A result on hypothesis testing for a multivariate normal distribution when some observations are missing

Let U_i = (X_i, Y_i), i = 1, 2,…, n, be a random sample from a bivariate normal distribution with mean μ = (μ_x, μ_y) and covariance matrix

. Let X_i, i = n + 1,…, N represent additional independent observations on the X population. Consider the hypothesis testing problem H₀ : μ = 0 vs. H₁ : μ ≠ 0. We prove that Hotelling's T² test, which uses (X_i, Y_i), i = 1, 2,…, n (and discards X_i, i = n + 1,…, N) is an admissible test. In addition, and from a practical point of view, the proof will enable us to identify the region of the parameter space where the T²-test cannot be beaten. A similar result is also proved for the problem of testing μ_x ? μ_y = 0. A Bayes test and other competitors which are similar tests are discussed.     

Structure and Aromaticity of AlCO-substituted Semibullvalene

The structures, energies and aromaticity (the nuclear-independent chemical shifts, NICS) of AlCO-substituted semibullvalenes were investigated at the B3LYP/6-311+G** level. Similar to BCO-substituted analogues, [2,6]-AlCO-semibullvalene is neutral bishomoaromatic. The NICS values reveal that the aromaticity of AlCO-substituted structures is smaller than that of BCO analogues.     

Solvothermal Synthesis and Crystal Structure of a Layered Thioantimonate(Ⅲ) [C4H9NH3]2Sb4S7

An inorganic-organic hybrid thioantimonate(Ⅲ) [CH3(CH2)3NH3]2Sb4S7 1 with layered structure was synthesized by solvothermal method.1 crystallizes in the triclinic system, space group P with a = 7.0124(11), b = 11.919(2), c = 14.879(3) (A), α = 108.791(3), β = 102.441(3), γ = 92.846(2)o, V = 1140.1(3) (A)3, Mr = 859.71, Z = 2, Dc = 2.504 g/cm3, μ= 5.324 mm-1, F(000) = 804, S = 1.013, the final R = 0.0297 and wR = 0.0618 for 3534 observed reflections with I＞2σ(I). 1 consists of [C4H9NH3] cations and two-dimensional [Sb4S7]n2n-anion which is composed of three SbS3 trigonal pyramids and one SbS4 unit joined by sharing common corners. The anionic layers are stacked perpendicularly to the c axis of the unit cell forming two-dimensional channels between the layers. The [C4H9NH3] cations interdigitate in a bilayer and reside in the 2D channels leading to a sandwich-like arrangement of the anion and cations.     

Fluorierung von Cyanurchlorid und Tieftemperatur-Kristallstruktur von [(ClCN)3F]+ [AsF6]−

Fluorination of Cyanuric Chloride and Low-Temperature Crystal Structure of [(ClCN)₃F]⁺[AsF₆]^? The low-temperature fluorination of cyanuric chloride, (ClCN)₃, with F₂/AsF₅ in SO₂F₂ solution yielded the salt [(ClCN)₃F]⁺ [AsF₆]^? ( 1 ) essentially in quantitative yield. Compound 1 was identified by a low-temperature single crystal X-ray structure determination: R 3 c, trigonal, a = b = 10.4246(23) Å, c = 15.1850(24) Å, V = 1429.1(4) Å 3, Z = 6, R_F = 0.056, R_w = 0.076 (for significant reflections), R_F = 0.088, R_w = 0.079 (for all reflections). Fluorination of neat (ClCN)₃ with [NF₄]⁺ [Sb₂F₁₁]^? yielded NF₃, CClF₃, SbF₃, N₂ and traces of CF₄. A qualitative scale for the oxidizing strength of the oxidative fluorinators NF₄⁺ and (XCN)₃F⁺ (X = H, F, Cl) has been computed ab initio.     

张青莲教授及其原子量新值测定研究

张青莲教授是中国科学院院士,我国同位素化学的奠基人.本文介绍他在90高龄之际在原子量新值测定方面所取得的杰出成就.从1990年代初以来,他主持一个科研小组采用质谱法,实施了测定10项原子量新值的长期计划.至2001年7月已经有In、Ir、Sb、Eu、Ce、Er、Ge、Dy和Zn等9个原子量新值被国际纯粹与应用化学联合会(IUPAC)的原子量与同位素丰度委员会(CAWIA)正式确定为原子量的国际新标准;另外一个Sm原子量新值也于2005年被国际组织确认.     

Correlation between excess adsorption data measured for solvent mixture/adsorbent systems and RM values obtained for different solutes chromatographed in binary mobile phases

This paper concerns the application of excess adsorption isotherms, measured for solvent mixture/adsorbent systems, to the characterization of TLC data. For this purpose the excess adsorption isotherms for three liquid mixtures: cyclohexane/ benzene, benzene/acetone, and carbon tetrachloride/ethyl acetate on silica gel at 20°C have been measured. These mixtures have been used as binary mobile phases in TLC measurements. It has been shown for a given solute in binary mobile phase that the quantity R_M is a simple function of the excess adsorption. Parameters of this function have been used to characterize chromatographic systems with binary mobile phases.     

ADSORPTION OF 2,4-D ON MODIFIED HYPERCROSSLINKED POLYSTYRENE （NDA-99） AND XAD-4 RESIN

The adsorption behavior of pesticide 2,4-dichlorophenoxyacetic acid (2,4-D) in aqueous solution has been investigated using a hypercrosslinked polystyrene adsorbent (NDA-99) modified by dimethylamine group as well as a nonionic macroporous adsorbent (XAD-4). The Langmuir and Freundlich isotherm models were employed to fit the experimental data to describe adsorption mechanism. It shows that NDA-99 resin exhibits an adsorption affinity for 2,4-D higher than XAD-4 resin owing to its exceptional micropore structure and the amine group of the hypercrosslinked matrix.Further studies indicate that the hydrogen bonding interaction and the stronger π-π conjugation play a significant role in the course of the adsorption of 2,4-D on NDA-99 resin, which is in agreement with the IR spectroscopic results and the △E values of HOMO (the highest occupied molecular orbit) of adsorbent and LUMO (the lowest unoccupied molecular orbit) of adsorbate calculated from the MINDO/3 model.     

An improved method of characterizing fatty acids by equivalent chain length values

A method has been developed for calculating more accurate and reproducible equivalent chain length (ECL) values of 33 straight-chain fatty acids (FA), with various positions and numbers of cis double bonds, chromatographed on DB-Wax and DB-1 columns. The dependence of ECL values on the position and the number of double bonds is described, as is a method of utilizing these relationships for the characterization of FA by gas chromatography.