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31.
Z. Naniewicz 《Journal of Optimization Theory and Applications》1994,83(1):97-112
The hemivariational inequality approach is applied to establish the existence of solutions to a large class of nonconvex constrained problems in a reflexive Banach space. The admissible sets are supposed to be star-shaped with respect to a ball. Due to a discontinuity property of the Clarke directional differential related to the corresponding distance functions, the proposed method permits one to attain the solution without passing to zero with the penalization parameter. Some applications to nonconvex constrained variational problems illustrate the theory. 相似文献
32.
N. B. Waite 《Journal of Optimization Theory and Applications》1994,80(3):537-549
We establish a smooth positive extension theorem: Given any closed subset of a finite-dimensional real Euclidean space, a function zero on the closed set can be extended to a function smooth on the whole space and positive on the complement of the closed set. This result was stimulated by nonlinear programming. We give several applications of this result to nonlinear programming.This paper is dedicated to the memory of Emily Sue Merkle Waite, Ph.D.The author wishes to thank W. Cunningham for suggesting the question about constraint qualifications, A. Karr for noticing the example of a Brownian motion sample path, R. Byrd and P. Hartman for discussions, and E. Waite for support and encouragement. 相似文献
33.
CongruentPairsOnaSetZhuZuotong;(朱作桐)HuangJunmin(黄军民)(NanjingNormalUniversity)(NanjingUniversity)Abstract:Inthispaper,weintrod... 相似文献
34.
设D是C中的单位圆盘及为[0,1)上的正规函数。对于0<P<∞,这样的函数用于定义一个带权为 ̄p(|z|)/(1-|z| ̄2)的Bergman空间A ̄p.本文刻画了A ̄p中函数之零点集的结构.作为应用,又给出了A ̄p中函数序列插值的条件。 相似文献
35.
Many processes in the sciences and in engineering are modelled by dynamical systems and—in discretized version—by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples. 相似文献
36.
TIAN CHOU 《高校应用数学学报(英文版)》1994,9(4):319-324
SYMMETRIESANDGROUP-INVARIANTSOLUTIONSOFDIFFERENTIALEQUATIONSTIANCHOUAbstract:Foradifferentialequation,atheoreticalproofofther... 相似文献
37.
该文研究一簇Lorenz映射犛犪:[0,1]→[0,1](0<犪<1)犛犪(狓)=狓+犪 狓∈ [0,1-犪){(狓+犪-1)/犪 狓∈ [1-犪,1].从拓扑的角度考虑了犛犪的混沌行为,证明了:犛犪有稠密轨道;犛犪的周期的集合犘犘(犛犪)={1,犿+1,犿+2,…},其中犿为使犪犿<1-犪成立的最小正整数;犛犪的拓扑熵犺(犛犪)>0;几乎所有(关于Lebesgue测度)的点狓的Lyapunov指数λ(犛犪,狓)=λ犪>0.从统计的角度讨论了犛犪的稳定性.我们用下界函数方法证明了犛犪是统计稳定的,并且狌犵犪(犃)=∫犃犵犪(狓)d狓(犃∈犅)为犛犪的唯一绝对连续(关于Lebesgue测度)不变概率测度.同时,不变密度犵犪在参数扰动和随机作用的随机扰动下是稳定的. 相似文献
38.
It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy. 相似文献
39.
40.
For real a correspondence is made between the Julia setB
forz(z–)2, in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB
is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325. 相似文献