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11.
鞅差序列的Bernstein型不等式及其应用 总被引:3,自引:2,他引:1
本文将独立随机变量序列的Bernstein型不等式推广到鞅差序列情形,给出该不等式的一个应用,并在一定条件下证明了非参数回归中函数估计的强相合性. 相似文献
12.
A. D. Rogers 《Acta Mathematica Hungarica》2006,110(1-2):13-21
Summary A lower bound is established for the strip discrepancy of a broad class of point distributions. The bound implies unbounded
strip discrepancy for equally weighted point distributions under favorable conditions. The methods of proof use notions from
integral geometry. 相似文献
13.
The multilevel generalized assignment problem is a problem of assigning agents to tasks where the agents can perform tasks at more than one efficiency level. A profit is associated with each assignment and the objective of the problem is profit maximization. Two heuristic solution methods are presented for the problem. The heuristics are developed from solution methods for the generalized assignment problem. One method uses a regret minimization approach whilst the other method uses a repair approach on a relaxation of the problem. The heuristics are able to solve moderately large instances of the problem rapidly and effectively. Procedures for deriving an upper bound on the solution of the problem are also described. On larger and harder instances of the problem one heuristic is particularly effective. 相似文献
14.
We show that the difference between the Schrödinger uncertainty relations (UR) and the Heisenberg UR is fundamental. We propose a modified version of stochastic mechanics that allows clearly demonstrating that the contributions from the anticommutator and the commutator to the Schrödinger UR are equally important. A classification of quantum states minimizing the Schrödinger UR at an arbitrary instant is proposed. We show that the correlation of the coordinate and momentum fluctuations in such correlated-coherent states (CCS) is largely determined by the contributions from not only the commutator but also the anticommutator of the corresponding operators. We demonstrate that the character of this correlation changes qualitatively in time from the antiphase correlation typical for the Heisenberg UR to the inphase correlation for which the contribution from the anticommutator is decisive. We comparatively analyze properties of a free microparticle and a quantum oscillator in CCS and show that the CCS correspond to traveling-standing de Broglie waves in both models. 相似文献
15.
Milan Medved? 《Journal of Mathematical Analysis and Applications》2002,267(2):643-650
A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality. 相似文献
16.
In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers
to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge
bounds equal one, stable multi-sets are equivalent to stable sets.
For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient
conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the
stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable
multi-sets and conditions for them to be facet defining are determined.
The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets
emerge as an important substructure in the design of optical networks.
Received: February 14, 2001/Revised version: September 7, 2001 相似文献
17.
陈泽乾 《数学物理学报(B辑英文版)》2002,22(3)
A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators dt and its dual, creation operators t*. 相似文献
18.
本文给出Riccati方程及另外一类具有代表性微分方程的亚纯解(n,1)级的上界估计,在一定条件下确立了文[2]中的猜测的正确性。 相似文献
19.
本文首先将文[1]中的BLD映射推广为弱(L1,L2)-BLD映射,并证明了如下正则性结果:存在两个可积指数 P1=P1(n,L1,L2)<n<q1=q1(n,L1,L2),使得对任意弱(L1,L2)-BLD映射f∈(Ω,Rn),都有f∈(Ω,Rn),即f为(L1,L2)-BLD映射. 相似文献
20.
Let
d−1{(x1,…,xd)
d:x21+···+x2d=1} be the unit sphere of the d-dimensional Euclidean space
d. For r>0, we denote by Brp (1p∞) the class of functions f on
d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on
d−1,
and Pλk(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of Brp in Lq(
d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces XN of Lq(
d−1).The main result in this paper is that for r2(d−1)2,where ANBN means that there exists a positive constant C, independent of N, such that C−1ANBNCAN.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions. 相似文献