Estimation of a quantile in some nonstandard cases

A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Convex polynomial and spline approximation in C[−1, 1]

We prove that a convex functionf C[–1, 1] can be approximated by convex polynomialsp _n of degreen at the rate of ₃(f, 1/n). We show this by proving that the error in approximatingf by C² convex cubic splines withn knots is bounded by ₃(f, 1/n) and that such a spline approximant has anL third derivative which is bounded by n³₃(f, 1/n). Also we prove that iff C²[–1, 1], then it is approximable at the rate ofn ^–2 (f, 1/n) and the two estimates yield the desired result.Communicated by Ronald A. DeVore.     

An exponent bound on skew Hadamard abelian difference sets

A difference setD in a groupG is called a skew Hadamard difference set (or an antisymmetric difference set) if and only ifG is the disjoint union ofD, D(^–1), and {1}, whereD(^–1)={d^–1|dD}. In this note, we obtain an exponent bound for non-elementary abelian groupG which admits a skew Hadamard difference set. This improves the bound obtained previously by Johnsen, Camion and Mann.     

Synthesis and structure characterization of a novel series of N-alkylphthalimidylaminocarbonylmethoxylcalix [4] arenes

A novel series of N-alkylphthalimidylaminocarbonylmethoxylcalix[4]arenes with the reaction between 4-(N-bromoacetyla- mino)-phthalimide derivatives and calix[4]arene has been synthesized and structurally characterized by IR,~1HNMR and MS.From their analysis data,it was found that compounds 7a-7d adopted a cone conformation.     

A New Triterpenoid from "Gualou-xiebai-baijiu-tang" Consisting of Fructus trichosanthis and Bulbus allii mtacrostemi

A new triterpenoid saponin was isolated by bioactivity-guided isolation from "Gualou-xiebai-baijiu-tang" consisting ofFructus trichosanthisi and Bulbus allii macrostemi. Its structure was determined as 3-O-β-D-galactopyranosyl-hederagenin 28-O-β-D-xylopyranosyl (1→6)- β-D-galactopyranosyl ester by means of chemical evidences and spectral analysis.     

S-(1-二茂铁烷基)硫代乙醇酸与胺的反应——一类新型二茂铁衍生物的合成与性质研究

Ratajczak等研究了S-(1-二茂铁烷基)疏代乙醇酸的合成与反应(?)Ugi等将它们与羟胺反应,合成了一种有用的手性模板试剂。最近,Czech等用键合载体液相色谱对它们进行了光学拆分研究。本文报导了此类化合物与胺的反应,合成了一类新的化合物(?)二茂铁烷基)硫代乙醇酸胺。     

Structural Characterization of Anhydroicaritin Glycosides Using ESI—FT—ICR Mass Spectrometry

Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) was used to determine the structures of anhydroicaritin glycosides by the MS/MS experiments of anhydroicaritin glycosides and their methylated derivatives,With high accuracy FT-ICR-MS provides much information about the structures of compounds ,FT-ICR-MS shows the great potential application in the structural characterization of unknown compounds.     

薄层色谱法在香兰素合成中的应用

应用薄层色谱法对愈创木酚、3－甲氧基－4－羟基扁桃酸和香兰素进行了分析，以硅胶GF254作为吸附剂，从几种溶剂系统中选出氯仿：乙酸乙酯：正丙醇：冰乙酸：水＝20：1：1：1：2溶液作为展开剂。建立了 香兰素的薄层扫描定量分析方法，测定波长为500nm，参比波长为570nm，线性范围为0．31－6．2μg。     

石墨炉原子吸收法测定钒的研究

本文比较了在标准石墨管,热解涂层和全热解石墨管中钒的吸收信号形状。用全热解石墨管和EDTA铵盐作基体改进剂,直接测定水系沉积物中痕量钒。方法的特征量为61pg/0.0044A。