生成Fibonacci数列的一个符号算法

本文基于牛顿迭代原理,提出一个生成Fibonacci数列的符号算法。文中对算法的导出进行了证明,最后对广义Fibonacci数列进行了讨论。

Molecular Phylogeny of the Lardizabalaceae Based on TrnL-F Sequences and Combined Chloroplast Data

The molecular phylogeny of the Lardizabalaceae is reconstructed based on chloroplast trn L_F sequences alone and combined trn L_F and rbc L sequences. The phylogenetic topologies agree well with Qin's and Takhtajan's tribal classification in both analyses. Decaisneae and Sinofranchetieae are basal clades in the phylogenetic trees and external to all other taxa in the family. Lardizabaleae consisting of Boquila and Lardizabala are well supported in both trn L_F (100%) analysis and trn L_F and rbc L combined analysis (99%). Tribe Akebieae are strongly supported by a bootstrap value of 100% in both trn L_F analysis and trn L_F and rbc L combined analysis. However, the new genus Archakebia is nested within the genus Akebia in the trn L_F trees. In the combined trees, Archakebia is sister to Akebia with high bootstrap support. The inter_relationships among three closely related genera Parvatia , Holboellia and Stauntonia are still problematic. P. brunoniana ssp. elliptica is sister to H. latifolia in both analyses with low bootstrap support. H. parviflora is nested within the Stauntonia and sister to S. cavalerieana . Therefore, these three genera of tribe Akebieae may not be monophylytic and their generic boundary and delimitation need to be further studied, by exploring more molecular data, together with more morphological characters.

高等数学:辩证法的渊薮(续)——例谈高等数学中的普遍联系

通过实例阐述高等数学不同领域知识间的多形式、多方面的相互制约、作用和影响,说明了整个高等数学虽然门类繁多,界限分明,但却是一个普遍联系的统一整体.

玄妙的自然节律——黄金分割律与人类生活

自然界充满数学的模式。将一条线段分成两部分,使两段的比值为(√5-1)÷2≈0.618,这种分法为“黄金分割”,分割点为“黄金点”,0.618为“黄金数”。它最早由古希腊毕达哥拉斯学派发现;被古希腊美学家柏拉图誉为“黄金分割律”,并断言:宇宙万物,凡符合黄金分割律的,总是最美的形体。

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.