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Let denote the maximum diameter among all subgraphs obtained by deleting q edges of G. Let denote the maximum diameter among all subgraphs obtained by deleting p vertices of G. We prove that for all meaningful a. We also define mixed fault diameter , where p vertices and q edges are deleted at the same time. We prove that for 0<la, , and give some examples. 相似文献
116.
S.M.Mefire 《计算数学(英文版)》2009,(4):495-524
From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes: the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method. 相似文献
117.
Gabriel Wittum 《计算数学(英文版)》2009,(5):563-572
In this paper, we obtain optimal error estimates in both L^2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L^2 error estimates into the L^2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nedelec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature. 相似文献
118.
The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic
hierarchy , where the second component takes values in operators on the infinite model cone of the local wedges. In the general understanding
of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying
the ellipticity of the principal edge symbol which includes the (in general not explicitly known) number of additional conditions of trace and potential type on the edge.
We focus here on these questions and give explicit answers for a wide class of elliptic operators that are connected with
the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation
and ellipticity for Dirichlet–Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues
of the Agranovich–Dynin formula for edge boundary value problems.
Nicoleta Dines and Bert-Wolfgang Schulze were supported by Chinese-German Cooperation Program “Partial Differential Equations”,
NNSF of China and DFG of Germany. Xiaochun Liu was supported by NNSF of China through Grant No. 10501034, and Chinese-German
Cooperation Program “Partial Differential Equations”, NNSF of China and DFG of Germany. 相似文献
119.
For a fixed value of a parameter k≥2, the Maximum k-Edge-Colorable Subgraph Problem consists in finding k edge-disjoint matchings in a simple graph, with the goal of maximising the total number of edges used. The problem is known to be -hard for all k, but there exist polynomial time approximation algorithms with approximation ratios tending to 1 as k tends to infinity. Herein we propose improved approximation algorithms for the cases of k=2 and k=3, having approximation ratios of 5/6 and 4/5, respectively. 相似文献
120.
We study the minimum number of weights assigned to the edges of a graph G with no component K2 so that any two adjacent vertices have distinct sets of weights on their incident edges. The best possible upper bound on this parameter is proved. 相似文献