPs. A much more accurate mapped barycentric Chebyshev differentiation matrix (MBCDM) is obtained to approximate the Sturm-Liouville operator. Compared with many other existing methods, the MBCDM method achieves higher accuracy and efficiency, i.e., it produces fewer outliers. When a large number of eigenvalues need to be computed, the MBCDM method is very competitive. Hundreds of eigenvalues up to more than ten digits accuracy can be computed in several seconds on a personal computer. 相似文献
90.
The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G - U, which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edges. Also, some applications of this interlacing property are explored and this interlacing property is extended to the edge weighted graphs. 相似文献