Synthesis and complexation studies of intra annularly linked bicyclic cyclophanes

The cyclophanes derived from 2,6-bis(chloromethyl)benzoquinone and suitable dithiols were reduced with sodium dithionate and then further coupled with various dibromides to give intra annularly linked bicyclic cyclophanes, which forms charge transfer complexes with TCNQ and TCNE.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Rank, term rank, and chromatic number

Let G be a graph with a nonempty edge set, and with rank rk(G), term rank Rk(G), and chromatic number χ(G). We characterize Rk(G) as being the maximum number of colors in certain proper colorings of G. In particular, we observe that χ(G)Rk(G), with equality holding if and only if (besides isolated vertices) G is either complete or a star. For a twin-free graph G, we observe the bound and we show that this bound is sharp.     

An example of a two-sided Wilcoxon signed rank test which is not unbiased

Although the theory of rank tests is rather complete in the one-sided case, it was not even known in 1959, whether the Wilcoxon two-sample test and other similar tests are unbiased against the two-sided alternatives (Lehmann (1959,Testing Statistical Hypotheses, p. 240, Wiley, New York)). A partial answer to this question was given by Sugiura in 1965, who found, that the test named above may be biased (Sugiura (1965,Ann. Inst. Statist. Math.,17, 261–263)). According to Lehmann (1986,Testing Statistical Hypotheses, 2nd ed., pp. 322–324, Wiley, New York) it seems to be still open, whether the same is true for the WILCOXON one-sample test, which is also known as WILCOXON signed rank test. This will be shown in the present paper.     

A new class of Ornstein transformations with singular spectrum

It is shown that for any family of probability measures in Ornstein type constructions, the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem [J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math. 84 (1993) 53–63], same result is proved for Rudolph's construction [D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math. 35 (1979) 97–122].     

二碘化钐作用下缺电子烯烃的还原偶联反应

室温下SmI2-HMPA-t-BuOH-THF体系能顺利地将丁烯二酸二酯还原偶联为1, 2, 3, 4-四烷氧基羰基丁烷, 同样条件下, 亚苄基氰乙酸乙酯,α-乙氧羰基肉桂酸乙酯, α-乙酰基肉桂酸乙酯和亚苄基丙二酸亚异丙酯等化合物也发生还原偶联反应得到相应的二聚体。     

含钼化合物及其配合物的抗癌抗肿瘤活性

钼是生命体所必需的微量元素。本文介绍了钼在人体中的作用，钼缺乏和钼过量对人体的影响，并介绍了含钼化合物以及配合物的抗癌抗肿瘤研究情况。     

动力学体系二维数据的秩分析及其应用

详细论证了动力学体系中存在的多种共线性情况,以及在此情况下二维数据阵的秩与独立反应数及组分数的关系.分析了通过增秩这一方式来判断体系组分数的条件.讨论了反应间存在物质交换对数据阵秩的影响.建立起一套通过秩分析判断未知动力学体系中存在的反应组分数、独立反应数以及可能反应机理的方法.将秩分析技术应用到聚苯胺与质子酸反应,初步分析了该体系存在的多种吸光性结构及结构变化.确定了[H＋]=0.01～0.1 mol•L－1范围内,聚苯胺与质子酸反应存在一个三结构两步互变过程.