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给出了有重复组合公式(r n+r-1)的四种证明方法,从不同的角度阐释了对这个公式的理解,且给出了两个应用例子,其中一个是关于偏导数的问题.此将对学生的学习有所帮助. 相似文献
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一个组合数恒等式的再推广 总被引:1,自引:0,他引:1
初等数学研究是提高数学教育工作者和对数学教育有浓厚兴趣读者的数学素养和数学水平 ,开阔眼界 ,活跃思想的一个组成部分 ,这方面的文章也深受一部分读者的喜爱 .因受本刊篇幅的限制 ,经编委会讨论 ,我们开设了“初等数学研究集锦”栏目 ,以摘要形式发表这类来稿的研究结果 ,感兴趣的读者可来稿向编辑部索取全文或与作者联系探讨 相似文献
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在学习排列组合时。我们往往会形成一种思维定式,拿起问题就开始用组合数,而没有把问题想清楚.实际上,组合数只是一个工具,我们不能过分依赖工具,而忘记本质.下面就一道例题介绍几种新解. 相似文献
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关于组合数的一项性质 总被引:8,自引:3,他引:5
对于∑ni =0(- 1 ) iCin =0相信大家都很熟悉 ,但笔者发现 ,该式可推广成 ∑ni=0ik(- 1 ) iCin =0 (k≤n - 1且k∈N) .证明 (1 )当n=2时 ,k=1左边 =∑2i=0i(- 1 ) iCi2 =- 2 2 =0 =右边等式成立 .(2 )假设当n=t时 ,对于 1≤k≤t- 1 k∈N等式均成立 ,那么当n=t 1时 :左边 =∑t 1i=0ik(- 1 ) iCit 1=∑t 1i=1ik(- 1 ) it 1i Ci- 1 t 0=- (t 1 ) ∑tj=0(j 1 ) k- 1 · (- 1 ) jCjt(令j =i- 1 )=- (t 1 ) ∑tj=0(∑k-1u =0(Cuk- 1 ·ju)·(- 1 ) jCjt=- (t… 相似文献
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在贝努里(Bemoulli)试验中,事件A发生的概率为p,若以ξ记A首次出现时所需的试验次数,则ξ是随机变量,它的所有可能取值为1,2,3,…,n,…,且概率函数为 相似文献
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Rodica Brânzei Giulio Ferrari Vito Fragnelli Stef Tijs 《Annals of Operations Research》2002,109(1-4):359-374
This paper concentrates on cost sharing situations which arise when delayed joint projects involve joint delay costs. The problem here is to determine fair shares for each of the agents who contribute to the delay of the project such that the total delay cost is cleared. We focus on the evaluation of the responsibility of each agent in delaying the project based on the activity graph representation of the project and then on solving the important problem of the delay cost sharing among the agents involved. Two approaches, both rooted in cooperative game theory methods are presented as possible solutions. In the first approach delay cost sharing rules are introduced which are based on the delay of the project and on the individual delays of the agents who perform activities. This approach is inspired by the bankruptcy and taxation literature and leads to five rules: the (truncated) proportional rule, the (truncated) constrained equal reduction rule and the constrained equal contribution rule. By introducing two coalitional games related to delay cost sharing problems, which we call the pessimistic delay game and the optimistic delay game, also game theoretical solutions as the Shapley value, the nucleolus and the -value generate delay cost sharing rules. In the second approach the delays of the relevant paths in the activity graph together with the delay of the project play a role. A two-stage solution is proposed. The first stage can be seen as a game between paths, where the delay cost of the project has to be allocated to the paths. Here serial cost sharing methods play a role. In the second stage the allocated costs of each path are divided proportionally to the individual delays among the activities in the path. 相似文献
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Juliana Bueno-Soler 《Logica Universalis》2010,4(1):137-160
In this paper we extend the anodic systems introduced in Bueno-Soler (J Appl Non Class Logics 19(3):291–310, 2009) by adding certain paraconsistent axioms based on
the so called logics of formal inconsistency, introduced in Carnielli et al. (Handbook of philosophical logic, Springer, Amsterdam, 2007), and define the classes of systems
that we call cathodic. These classes consist of modal paraconsistent systems, an approach which permits us to treat with certain kinds of conflicting
situations. Our interest in this paper is to show that such systems can be semantically characterized in two different ways:
by Kripke-style semantics and by modal possible-translations semantics. Such results are inspired in some universal constructions in logic, in the sense that cathodic systems can be seen as a
kind of fusion (a particular case of fibring) between modal logics and non-modal logics, as discussed in Carnielli et al.
(Analysis and synthesis of logics, Springer, Amsterdam, 2007). The outcome is inherently within the spirit of universal logic,
as our systems semantically intermingles modal logics, paraconsistent logics and many-valued logics, defining new blends of
logics whose relevance we intend to show. 相似文献
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Catherine Rainer 《Applied Mathematics and Optimization》2007,56(1):131-144
We make the link between two approaches to Nash equilibria for nonzero-sum stochastic differential games: the first one using
backward stochastic differential equations and the second one using strategies with delay. We prove that, when both exist,
the two notions of Nash equilibria coincide. 相似文献
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Siberian Mathematical Journal - We prove that the two approaches to describing homeomorphisms in modern quasiconformal analysis are equivalent: A homeomorphism changes under control the... 相似文献
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给出了一道曲线积分题目的六种解法,这有利于提高学生对综合运用数学知识的能力,同时也可以启发学生思维和开阔他们的思路. 相似文献
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T. B. Boffey E. D. Edmond A. I. Hinxman C. J. Pursglove 《The Journal of the Operational Research Society》1979,30(5):413-425
The development of an interactive computer program and a heuristic optimising model for scheduling container ships on the North Atlantic is described. The constraints and multiple objective criteria governing these schedules are discussed and sample results of both approaches given. 相似文献