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61.
Lynn ERBE Christopher C. TISDELL Patricia J. Y. WONG 《数学学报(英文版)》2007,23(3):549-556
Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions. 相似文献
62.
H. Hu 《Journal of Optimization Theory and Applications》2005,126(2):287-308
In this paper, we study geometric condition measures and smoothness condition measures of closed convex sets, bounded linear regularity, and linear regularity. We show that, under certain conditions, the constant for the linear regularity of infinitely many closed convex sets can be characterized by the geometric condition measure of the intersection or by the smoothness condition measure of the intersection. We study also the bounded linear regularity and present some interesting properties of the general linear regularity problem.The author is grateful to the referees for valuable and constructive suggestions. In particular, she thanks a referee for drawing her attention to Corollary 5.14 of Ref. 3, which inspired her to derive Theorem 4.2 and Corollary 4.2 in the revision of this paper. 相似文献
63.
Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation. 相似文献
64.
Optimal lower bounds for cubature error on the sphere 总被引:6,自引:1,他引:5
We show that the worst-case cubature error E(Qm;Hs) of an m-point cubature rule Qm for functions in the unit ball of the Sobolev space Hs=Hs(S2),s>1, has the lower bound , where the constant cs is independent of Qm and m. This lower bound result is optimal, since we have established in previous work that there exist sequences of cubature rules for which with a constant independent of n. The method of proof is constructive: given the cubature rule Qm, we construct explicitly a ‘bad’ function fmHs, which is a function for which Qmfm=0 and . The construction uses results about packings of spherical caps on the sphere. 相似文献
65.
66.
Upper bounds for survival probability of the contact process 总被引:3,自引:0,他引:3
67.
Cristian Barbarosie Anca‐Maria Toader 《Mathematical Methods in the Applied Sciences》2005,28(9):1089-1114
We prove bounds on the homogenized coefficients for general non‐periodic mixtures of an arbitrary number of isotropic materials, in the heat conduction framework. The component materials and their proportions are given through the Young measure associated to the sequence of coefficient functions. Upper and lower bounds inequalities are deduced in terms of algebraic relations between this Young measure and the eigenvalues of the H‐limit matrix. The proofs employ arguments of compensated compactness and fine properties of Young measures. When restricted to the periodic case, we recover known bounds. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
68.
Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade. This study examines this behaviour in terms of the concepts of approximately invariant subspace and what we have called the analytic grade of a Krylov sequence. It is shown how the small Ritz values play a vital role in the convergence and how this knowledge helps in the construction of an effective preconditioner. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
69.
Christian Lubich. 《Mathematics of Computation》2005,74(250):765-779
The Dirac-Frenkel-McLachlan variational principle is the basic tool for obtaining computationally accessible approximations in quantum molecular dynamics. It determines equations of motion for an approximate time-dependent wave function on an approximation manifold of reduced dimension. This paper gives a near-optimality result for variational approximations. It bounds the error in terms of the distance of the exact wave function to the approximation manifold and identifies the parameters that control the deviation of the variational approximation from the best approximation on the manifold.
70.
Zhu Yongliang; Pagilla Prabhakar R. 《IMA Journal of Mathematical Control and Information》2005,22(2):181-186
We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived. 相似文献