Minimal clones generated by majority operations

The minimal majority functions of the four-element set are determined. Received October 10, 1997; accepted in final form February 8, 2000.     

Some universal properties of the category of clones

In [6], O. C. García and W. Taylor asked if the breadth of the lattice of interpretability types of varieties is uncountable. The present paper solves the problem by two different constructions. Both of them show that any cardinal number is the cardinality of an antichain in the named lattice and that the existence of a proper class antichain is equivalent to the negation of Vopěnka's principle. The first construction gives in a way a minimal solution of the problem, whereas the second one gives stronger results about the category of clones. Received November 12, 1999; accepted in final form June 19, 2001.     

On Boolean primitive positive clones

Kuznecov introduced the concept of primitive positive clones and proved in 1977 that there are 25 Boolean primitive positive clones in a notoriously unavailable article. This paper presents a new proof of his result, relating it to Post's lattice and exhibiting finite bases for those clones.     

Clones in matroids representable over a prime field

We show that for every prime number $p$, a 3-connected non-uniform $GF\left(p\right)$-representable matroid can have a clone set of size at most $p?2$.     

黑杨派新无性系研究——Ⅳ.树冠结构与生长的关系

<正>本文分别讨论了Ⅰ-69杨×小叶杨和Ⅰ-69杨×欧洲黑杨F_1无性系树冠结构各组成部分与生长的表型和遗传相关;利用通径分析具体剖析这种相关的直接和间接作用,确立不同F_1无性系的理想冠型;并据此计算生长选择指数,比较各种性状组合的选择效果。利用一个最合理的选择指数式对各无性系的生长进行预测,结果表明,通过苗期测定选出的几个优良无性系之所以能保持速生特性,是因为具有较为合理的树冠结构。     

黑杨派新无性系研究——Ⅴ.树冠结构与干形改良

<正>本文分析了Ⅰ-69杨×小叶杨和Ⅰ-69杨×欧洲黑杨F_1无性系干形性状的遗传变异度,结果表明对干形实行直接选择是可行的。为了充分挖掘干形改良的遗传潜力和为多世代育种提供理论依据,探讨了从树冠结构方面对干形实行间接选择的可能性。遗传相关分析提供了树冠各组成性状与干形的联系情况,通径分析具体剖析了它们的直接和间接作用,确立各F_1无性系干形改良的理想冠型。在比较不同性状组合的干形选择指数效果基础上,利用一个合理的选择式预测了各F_1无性系的干形。将干形选择效果与生长选择效果进行比较,具体评述了生长与干形同时进行改良的可能性。     

日本落叶松无性系木材组织比量的遗传变异

对10个10年生的日本落叶松无性系木材组织比量进行了测定,结果表明,无性系间木射线比量、树脂道比量和管胞比量差异极显著。日本落叶松组织比量的径向变异规律为:管胞比量由髓心向外,前期变化曲线呈“梯形”,后期变化曲线呈“V”型;木射线比量由髓心向外,开始迅速下降,到第2年轮后缓慢波动下降或上升;树脂道比量由髓心向外,开始缓慢下降,然后迅速上升达最大值后又迅速下降。木射线比量与树木年轮间的变异模式(径向变异)以双曲线和乘幂式方程拟合效果较好,R2均在0.7以上;树脂道比量与树木年轮间的变异模式(径向变异)以指数式方程拟合效果较好,R2为0.609;管胞比量与树木年轮间的变异模式(径向变异)以三次多项式方程拟合效果较好,R2为0.845。日本落叶松的木射线比量、树脂道比量、管胞比量与树高、形率、冠幅、皮厚、主枝粗、枝干比、主枝夹角的相关关系不显著;木射线比量与主枝长显著负相关;木射线比量、树脂道比量与管胞比量之间的相关显著。木射线比量、树脂道比量和管胞比量都受到中等水平的遗传控制,无性系重复力分别是:0.571、0.453和0.607。按照20%的选择率,日本落叶松木射线比量、树脂道比量的遗传增益为16.70%和207.72%。     

杉木无性系结实系数的遗传变异

以杉木无性系着生球果的树冠表面积占树冠总表面积的比例为结实系数，对安徽、福建，广东三省的73个杉木种子园无性系进行了结实遗传变异的研究，结果表明，杉木性系间结实系数差异极显，主差分量达33．48％－61．05％，对结实系数重复力估算得出单株为0．335－0．611，无性系为0．602－0．825，说明结实系数指标受中上等遗传控制，利用结实系数作为评价实性状的指标，可有效地进行无性系再选择。     

Binary Relations and Permutation Groups

We discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed and essentially unique. Thus, we obtain the surprising result that on such sets, logic with three variables is as powerful in expression as full first order logic.