关于Fibonacci数列的两点注记

注记给出了Fibonacci数列两个重要公式的组合表达式,以及Fibonacci数与级数有关的两个新结果。     

一个快速的二进制多重精度gcd算法

求两个整数的最大公因子（gcd)的经典的Euclid算法时间复杂度为O（ln^3n)，不适宜于多重精度运算。论文证明了gcd的相关性质，提出了一个基于二进制的、适用于多重精度运算的改进算法，其时间复杂度为O（ln^2n)。     

RECONSTRUCTION OF BINARY RELATIONS FROM THEIR RESTRICTIONS OF CARDINALITY 2, 3, 4 and (n - 1) II

We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and (n - 1). This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2-, 3- and 4-hypomorphic. As a corollary we obtain that any binary relation is (n - 4)-reconstructible (when n > 9).     

二元光学波面变形器件的研究

基于计算全息原理设计了二元光学波面变形器件，一块二元光学器件的衍射效率比计算全息可提高４倍，高斯波面整形需要二块整形光学器件，二元光学器件的激光利用率比计算全息提高１６倍，而且制做工艺简单．     

多目标最优化的一种积分型实现算法

在文[1]中给出了求解多目标最优化的一种积分总极值的概念性算法．本文利用数论中的一致分布佳点集列，较为简便的得出了多目标最优化的积分总极值的实现算法和算法终止准则．并经过有关函数数值计算表明该算法是有效的，可用来求解多目标最优化问题的有效解．     

Artinian level modules and cancellable sequences

In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain artinian modules. As in the case of algebras a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences involving Macaulay representations.     

C_nP_4~4(n=1～7)团簇结构与能量的密度泛函研究

使用分子图形软件设计出多种CnP-4(n =1～ 7)的结构模型 ,并进行B3LYP密度泛函几何构型优化和振动频率计算 .最稳定的CP-4和C2 P-3 都是平面环状结构 .最稳定的CnP-4(n =3 ,5 ,7)结构在直碳链的一端连接 1个磷原子且另一端是P3 C的四元环的平面结构 .最稳定的CnP-4(n =4,6)结构在直碳链的一端连接 1个磷原子且另一端是P3 的三元环的锄状结构 .直碳链可与平面环的磷原子生成大π键 .大多数构型是由C2 ,C3 ,C4子结构以环状或链状方式组成的 .碳原子与磷原子以交替方式排列的结构数量少、能量高 .     

半参数回归模型估计的平均相合性

在误差序列为Lqmixingale情形下，给出了半参数回归模型中β和g(t)估计，研究了估计量的q阶平均相合性在较一般的条件下，得到了理想的结果     

Almost strongly regular matrices and a core theorem for double sequences

The idea of almost convergence for double sequences was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283-294] and they also characterized the four dimensional strong regular matrices. In this paper we define and characterize the almost strongly regular matrices for double sequences and apply these matrices to establish a core theorem.