共查询到20条相似文献,搜索用时 93 毫秒
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表达一个判断的语句称为命题,命题是由题设和题断构成。证明一个命题成立,有直接证法和间接证法。反证法属于间接证法。一般来说,大多数命题的证明是由直接证法给出的,但是当直接证法不易证明甚至无法证明时,运用反证法,有时可以收到证明既简练又确切的良好效果。因此反证法是一种重要的证明方法。然而多年来,一些人有片面的认识,认为反 相似文献
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设△ABC三边长度BC=a,CA=b,AB=c,面积为△,并记s=1/2(a b c),则△=s(s-a)(s-b)(s-c)/~(1/2) (1)式就是众所周知的秦九韶—海伦公式.至于秦九韶一海伦公式的证明已有种种,这里再给出两种证法.其证法1,回避了一般考参书上所用的三角方法,连初二同学都能看懂的代数证法.其证法2乃是一种构思独特的解析证法. 证法1:如图所示,设∠B,∠C为锐角,作BC边上的高 相似文献
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In this paper,we obtain thorem 1 on volum of a n-dimensional simplex and theorem 2 on dihedral angles of a simplex.Besides.We obtain Vasic inequality in E^n and its extension.The results in this paper contain and improve the results in paper[1]、[2]、[3]、[4]. 相似文献
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复模糊数及其收敛性 总被引:6,自引:2,他引:4
毕淑娟 《数学的实践与认识》2007,37(1):126-132
在新的模糊数序关系意义下,将定义在所有实模糊数上的模糊距离推广到所有复模糊数集上的模糊距离.并以此为基础,定义了复模糊数列的极限,讨论了复模糊数列的保号性、有界性等收敛性质及C auchy收敛判别法等. 相似文献
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研究广义Birkhof自治系统的平衡稳定性问题·首先建立了广义Birkhof自治系统的平衡方程,然后研究平衡状态稳定性的一次近似方法和直接法,并应用Ляпунов定理得到了广义Birkhof自治系统平衡稳定性的一些结果·最后举例说明了这些结果的应用 相似文献
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重建极性连续统理论的基本定律和原理(Ⅹ)——主均衡定律 总被引:3,自引:1,他引:2
通过对诸主均衡定律和应用Noether定理得出的守恒定律进行比较,自然地导出微极连续统力学的1个统一的主均衡定律和6个物理上可能的均衡方程.其中,通过扩展众所周知和惯用的能量动量张量的概念,得到相当一般的定名为能量-动量的、能量-角动量的和能量-能量的守恒定律和均衡方程.显然,在这后3种情况下的主均衡定律中,物理场量是难以凭借直觉假定出来的.最后,作为特殊情形,直接推演出若干现有的结果. 相似文献
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Marilyn Breen 《Israel Journal of Mathematics》1972,11(4):347-348
It is possible to prove the following “Helly-type” thorem fork-almost-neighborly sets.
Theorem.A ⊆R
d is k-almost-neighborly if and only if every 2d+1 member subset of A is k-almost-neighborly. Moreover, if A ⊆bdry conv A, then A is k-almost-neighborly if and only if every 2d member subset of A is k-almost-neighborly. Each bound is best possible. 相似文献
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C.C. Tisdell 《International Journal of Mathematical Education in Science & Technology》2017,48(6):913-918
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using ‘exact methods’, illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth. 相似文献
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复变函数论中的多值函数教学是一个难点.钟玉泉先生的教材在这一难点的处理方面是较成功的.他通过例题,介绍多值函数分成单值分支的方法,介绍求函数值的方法,并对这些方法进行了总结,得出的结论是:当给定初值后,只有通过连续变化才能得到其它点的函数值.这一点和传统的代入法求函数值完全不同.然而该教材就在这一总结之后,又用代入法求Arcsin2.我们认为这自我否定了刚刚建立起来的求值方法,扰乱了读者的思想.本文通过对Arcsinz分成单值解析分支的讨论,对求Arcsin2提出了新的教材处理方案,以期和读者商榷. 相似文献
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Wolfgang Stadje 《Mathematische Nachrichten》2005,278(10):1209-1229
We consider several aspects of the relationship between a [0, 1]‐valued random variable X and the random sequence of digits given by its m‐ary expansion. We present results for three cases: (a) independent and identically distributed digit sequences; (b) random variables X with smooth densities; (c) stationary digit sequences. In the case of i.i.d. an integral limit thorem is proved which applies for example to relative frequencies, yielding asymptotic moment identities. We deal with occurrence probabilities of digit groups in the case that X has an analytic Lebesgue density. In the case of stationary digits we determine the distribution of X in terms of their transition functions. We study an associated [0, 1]‐valued Markov chain, in particular its ergodicity, and give conditions for the existence of stationary digit sequences with prespecified transition functions. It is shown that all probability measures induced on [0, 1] by such sequences are purely singular except for the uniform distribution. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献