On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators

Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by μ. We prove that the uniform law of large numbers holds if the class has an envelope function that is μ-integrable, or if is bounded in L _p(μ) for some p>1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of the class in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE) and to prove consistency for a class of simple M-estimators. This revised version was published online in June 2006 with corrections to the Cover Date.     

Sub-bundles of the complexified tangent bundle

We study embeddings of complex vector bundles, especially line bundles, in the complexification of the tangent bundle of a manifold. The aim is to understand implications of properties of interest in partial differential equations.

     

Upper bounds for Ramsey numbers

The Ramsey number R(G₁,G₂,…,G_k) is the least integer p so that for any k-edge coloring of the complete graph K_p, there is a monochromatic copy of G_i of color i. In this paper, we derive upper bounds of R(G₁,G₂,…,G_k) for certain graphs G_i. In particular, these bounds show that R(9,9)6588 and R(10,10)23556 improving the previous best bounds of 6625 and 23854.     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。     

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON-PISOT NUMBERS

1　IntroductionForany 0 <λ <1 ,letνλ　denotethedistributionof ∞n=0 εnλn wherethecoefficientsεnareeither0or1 ,chosenindependentlywithprobability12 foreach .Itistheinfiniteconvo lutionproductofthedistributions 12 (δ0 +δλn) ,givingrisetotheterm“infiniteBernoulliconvolution”orsimply“Bernoulliconvolution” .TheBernoulliconvolutioncanbeexpressedasaself similarmeasureνλsatisfyingtheequationνλ =12 νλ φ- 10 + 12 νλ φ- 11,( 1 .1 )whereφ0 (x) =λxand φ1(x) =λx + 1 .Thisme…     

非交换陈特征的一个注记

此注记利用Moscovici的一个想法和热核渐近展开技术,给出了Clifford模 上Dirac算子的整循环陈特征的一个计算公式.     

Oscillations of certain second order nonlinear differential equations

A second order nonlinear differential equation

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

Factorization of the (relative) Chern character through Lie algebra homology

Karoubi's relative Chern character is constructed as a chain map factoring through Lie algebra chains.This is part of the author's doctoral thesis, Stanford University 1990.     

Preparation and electrical characterization of (PVC + KBrO3) polymer electrolytes for solid state battery applications

This paper presents results of studies on dc electrical conductivity and transference number measurements on potassium bromate (KBrO₃) complexed polyvinyl chloride (PVC) films prepared by solution cast technique. Temperature dependence of dc electrical conductivity and transference number data indicated the dominance of ion type charge transport in these specimens. The magnitude of conductivity increased with increase in concentration of the salt and temperature. Using this (PVC + KBrO₃) electrolyte, solid-state electrochemical cells were fabricated, and their discharge profiles were studied under a constant load of 100 kΩ. Several cell profiles such as open circuit voltage, short circuit current, power density, and energy density associated with these cells were evaluated and were reported. The features of complexation of the electrolytes were studied by X-ray diffraction and Fourier transform infrared spectroscopy. Paper presented at the Third International Conference on Ionic Devices (ICID 2006), Chennai, Tamilnadu, India, Dec. 7–9, 2006