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1.
Almost-Sure Results for a Class of Dependent Random Variables   总被引:17,自引:0,他引:17  
The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by d + —the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.  相似文献
2.
The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle for strongly mixing sequences of random variables in the absence of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences.  相似文献
3.
The local index formula in noncommutative geometry   总被引:13,自引:0,他引:13  
In noncommutative geometry a geometric space is described from a spectral vantage point, as a tripleA, H, D consisting of a *-algebraA represented in a Hilbert spaceH together with an unbounded selfadjoint operatorD, with compact resolvent, which interacts with the algebra in a bounded fashion. This paper contributes to the advancement of this point of view in two significant ways: (1) by showing that any pseudogroup of transformations of a manifold gives rise to such a spectral triple of finite summability degree, and (2) by proving a general, in some sense universal, local index formula for arbitrary spectral triples of finite summability degree, in terms of the Dixmier trace and its residue-type extension.We dedicate this paper to Misha Gromov  相似文献
4.
A note on the three color problem   总被引:11,自引:0,他引:11  
It is shown that a planar graph withouti-circuits, 4 i 9, is 3-colorable. This result strengthens the result obtained by H.L. Abbott and B. Zhou.The author's research was partially supported by the Office of Naval Research, Grant number N00014-92-J-1965.  相似文献
5.
Location Science Research: A Review   总被引:10,自引:0,他引:10  
This document presents a broad review of facility location and location science research. The goal of this report is not to provide an exhaustive list of location science topics (an undertaking far beyond the scope of a single journal article), but rather to provide the reader with a more general review of the location science research landscape. This document starts with a short introduction to some of the more germane aspects of all location science research.  相似文献
6.
Transportation cost for Gaussian and other product measures   总被引:9,自引:0,他引:9  
Consider the canonical Gaussian measure N on , a probability measure on N , absolutely continuous with respect to N . We prove that the transportation cost of to N , when the cost of transporting a unit of mass fromx toy is measured by xy2, is at most d. As a consequence we obtain a completely elementary proof of a very sharp form of the concentration of measure phenomenon in Gauss space. We then prove a result of the same nature when N is replaced by the measure of density 2N exp (– iN |x i |). This yields a sharp form of concentration of measure in that space.Work partially supported by an NSF Grant.  相似文献
7.
Stability analysis of a rotating flexible system   总被引:9,自引:0,他引:9  
We analyse here the equations of motion of a planar body consisting of a rigid body with attached flexible rod. These equations take the form of coupled ordinary and partial differential equations. We analyse the equations both with and without centrifugal stiffening effects. Using the energy-momentum method, we analyse nonlinear stability of the equilibria in each case. We also analyse the Hamiltonian and Poisson bracket structure of the system as well as the energy-momentum map and associated relative equilibria.Partly supported by NSF grant DMS-8701574 and AFOSR grant AFOSR-1SSA-87-0077 and by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.  相似文献
8.
Convergence rates of the strong law for stationary mixing sequences   总被引:8,自引:0,他引:8  
Summary In this note we estimate the rate of convergence in Marcinkiewicz-Zygmung strong law, for partial sumsS n of strong stationary mixing sequences of random variables. The results improve the corresponding ones obtained by Tze Leung Lai (1977) and Christian Hipp (1979).  相似文献
9.
Let K be a nonempty closed convex subset of a real Hilbert space H. The approximate solvability of a system of nonlinear variational inequality problems, based on the convergence of projection methods, is discussed as follows: find an element (x*, y*)K×K such that
where T: K×KH is a nonlinear mapping on K×K.  相似文献
10.
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