Local approximations and intrinsic characterization of spaces of smooth functions on regular subsets of ℝn

We give an intrinsic characterization of the restrictions of Sobolev (?ⁿ ), Triebel–Lizorkin (?ⁿ ) and Besov (?ⁿ ) spaces to regular subsets of ?ⁿ via sharp maximal functions and local approximations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simpson不等式的改进及其应用

通过一阶导数对Simpson不等式进行了改进,并推导出了相应的数值积分公式和最佳误差限,扩大了Simpson积分公式的适用范围,最后给出了具体的数值应用.     

Weak sharp minima revisited, part II: application to linear regularity and error bounds

The notion of weak sharp minima is an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. It has been studied extensively by several authors. This paper is the second of a series on this subject where the basic results on weak sharp minima in Part I are applied to a number of important problems in convex programming. In Part II we study applications to the linear regularity and bounded linear regularity of a finite collection of convex sets as well as global error bounds in convex programming. We obtain both new results and reproduce several existing results from a fresh perspective. We dedicate this paper to our friend and mentor Terry Rockafellar on the occasion of his 70th birthday. He has been our guide in mathematics as well as in the backcountry and waterways of the Olympic and Cascade mountains. Research supported in part by the National Science Foundation Grant DMS-0203175.     

一类具非线性二阶导数项的Schrōdinger方程整体解存在的最佳条件

本文讨论一类具非线性二阶导数项的Schrodinger方程,它在物理上描述了上混合振荡传播．根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在．     

Development of a surface acoustic wave wireless and passive temperature sensor incorporating reflective delay line

based on optimal design on the core element of the sensor,a wireless and passive surface acoustic wave(SAW)temperature sensor integrated with ID Tag was presented.A reflective delay line,which consists of a transducer and eight reflectors on YZ LiNbO3 substrate.Was fabricated as the sensor element,in which,three reflectors were used for temperature sensing,and the other five were for the ID Tag using phase encoding.Single phase unidirectional transducers(SPUDTs)and shorted grating were used to structure the sAW device,leading to excellent signal to noise ratio(SNR).The performance of the SAW device was simulated by the coupling of modes(COM)prior to fabrication.Using the network analyzer,the response in time domain of the fabricated 434 MHz SAW sensor was characterized,the measured S11 agrees well with the simulated one,sharp reflection peaks,high signal/noise,and low spurious noise between the reflection peaks were observed.Using the radar system based on FSCW as the reader unit.the developed SAW temperature sensors were evaluated wirelessly.Excellent1 inearity and good resolution of士1℃ were observed.     

交通流突变点的无标度特征分析

交通流时间序列在不同时间尺度上具有不同的波动特征.为了分析交通流的突变特征,以一段实际的交通流量序列为研究对象进行实证研究.采用小波变换的方法求得交通流在不同尺度上的突变点,按照小波函数过零点数目将交通流的尺度划分为若干层次,并分析了交通流突变的层次性.计算表明:以突变点数目为测度时,在一定的尺度范围内,交通流在突变层次上的突变点数目满足自相似性特征.因此,交通流的突变在不同尺度上具有无标度性.     

一类多线性奇异积分算子的加权估计

In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf(x) = p. v.RnΩ(x- y)|x- y|n+1 A(x)- A(y)- A(y)(x- y) f(y)dy,where Ω is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ(Sn-1) with γ∈(0, 1], A has derivatives of order one in BMO(Rn).     

Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels

By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.     

Commutators of Lipschitz Functions and Singular Integrals with Non-Smooth Kernels on Euclidean Spaces

In this article, we obtain the L p-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.     

尖锐前缘气动加热机理与激波脱体距离研究

针对尖锐前缘所处的气动环境,分析了由于前缘尖化所带来的稀薄效应影响。应用理论方法推导了尖锐前缘驻点气动热的计算方法和计算公式,并结合CFD方法、DSMC方法和Fay-Riddel工程方法对其前缘钝头的流场、驻点热流进行了计算和对比分析。计算结果表明,由于前缘的尖化使得稀薄气体效应提前出现,从而影响到前缘的激波厚度、激波形状和激波脱体距离等流动现象,导致激波结构复杂化,可能会对进气道唇口的斜激波带来不利的影响。另外稀薄效应的影响降低了驻点热流,缓解了尖化前缘的气动热环境。