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991.
A new a posteriori L2 norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H2 regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-calledmatching function. A numerical example supports the anisotropic error analysis. 相似文献
992.
Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual multiplier vector. This paper investigates the behavior of such a primal-dual pair with respect to perturbations in parameters on which the problem depends. A necessary and sufficient condition in terms of certain matrices is developed for the mapping from parameter vectors to saddle points to be single-valued and Lipschitz continuous locally. It is shown that the saddle point mapping is then semi-differentiable, and that its semi-derivative at any point and in any direction can be calculated by determining the unique solutions to an auxiliary problem of extended linear-quadratic programming and its dual. A matrix characterization of calmness of the solution mapping is provided as well. 相似文献
993.
Yong-Zhuo Chen 《Proceedings of the American Mathematical Society》2001,129(1):203-210
Let be a real Banach space partially ordered by a closed convex cone with nonempty interior . We study the continuation method for the monotone operator which satisfies
for all , , where . Thompson's metric is among the main tools we are using. 相似文献
for all , , where . Thompson's metric is among the main tools we are using. 相似文献
994.
In this note, we show that a well-known integral method, which was used by Mayne and Polak to compute an -subgradient, can be exploited to compute deterministically an element of the plenary hull of the Clarke generalized Jacobian of a locally Lipschitz mapping regardless of its structure. In particular, we show that, when a locally Lipschitz mapping is piecewise smooth, we are able to compute deterministically an element of the Clarke generalized Jacobian by the adaptive smoothing method. Consequently, we show that the Newton method based on the plenary hull of the Clarke generalized Jacobian can be implemented in a deterministic way for solving Lipschitz nonsmooth equations. 相似文献
995.
Generalized Steiner systems GS(2, 4, v, g) were first introduced by Etzion and were used to construct optimal constant weight codes over an alphabet of size g + 1 with minimum Hamming distance 5, in which each codeword has length v and weight 4. Etzion conjectured that the necessary conditions v 1 (mod 3) and v ; 7 are also sufficient for the existence of a GS(2,4,v,2). Except for the example of a GS(2,4,10,2) and some recursive constructions given by Etzion, nothing else is known about this conjecture. In this paper, Weil's theorem on character sum estimates is used to show that the conjecture is true for any prime power v 7 (mod 12) except v = 7, for which there does not exist a GS(2,4,7,2). 相似文献
996.
In this paper, we obtain some new results about the existence of multiple fixed points of a kind of quasimonotone increasing operator by the new method of decreasing flow invariant set.
997.
A high concentration (0.8 M) zirconium solution turned into a stable aqueous colloid of about 60 nm in size upon low temperature (96°C) incubation. Changing the acid concentration did not affect the colloidal growth rate nor the final colloid size much. However, the induction time before the rapid growth of colloidal particle could be altered. By limiting the incubation to just before the rapid growth of colloidal zirconia, and the addition of organic acids as surface modifiers, non-agglomerated primary crystallites (10 nm) of m-ZrO2 could be recovered. These modified primary crystallites could then be repeatedly flocculated and redispersed in water by adjusting the pH. 相似文献
998.
L. P. Falaleev 《Mathematical Notes》2000,67(4):505-511
We obtain a sharp value for the constant in the leading term of the deviation of a function belonging to the class Lip1 α from the generalized Abel-Poisson operators specified by the summation factors
of the conjugate Fourier series in the case 0 < α <l ≤ 1.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 595–602, April, 2000. 相似文献
999.
Eva Špániková 《Czechoslovak Mathematical Journal》2000,50(4):879-887
The purpose of this paper is to obtain oscillation criteria for the differential system
相似文献
1000.
A nonlinear integral operator T of the form (Tf)(s)=∫G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T. 相似文献