大环二萜类化合物的研究(Ⅳ)——Isosarcophytol—A前体化合物的合成

Isosarcophytol-A(1)是1982年首次从澳大利亚软珊瑚(Nephthea brassica)中分离鉴定的西松烷型(Cembrane)大环二萜类化合物,其结构为6,10,14-三甲基-3-异丙基-3E,5E,9E,13E-环十四碳四烯-1-醇,是Sarcophytol—A(2)的异构体,但有关1的生物活性试验和全合成研究尚未见报道.我们在前文报道了以低价钛诱导的分子内二羰基偶联为环化方法,完成了天然大环二萜类化合物Cembrene—C的全合成和Sarcophytol—A(2)苄醚衍生物(3)的合成.本文报道以天然法呢醇4为起始原料,经区域选择性氧化、羟醛缩合等六步反应,合成了1的前体化合物11.合成路线如下:     

反相高效液相色谱法半制备分离[T(4-MOP)PS4]卟啉的研究

本文研究了新水溶性５，１０，１５，２０－四（４－甲氧基－３－磺酸苯基）卟啉［Ｔ（４－ＭＯＰ）ＰＳ４］的反相高效液相色谱（ＨＰＬＣ）分离条件。采用ＳｈｉｍｐａｃｋＰＲＥＰ－ＯＤＳ半制备色谱柱，用含有１０ｍｍｏｌ／Ｌ四乙基碘化铵的乙腈－水（体积比２５：７５）为流动相，流速１８ｍＬ／ｍｉｎ，于４１８ｎｍ波长下检测。［Ｔ（４－ＭＯＰ）ＰＳ４］与合成中生成的杂质组分完全分离。经此制备的卟啉纯度高，已成功地应用于自来水样中微量钴、锌、铜离子的ＨＰＬＣ测定中。     

On a characterization of the normal distribution by means of identically distributed linear forms

Let X₁, X₂,…, be independent, identically distributed random variables. Suppose that the linear forms L₁ = Σ_j=1^∞a_jX_j and L₂ = Σ_j=1^∞b_jX_j exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X₁ is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L₁ and L₂ have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions.     

从蓖麻油制取10-羟基癸酸的研究

本文报道了从蓖麻油制取10-羟基癸酸的研究,发现了从蓖麻油制取10-羟基癸酸的新的工艺路线和最佳的工艺条件,用氢氧化钠用量、2-辛醇量、反应时间和反应温度四因子三水平L_9(3~4)进行了正交试验,发现最佳工艺条件是:氢氧化钠(g)/蓖麻油(g):1.25:2-辛醇量(g)/蓖麻油(g):2:反应时间:6h;反应温度:180℃。在这一新的工艺路线和最佳工艺条件下,10-羟基癸酸产率可达75％。     

Das asymptotische Verhalten der Peanokerne einiger interpolatorischer Quadraturverfahren

Summary Interpolatory quadrature formulae consist in replacing by wherep _f denotes the interpolating polynomial off with respect to a certain knot setX. The remainder may in many cases be written as wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP _X (t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis.

     

Regressions and monotone chains II: The poset of integer intervals

A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x ₁<...ksuch that (x ₁)...(x_k). Let P _nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P _nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x ^t(x,j–1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) < f(K) <t( + _k, k) , where _k 0 as k. Alternatively, the largest k such that every regression on P _nis guaranteed to have a monotone k-chain lies between lg^*(n) and lg^*(n)–2, inclusive, where lg^*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element.     

Some inequalities for partial orders

We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most maximal chains, if some antichain has cardinality v, and if there are ₁ chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ₁v (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).This paper was written while the authors were visitors at the Laboratoire d'algèbre ordinale, Département de Mathématiques, Université Claude Bernard, Lyon 1, France.Research supported by NSERC grant # A5198.     

The fixed point property in ordered sets of width two

We consider the fixed point property (FPP) in an ordered set of width two (every antichain contains at most two elements). The necessary condition of the FPP and a number of equivalent conditions to the FPP in such sets is established. The product theorem is proved, as well.     

Estimation of density functions by order statistics

The properties of the empirical density function,f _n(x) = k/n( _j ⁺ – _j-1 ⁺ ) if _j-1 ⁺ < x ⁺ where _j-1 ⁺ and _j ⁺ are sample elements and there are exactlyk – 1 sample elements between them, are studied in that practical point of view how to choose a suitablek for a good estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions.