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前n个自然数的方幂和,Σi=1 i^m(简称等幂和)是一个古老的难题。从著名的Euler-Machaurin定理出发,给出了任意一个等差列方幂和公式,更一般地得到了等幂和的计算公式。 相似文献
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等幂和与Bernoulli数的简捷方法 总被引:1,自引:0,他引:1
王云葵 《商丘师范学院学报》2000,16(4):53-56
自然数的方幂和:Sm(n)=Σk=1 K^m(简称等幂和)是一个古老的难题。它与著名的伯努利数有着密切的联系;利用数论方法获得了等幂和的简单递推公式和Bernoulli数的通解公式,得到了前107个等幂和公式及前106个Bernoulli数的值。 相似文献
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研究了自然数方幂和的生成函数的递推公式,并给出了方幂和新的计算公式,利用递推公式很容易得到幂和的计算,为计算机解题提供了依据。 相似文献
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汪显林 《中学数学教学参考》1996,(5)
在p进制下的方幂和与和方幂问题杨之在[1]中介绍了自然数在数码平方和与和平方变换下进入循环的问题,并提出问题:p进制下的m次方幂和与和方幂变换下有无类似性质?进而,在[2]中介绍了冯跃峰的结果,并预示p进制下可类似证明,并进而提出了p进制下的和方幂问... 相似文献
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张凤玲 《重庆职业技术学院学报》2008,17(4):108-111
文献[1]、[2]中曾通过判别矩阵△是幂零矩阵,文献[3]通过幂等矩阵对一般矩阵的方幂作出了讨论。本文通过三次幂等矩阵对矩阵方幂作出初步讨论,并同时指出文献[2]的两处疏漏,把文献[3]中的结果再推广一点。 相似文献
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关于计算前n个正整数的方幂和Sm(n)=∑km问题,一直是人们研究和讨论的一个热点问题.本文应用初等微积分的知识,首先给出一个十分有用的积分恒等式,然后借助于这个积分恒等式并且适当运用数学技巧,构造出一个新的结构简单,便于使用的计算方幂和Sm(n)的递推公式,最后利用这个递推公式递归地求出S1(n)到S10(n)的计算公式以及有关方幂和的几个平方关系式与乘积关系式. 相似文献
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运用算子论的方法,把有限维情况下幂等算子的和与差仍是幂等算子成立的一些条件推广到无限维的情况,给出了在无限维的情况下幂等算子的和与差仍是幂等算子的充要条件,并且进一步得到了幂等算子的线性组合也是幂等算子的充要条件。 相似文献
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关于计算前n个正整数的方幂和Sm(n)=∑k^m问题,一直是人们研究和讨论的一个热点问题.本文应用初等微积分的知识,首先给出一个十分有用的积分恒等式,然后借助于这个积分恒等式并且适当运用数学技巧,构造出一个新的结构简单,便于使用的计算方幂和Sm(n)的递推公式,最后利用这个递推公式递归地求出S1(n)到S10(n)的计算公式以及有关方幂和的几个平方关系式与乘积关系式. 相似文献
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《海外英语》2007,(5):10-11
Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help? 相似文献
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罗艳萍 《读与写:教育教学刊》2008,5(6)
The communication of people partially is the communication of cultures. Culture has a direct effect on international commercial activities in all aspects. Different conceptions about time, space, equality, law and the like, lead people to deal with things in different ways. So to know cultures of the counterpart is to facil-itate our enterprises so as to have a smooth and successful communication in commercial activity. 相似文献
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《海外英语》2007,(4):36
There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love. 相似文献
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Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject. 相似文献
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Richard Denner 《海外英语》2007,(4):14-15
Rosco and I wait for the fishermen to return.I sit at a wooden bench near the store at Mt.Baker Resort and watch the clouds change shape. Rosco has my belt around his neck and an eight foot tow chain hooked to a tree. Dogs must be on a leash. Ducks and rabbits are loose. 相似文献
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Given a graph G,a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and |C|≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as TC (G), is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K (G), is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F={G|K(G) is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus TC (G)/|G|≤1/2 for all G ∈ F. 相似文献
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Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities. 相似文献