A Hypothesis Testing Problem in the Linear Model (in English)

本文讨论了多元线性模型中的一个假设检验问题。假定 $\[{E(Y) = A\theta + B\eta }\]$ $Y的各行独立、正太、同协差阵V$ 现在要检验假设H_0:存在矩阵C使$\theta= C\eta$ 是否成立。首先可将问题化为法式的形式，对法式分两种情况进行讨论： （一）$[V = {\sigma ^2}I,{\sigma ^2}\]$未知，此时可求出 \theta,C，\sigma ^2的最大似然估计（当 H^0成立时）是 $[\left\{ {\begin{array}{*{20}{c}} {\hat \theta = {{({I_p} + \hat C'\hat C)}^{ - 1}}({y_1} + \hat C'{y_2})}\{\hat C = - {{({{T'}_{22}})}^{ - 1}}{{T'}_{12}}}\{{{\hat \sigma }^2} = \frac{1}{{nk}}(\sum\limits_{j = p + 1}^{p + q} {\lambda _j^* + \sum\limits_{j = 1}^k {{d_j})} } } \end{array}} \right.\]$ 其中y_1,y_2是法式 $[E\left( {\begin{array}{*{20}{c}} {{y_1}}\{{y_2}}\{{y_3}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} \theta \\eta \0 \end{array}} \right)\begin{array}{*{20}{c}} p\q\{n - (p + q)} \end{array}\]$ 中的资料阵y_1,y_2,d_1,\cdots，d_k是y^'_3y_3的全部特征根，$[\lambda _1^* \ge \cdots \lambda _{p + q}^*\]$是$[\left( {\begin{array}{*{20}{c}} {{y_1}}\{{y_2}} \end{array}} \right)\left( {\begin{array}{*{20}{c}} {{{y'}_1}}&{{{y'}_2}} \end{array}} \right)\]$的全部特征根，相应特征向量依$\lambda^*_i$的大小顺序从左到右排成矩阵T，T的分块子阵是T_ij，即 $[T = \left( {\begin{array}{*{20}{c}} {{T_{11}}}&{{T_{12}}}\{{T_{21}}}&{{T_{22}}} \end{array}} \right)\begin{array}{*{20}{c}} p\q \end{array}\]$ 对H_0的广义似然比检验是 $[\Lambda = \sum\limits_{j = p + 1}^k {{\lambda _j}/\sum\limits_{j = 1}^k {{d_j}} } \]$ $=lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_k$是$y_1^'y_1+y_2^'y_2$的全部特征根。 （二）一般情形V未知，此时 \theta,C的估计量同前，可求出 $[\hat V = \frac{1}{n}({y_2}^\prime {T_{22}}{T_{22}}^\prime {y_2} + {y_2}^\prime {y_2})\]$ H_0相应的Lawley不变检验是 $[\sum\limits_{j = p + 1}^k {{\beta _j}} \ge {\alpha _1}\]$ 其中 $\beta_1 \geq \beta_2 \geq \cdots \beta_k$是$y'_1y_1+y'_2y_2$的相应于$y'_sy_s$的全部特征根。 有关$\Lambda \$的以及$[\sum\limits_{j = p + 1}^k {{\beta _j}} \]$的极限分布将在另外的文章中讨论。     

Highly regio- and enantioselective thermal [2 + 2] cycloaddition of coumarin in a crystalline inclusion complex under high vacuum

Coumarin and thiocoumarin, which are usually thermally unreactive for dimerization, were dimerized in their inclusion crystalline complexes under thermal and high vacuum conditions.     

脑电信号的标度分析及其在睡眠状态区分中的应用

脑电信号具有长程幂律相关性及多重分形的标度特性,并随生理病理状态改变.本文首次针对睡眠脑电信号应用单重分形去趋势波动分析(detrended fluctuation analysis,简记为DFA)方法与多重分形奇异谱对睡眠脑电信号的标度特征进行系统的对比研究.发现DFA标度指数α对于不同导联和样本组间的差异较为敏感,随睡眠状态的变化不规律;而多重分形奇异强度区间Δα随睡眠状态的变化更为规律,睡眠Ⅰ期至Ⅳ期不断增大,并且导联间差异和样本组间差异均较小.多重分形Δα参数更适合作为判定睡眠状态的定量参数.     

周期量级激光脉冲在不同密度的原子介质中传播行为的比较(英文)

利用不含慢变包络近似和旋波近似的全波Maxwell-Bloch方程组的数值解,研究了周期量级超短激光脉冲在Ladder型三能级原子介质中的传播行为并与在相应的稀疏介质中的情况进行了比较.我们发现,在传播过程中,超短脉冲在稠密介质中的时间演化规律与在稀疏介质中明显不同,而且这种差别将随初始脉冲面积的增大而加大.当初始脉冲面积较小时,在传播过程中,脉冲形状在稀疏介质中只有小的改变而在稠密介质中却有显著的变化.当初始脉冲面积足够大时,在稠密介质中在不同的传播距离处脉冲分裂为不同数量和形状的亚脉冲;在稀疏介质中脉冲形状在传播过程中仍然只有小的改变。产生以上差别的原因在于稠密原子介质中近偶极-偶极(NDD)相互作用导致的局域场修正(LFC)及比稀疏原子介质更强的极化电场的影响.其中,更强的极化电场的影响起着主要的作用,但局域场修正的作用也不能忽略,而极化电场的增强是由于原子密度的增加.     

The allylation reactions of aromatic aldehydes and ketones with tin dichloride in water

The allylation reactions of aromatic aldehydes and ketones were carried out in 31–86% yield using SnCl₂–H₂O system under ultrasound irradiation at r.t. for 5 h. The reactions in the same system gave homoallyl alcohols in 21–84% yield with stirring at r.t. for 24 h. Compared with traditional stirring methods, ultrasonic irradiation is more convenient and efficient.     

Spectrofluorimetric determination of trace amount of coenzyme II using ciprofloxacin-terbium complex as a fluorescent probe

A new spectrofluorimetric method was developed for the determination of trace amount of nicotinamide adenine dinucleotide phosphate (NADP). Using terbium ion (Tb³⁺)-ciprofloxacin (CIP) complex as a fluorescent probe, in the buffer solution of pH=9.00, NADP can remarkably enhance the fluorescence intensity of the Tb³⁺-CIP complex at and the enhanced fluorescence intensity of Tb³⁺ ion is in proportion to the concentration of NADP. Optimum conditions for the determination of NADP were also investigated. The dynamic range for the determination of NADP is 4.9×10⁻⁷−3.7×10⁻⁶ mol L⁻¹ with detection limit of 1.3×10⁻⁷ mol L⁻¹. This method is simple, practical and relatively free interference from coexisting substances and can be successfully applied to determination of NADP in synthetic water samples. Moreover, the enhancement mechanisms of the fluorescence intensity in the Tb³⁺-CIP system and the Tb³⁺-CIP-NADP system have been also discussed.     

Highly sensitive spectrofluorimetric determination of trace amounts of lecithin

A new spectrofluorimetric method was developed for the determination of trace amounts of lecithin using the ciprofloxacin (CIP)–terbium (Tb³⁺) ion complex as a fluorescent probe. In a buffer solution at pH=5.60, lecithin can remarkably reduce the fluorescence intensity of the CIP–Tb³⁺ complex at λ=545 nm. The reduced fluorescence intensity of the Tb³⁺ ion is proportional to the concentration of lecithin. Optimum conditions for the determination of lecithin were also investigated. The linear range and detection limit for the determination of lecithin were 1.0×10⁻⁶–3.0×10⁻⁵ mol L⁻¹ and 3.44×10⁻⁷ mol L⁻¹, respectively. This method is simple, practical, and relatively free of interference from coexisting substances. Furthermore, it has been successfully applied to assess lecithin in serum samples.      

A theoretical study of the reaction of O(3P) with isobutene

The reaction of O((3)P) with isobutene ((CH(3))(2)C=CH(2)) is investigated using the unrestricted second-order M?ller-Plesset perturbation (UMP2) and complete basis set CBS-4M level methods. The minimum energy crossing point (MECP) between the singlet and triplet potential energy surfaces is located using the Newton-Lagrange method, and it is shown that the MECP plays a key role. The calculational results indicate that the site selectivity of the addition of O((3)P) to either carbon atom of the double bond of isobutene is weak, and the major product channels are CH(2)C(O)CH(3) + CH(3,) cis-/trans-CH(3)CHCHO + CH(3), (CH(3))(2)CCO + H(2), and CH(3)C(CH(2))(2) + OH, among which (CH(3))(2)CCO + H(2) is predicted to be the energetically most favorable one. The complex multichannel reaction mechanisms are revealed, and the observations in several recent experiments could be rationalized on the basis of the present calculations. The formation mechanisms of butenols are also discussed.     

A miniaturized HTS microwave receiver front-end subsystem for radar and communication applications

This paper presents a miniaturized high performance high temperature superconducting (HTS) microwave receiver front-end subsystem, which uses a mini stirling cryocooler to cool a high selective HTS filter and a low noise amplifier (LNA). The HTS filter was miniaturized by using specially designed compact resonators and fabricating with double-sided YBCO films on LAO substrate which has a relatively high permittivity. The LNA was specially designed to work at cryogenic temperature with noise figure of 0.27 dB at 71 K. The mini cryocooler, which is widely used in infrared detectors, has a smaller size (60 mm × 80 mm × 100 mm) and a lighter weight (340 g) than the stirling cryocoolers commonly used in other HTS filter subsystem. The whole front-end subsystem, including a HTS filter, a LNA, a cryocooler and the vacuum chamber, has a size of only φ120 mm × 175 mm and a weight of only 3.3 kg. The microwave devices inside the subsystem are working at 71.8 K with a consumed cooling power of 0.325 W. The center frequency of this subsystem is 925.2 MHz and the bandwidth is 2.7 MHz (which is a fractional bandwidth of 0.2%), with the gain of 19.75 dB at center frequency and the return loss better than ?18.11 dB in the pass band. The stop band rejection is more than 60 dB and the skirt slope is exceeding 120 dB MHz^?1. The noise figure of this subsystem is less than 0.8 dB. This front-end subsystem can be used in radars and communication systems conveniently due to it’s compact size and light weight.