SL(2,R)上球函数的求和定理

基于经典的Fourier级数求和法,利用逼近恒同核与函数做卷积和球函数的Fourier展开公式给出了SL(2,R)上球函数的一般求和定理.     

球面径向基函数插值逼近的误差估计

研究了球面上由不同光滑度的核所生成且嵌套的两个再生核Hilbert空间之间的插值逼近问题．证明了一个空间的函数可用光滑性更好的子空间中的函数进行插值逼近，并给出了插值误差的上界估计．     

偏心率对双层搅拌桨偏心搅拌槽内流场的影响

偏心搅拌大都集中在对单层桨叶搅拌槽的研究,对双层的研究很少且集中在数值模拟研究,文章利用粒子图像 测速技术对轴偏心搅拌釜内流场进行实验研究。分析了不同偏心率对搅拌槽内宏观流场的影响,探讨了桨间轴向位置 处无因次化径向和轴向速度的分布。结果表明：搅拌槽内的速度最大值并不是随着偏心距的增大而增大;当偏心率e分 别为0.1和0.2时,可以提高径向速度的分布区间;当偏心率e>0.2时,内部存在一些漩涡导致速度波动比较大,这种流 体趋势并不有利于筒体内部流体的混合。研究结果对双层桨偏心搅拌器的设计具有指导意义。     

基于国内外安全系数标准对比的球墨铸铁储罐强度研究

针对目前球墨铸铁越来越多地应用于压力容器的制造中,而我国尚未更新相关标准中球墨铸铁压力容器安全系 数的现状,分析比较了我国TSG R00042009《固定式压力容器安全技术监察规程》、美国ASMEⅧ 1和欧盟EN 13445 6等国内外标准规范对球墨铸铁压力容器许用应力安全系数的规定。采用ANSYS Workbench有限元分析软件 对球墨铸铁储气罐进行计算,依据国内外不同的评定标准进行强度评定,并通过爆破试验验证了该空气储罐的安全性。 分析结果表明我国球墨铸铁压力容器安全系数偏大,过于保守;应在保证安全性的条件下,适当地降低安全系数。     

环境社会治理与国家“绿库”建设

绿色智库（“绿库”）,是近年来逐渐受到国际学界与传媒关注的一个现象。“绿库”是指一个较为制度化的实体机构,通过一种综合性的内容涉指对生态环境难题的理解与应对提出独创性的科学见解和政策建议。到目前为止,我国的全国性“绿库”还主要集中于“国办”的研究院所、高校机构和各种联合会,而民间“绿库”的发展尚处于一种起步或萌生阶段。因此,政府在我国“绿库”建设中理应发挥更为重要与积极的作用。     

Detecting Abrupt Leaks in Blended Underground Storage Tanks

We suggest and compare two multiple change-point algorithms (segmentation and sequential) for accurate detection of the onset of abrupt leaks in blended underground storage tanks. We apply these algorithms to two simulated scenarios to demonstrate the advantages of the sequential algorithm, and then we apply the sequential algorithm to the Cary blended site data. In addition, we obtain a confidence set for the locations of the change points conditional on the number of change points by inverting the related hypothesis test.     

Testing high-dimensional normality based on classical skewness and Kurtosis with a possible small sample size

Abstract

By using the idea of principal component analysis, we propose an approach to applying the classical skewness and kurtosis statistics for detecting univariate normality to testing high-dimensional normality. High-dimensional sample data are projected to the principal component directions on which the classical skewness and kurtosis statistics can be constructed. The theory of spherical distributions is employed to derive the null distributions of the combined statistics constructed from the principal component directions. A Monte Carlo study is carried out to demonstrate the performance of the statistics on controlling type I error rates and a simple power comparison with some existing statistics. The effectiveness of the proposed statistics is illustrated by two real-data examples.     

PLUG-IN ESTIMATION OF GENERAL LEVEL SETS

Given an unknown function (e.g. a probability density, a regression function, …) f and a constant c, the problem of estimating the level set L(c) ={f≥c} is considered. This problem is tackled in a very general framework, which allows f to be defined on a metric space different from . Such a degree of generality is motivated by practical considerations and, in fact, an example with astronomical data is analyzed where the domain of f is the unit sphere. A plug‐in approach is followed; that is, L(c) is estimated by L_n(c) ={f_n≥c} , where f_n is an estimator of f. Two results are obtained concerning consistency and convergence rates, with respect to the Hausdorff metric, of the boundaries ?L_n(c) towards ?L(c) . Also, the consistency of L_n(c) to L(c) is shown, under mild conditions, with respect to the L₁ distance. Special attention is paid to the particular case of spherical data.     

Supersmooth testing on the sphere over analytic classes

We consider the nonparametric goodness-of-fit test of the uniform density on the sphere when we have observations whose density is the convolution of an error density and the true underlying density. We will deal specifically with the supersmooth error case which includes the Gaussian distribution. Similar to deconvolution density estimation, the smoother the error density the harder is the rate recovery of the test problem. When considering nonparametric alternatives expressed over analytic classes, we show that it is possible to obtain original separation rates much faster than any logarithmic power of the sample size according to the ratio of the regularity index of the analytic class and the smoothness degree of the error. Furthermore, we show that our fully data-driven statistical procedure attains these optimal rates.     

夫琅和费衍射区内的Talbot效应

本文对球面波照明一维振幅型光栅时，在夫琅和费衍射区内的Ｔａｌｂｏｔ自然像进行了研究，得到了其成像条件，并与菲涅尔衍射区的成像条件作了比较。