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Measure-theoretic entropy for flows 总被引:2,自引:0,他引:2
Wenxiang Sun 《中国科学A辑(英文版)》1997,40(7):725-731
New definitions of measure-theoretic entropy for flows are given and the invariant property of the entropy under conjugacy
is discussed.
Project supported by China Postdoctoral Funds. 相似文献
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求根问题在计算机图形学、机器人技术、地磁导航等领域应用广泛。基于重新参数化方法(reparamaterization-based method,RBM),给出了用于计算给定光滑函数在某区间内唯一实根的渐进式显式公式。给定光滑函数f (t ),用有理多项式Ai (s )对曲线C (t )=(t ,f (t ))进行插值,得到重新参数化函数t =?i (s ),使得Ai (sj )=C (?i (sj ))。提出了基于重新参数化函数?i (s )的显式公式用于渐进式逼近f (t )对应的实根,在n 个函数计算的成本下,收敛阶可达到3·2n -2,其中n ≥3。与类牛顿法相比,本文方法提高了计算稳定性,且收敛速度更快、计算效率更高。与裁剪法相比,本文方法不需要求解包围多项式,且可用于非多项式函数计算,计算效率更高。数值实例表明,每增加一个插值点,逼近阶可提高一倍,且可获得较传统裁剪法更高的计算效率。 相似文献
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Many works have investigated the problem of reparameterizing rational B~zier curves or surfaces via MSbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after MSbius transfor- mation. What's more the users of computer aided design softwares may require some guidelines for designing rational B6zier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway. The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational B6zier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal para- metric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational B6zier surfaces with compact derivative bounds. 相似文献
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Many works have investigated the problem of reparameterizing rational Bézier curves or surfaces via Mbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after Mbius transformation. What's more the users of computer aided design softwares may require some guidelines for designing rational Bézier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway.The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational Bézier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal parametric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational Bézier surfaces with compact derivative bounds. 相似文献
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A. Yu. Morozov 《Theoretical and Mathematical Physics》2008,157(2):1542-1549
We briefly review basic formulas of the Hamiltonian formalism in classical mechanics in the case where the Lagrangian contains
N time derivatives of n coordinate variables. For nonlocal models, N = ∞.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 208–216, November, 2008. 相似文献
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In this paper the amalgamation of (I+1)×J tables under consistent significance is considered and the sufficient condition is obtained. The sufficient and necessary conditions are given to avoid the famous paradoxes "YAP" and "YRP". A practical algorithm is given to compute the critical value when pooling tables with odds ratio less than 1. 相似文献
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