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计算旋转体体积的一般积分公式 总被引:1,自引:0,他引:1
0引言本文首先讨论了平面曲线在直线上的投影长函数 ,平面曲线 (图形 )绕一共面直线旋转所得旋转体的体积函数 ,给出了它们的积分表示式 ,进而得出计算旋转体体积的一般积分公式。关于旋转体体积的计算问题 ,一般标准分析教材 [1,2 ] 中只讨论了平面图形绕坐标轴旋转所得旋转体的体积的积分公式 ,为了应用上的便利本文将其推广 ,给出平面图形绕任一共面直线旋转所得旋转体体积计算的一般积分公式。一般认为平面曲线是 (开 )直线段到平面内的一一的 ,双方连续的 ,在上映射的象[3] .在直线段a≤ t≤ b上引入坐标 t,在平面上引入笛卡尔直角坐标… 相似文献
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基于定积分的数值计算方法,解决了空间一般式曲线绕任意轴所形成的旋转体体积的近似计算问题,给出了相应的Matlab程序,并用两个实例进行说明. 相似文献
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对极坐标表示的面积绕轴旋转的体积计算问题分别从积分元素法、P.Guldin定理及球坐标下三重积分计算 ,给出三种计算方法 .本文不仅导出了一类旋转体体积的简单计算公式 ,而且其中的解题思想方法有助于学生提高解题能力和数学素养 . 相似文献
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F. J. Schuurmann P. R. Krishnaiah A. K. Chattopadhyay 《Journal of multivariate analysis》1973,3(4):445-453
In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed. 相似文献
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《European Journal of Operational Research》2005,161(2):377-385
The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model. 相似文献
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用常微分方程模型分析预防和隔离措施对SARS发病率的影响 总被引:2,自引:2,他引:0
通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 . 相似文献
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《Chaos, solitons, and fractals》2001,12(6):1101-1109
Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously. 相似文献
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Hans Jürgen Borchers 《Annales Henri Poincare》2002,3(1):1-17
The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m1 there is no gap in the spectrum which is larger than 2m1. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables. 相似文献
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Presented by A. F. Pixley. 相似文献
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For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues
denote by E(λi; T) the eigen-projection corresponding to an eigenvalue λi. In this paper we will show that if the operator sequence
is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators Tp and Tr: T = Tp + Tr, where Tp is the weak limit of Tn and Tr is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body. 相似文献
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A. G. Shukhov 《Mathematical Notes》1999,65(4):510-515
Let {
} be a sequence of finitely presented groups with generating setA={a1, …, am}, and letRk be the symmetrized set of words over the alphabetA∪A−1 obtained from the defining words and their inverses by all cyclic shifts. We shall assume that the words inRk are cyclically irreducible, and their lengths tend to ∞ ask increases. In the paper, it is proved that ifRk satisfies the small cancellation conditionC'(1/6) and the number of relators increases not very rapidly with increasingk, then the growth rate ψ(Gk) tends to 2m−1 ask→∞.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 611–617, April, 1999. 相似文献