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751.
本文从三种构成完备集的对称函数的定义及有关性质出发,讨论了对称函数在各完备集中展开系数之间的转换,给出了相应的变换矩阵,从而建立了各完备集之间的相互联系. 相似文献
752.
J. H. Dulá 《Journal of Optimization Theory and Applications》1994,81(1):35-52
In 1967, Wets and Witzgall (Ref. 1) made, in passing, a connection between frames of polyhedral cones and redundancy in linear programming. The present work elaborates and formalizes the theoretical details needed to establish this relation. We study the properties of optimal value functions in order to derive the correspondence between problems in redundancy and the frame of a polyhedral cone. The insights obtained lead to schemes to improve the efficiency of procedures to detect redundancy in the areas of linear programming, stochastic programming, and computational geometry.The author is indebted to G. Dewan for his review and discussions. 相似文献
753.
We describe the problem of the equivalence of ensembles at the level of states for classical lattice systems. We discuss circumstances where the vanishing of the specific information gain of a sequence of microcanonical measures with respect to a sequence of grand canonical measures implies the equivalence of ensembles. We give a simple derivation of a criterion for the vanishing of the specific information gain in terms of thermodynamic functions. The proof uses ideas from the theory of large deviations but is self-contained. We show how the criterion works in a simple model of a paramagnet and in the Ising model of a ferromagnet in any dimension but fails in the case of the Curie-Weiss mean-field model. 相似文献
754.
In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems. 相似文献
755.
In several applications, underestimation of functions has proven to be a helpful tool for global optimization. In protein–ligand
docking problems as well as in protein structure prediction, single convex quadratic underestimators have been used to approximate
the location of the global minimum point. While this approach has been successful for basin-shaped functions, it is not suitable
for energy functions with more than one distinct local minimum with a large magnitude. Such functions may contain several
basin-shaped components and, thus, cannot be underfitted by a single convex underestimator. In this paper, we propose using
an underestimator composed of several negative Gaussian functions. Such an underestimator can be computed by solving a nonlinear
programming problem, which minimizes the error between the data points and the underestimator in the L
1 norm. Numerical results for simulated and actual docking energy functions are presented. 相似文献
756.
We obtain approximate solutions of Altarelli-Parisi equations beyond leading logarithmic approximation. Our results suggest
quantitative utility of higher order terms in the structure function analysis of deep inelastic scattering. 相似文献
757.
M. Oberguggenberger D. Scarpalézos 《Journal of Mathematical Analysis and Applications》2007,328(2):1321-1335
The definitions of positivity and positive definiteness are extended to generalized function algebras in coherence with the corresponding notions for distributions. Versions of Bochner's theorem for a positive definite Colombeau generalized function are given. 相似文献
758.
Interval arithmetic and Taylor's formula can be used to bound the slope of the cord of a univariate function at a given point. This leads in turn to bounding the values of the function itself. Computing such bounds for the function, its first and second derviatives, allows the determination of intervals in which this function cannot have a global minimum. Exploiting this information together with a simple branching rule yields an efficient algorithm for global minimization of univariate functions. Computational experience is reported.The first and second authors have been supported by FCAR (Fonds pour la Formation de Chercheurs et l'Aide à la Recherche) Grant 92EQ1048 and AFOSR Grant 90-0008 to Rutgers University. The first author has also been supported by NSERC (Natural Sciences and Engineering Research Council of Canada) Grant to HEC and NSERC Grant GP0105574. The second author has been supported by NSERC Grant GP0036426, FCAR Grant 90NC0305, and a NSF Visiting Professorship for Women in Science at Princeton University. Work of the third author was done in part while he was a graduate student at the Department of Mathematics, Rutgers University, New Brunswick, New Jersey, USA and during a visit to GERAD, June–August 1991. 相似文献
759.
Hitoshi Tanaka 《数学学报(英文版)》2002,18(3):447-454
Let K
δ, 0 < δ≪1, be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity δ. The (so-called)
Fefferman-Stein-type inequality: is shown, where C
d
and α
d
are constants depending only on the dimension d and w is a weight. The result contains the exponent (d−2)/2d which is smaller than the exponent (d−2)(d−1)/d(2d−3) obtained in [7].
Received October 8, 2001, Accepted February 28, 2002 相似文献
760.
Ngc-Minh Lê 《Computational Geometry》1997,8(6):279-298
We introduce the simple abstract Voronoi diagram in 3-space as an abstraction of the usual Voronoi diagram. We show that the 3-dimensional simple abstract Voronoi diagram of n sites can be computed in O(n2) expected time using O(n2) expected space by a randomized algorithm. The algorithm is based on the randomized incremental construction technique of Clarkson and Shor (1989). We apply the algorithm to some concrete types of such diagrams: power diagrams, diagrams under ellipsoid convex distance functions, and diagrams under the Hausdorff distance for sites that are parallel segments all having the same length. 相似文献