积分中值ξ=ξ(x)的渐近性

对一类不满足g(n)≠0的函数g讨论了第一积分中值定理中ξ=ξ(x)在x→+∞时的渐近性质,并对第二积分中值定理的中值ξ=ξ(x)的渐近性进行了探讨,给出一些相关的结果.     

An intrinsic approach to Lichnerowicz conjecture

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.     

Weak Convergence of the Empirical Mean Excess Process with Application to Estimate the Negative Tail Index

Let Y _i , 1 ≤ i ≤ n be i.i.d. random variables with the generalized Pareto distribution W _γ,σ with γ < 0. We define the empirical mean excess process with respect to {Y _i , 1 ≤ i ≤ n} as in Eq. 2.1 (see below) and investigate its weak convergence. As an application, two new estimators of the negative tail index γ are constructed based on the linear regression to the empirical mean excess function and their consistency and asymptotic normality are obtained.      

Fluctuations in the mean of Euler’s phi function

We consider the error term in the mean value estimate of Euler’s phi function ψ(n), and show that it is Ω_+- (x(log log x)^1/2). This improves on the earlier results of Pillai and Chowla, and of Erdös and Shapiro.     

Commutators of fractional integral operators on Vanishing-Morrey spaces

In this note we prove a sufficient condition for commutators of fractional integral operators to belong to Vanishing Morrey spaces VL ^p,λ. In doing this we use an extension on Morrey spaces of an inequality by Fefferman and Stein concerning the sharp maximal function and the fractional maximal function and related Morrey inequalities.      

Integral formula of Minkowski type and new characterization of the Wulff shape

Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n＋1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n＋1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results.     

积分学第一中值定理“中间点”的渐近性研究新进展

对积分学第一中值定理的中间点当区间长度趋于零时的渐近性研究.新得到的结果不仅包含了过去若干已有结果,而且对涉及函数f(x),g(x)要求的条件几乎就是中值定理的,一个为连续,一个为可积不变号.     

Proficiency testing scheme for the harmonization and comparability of analytical measurements

According to the experience of the successful implementation of proficiency tests (PT) by using the certified reference value as the assigned value, a new scheme of evaluation is presented by suggesting the use of the uncertainty associated with the certified value. The technical performance of laboratories is evaluated by the parameter quadratic mean error (QME), which is the square root of the sum of the square of the bias and that of the standard deviation of the laboratory. This parameter is considered as the estimate of the measurement uncertainty of the laboratory and is compared to the uncertainty (U) associated with the certified value provided by an NMI. Considering that the calibration and measurement capability, known as the CMC, is recognized among NMIs, the ratio QME/U enables us to compare the PT relative to the CMC of an NMI, and, consequently, to any other comparison results based on the CMC of signatories of the mutual recognition arrangement (MRA) of the International Committee of Weights and Measure (CIPM). Presented at BERM-11, October 2007, Tsukuba, Japan.     

反向Chrystal不等式

利用控制不等式理论建立了三个反向Chrysta l不等式,并给出了若干应用.     

多项式的特征和与二项指数和的混合均值

本文主要利用解析方法以及二项指数和与Dirichlet特征的性质，研究多项式的特征和与二项三次指数和的混合均值的计算问题，并得到一个较强的渐近公式.