非减次矩阵的标准形及其应用

给出了非减次矩阵的概念及其在相似变换下的标准形,研究了非减次矩阵的一些性质和应用.     

Spectral Characterizations of Veronese Surface in S^4

In this paper,we prove that the Veronese surface can be determined by the 1-spectrum of the Laplace operator.     

极小旋转曲面的生成曲线

用分析的方法导出了极小旋转曲面的生成曲线的方程。     

从换路定律证明看扩充实数的必要性

指出了在电路分析课程中换路定律证明方面存在的矛盾,证明矛盾的根源在于实数的完备性,并依此说明了建立广义实数概念的必要性.     

Results on energies for trees with a given diameter having perfect matching

Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd+1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd+1.It can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] + 1 q2d 33 1.     

黎曼流形上具有平行平均曲率的2-调和子流形

研究黎曼流形上具有平行平均曲率向量的2-调和子流形.     

丁广义割圆序列的线性复杂度

Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.     

普里姆（Prim）算法另解

在《数据结构》有关图的章节中,对最小生成树两大算法的解释都是基于MST性质来说明的。由于MST性质每次是选取原图集中值最小两栖边来构造最小生成树,这个过程较为复杂,现可以反其道而行之,采用“破圈法”——每次删除权值最大的边,来产生最小生成树,过程简洁、结果相同,同时可以证明其正确性,不失为一好算法。     

关联规则中一种负增量更新算法的探讨

针对关联规则负增量更新的挖掘问题,提出了一种高效的关联规则负增量更新算法,即NIUA。该算法充分利用原数据库中已有的频繁项集、所有1-项集来生成最小非频繁项集;并采用选样等策略求出删减数据后的频繁项集。整个算法只需扫描删减后的事务数据库一遍,从而提高了关联规则的更新效率。     

HP3中共形极小曲面的几何

通过扭映射π：CP⁷→HP³构造出HP³中曲率为4/7,4/19,4/27的6个共形极小二维球面的例子.由于扭映射π：CP²ⁿ⁺¹→HPⁿ给出了CP²ⁿ⁺¹的水平极小曲面与HPⁿ中极小曲面的一个自然等同,利用Bolton等得出的在CPⁿ中常曲率共形极小二维球面的结论,根据CHEN Xiaodong和JIAO Xiaoxiang给出的HPⁿ中常曲率共形极小二维球面的一般方法,构造出HPⁿ中的共形极小曲面的例子.