共查询到20条相似文献,搜索用时 109 毫秒
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《数学的实践与认识》2020,(13)
为了给物理学中的动力学行为研究提供依据,更好解释一些物理现象.首先使用分数阶复变换将时空-分数阶MKdV-ZK方程转换为非线性常微分方程组,其次使用除法定理寻求常微分方程组的首次积分,最后使用首次积分求解出原方程的许多精确解,得到了时空-分数阶MKdV-ZK方程的新精确解.数值结果表明首次积分法是有效的,该方法具有简单便捷等优点. 相似文献
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Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程, 再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组, 求解非线性代数方程组就能直接得到非线性偏微分方程的行波解.对Davey-Stewartson方程应用这种方法, 得到了该方程的精确行波解.同时也得到了该方程的一个Backlund变换.所得结果与首次积分法的结果作了比较.Riccati-Bernoulli辅助常微分方程方法是一种简单、有效地求解非线性偏微分方程精确解的方法. 相似文献
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仿样有限条法(spline finite strip method)是分析等截面结构最流行的数值方法之一.在以往的研究中,与一些基准问题的解析结果相比较,论证了该方法数值结果的有效性和收敛性,但至今未对该方法的精确解和显式误差项进行过数学推导,解析地论证过其收敛性.该文在对平板的分析中,使用酉变换(简称U变换)逼近法,导出了仿样有限条法精确的数学解,这是首次在公开文献中给出的精确解.和常规的仿样有限条法相比较,总矩阵方程的集成及其数值解都不同,U变换法的总矩阵方程,减少为仅含有2个未知量的方程,然后导出仿样有限条法显式的精确解.精确解按Taylor级数展开,导出误差项和收敛率,并和其他数值方法直接比较.在这一点上可以发现,仿样有限条法收敛速度和非协调有限元相同时,包含的未知量少得多,收敛率比常规的有限差分法快得多. 相似文献
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本文主要研究了一类高阶周期系数线性微分方程解的超级,e-型级,相关性等问题,并得到了e-型级与超级之间的一些关系,以及这两种级与系数的精确关系.本文是首次使用e-型级来估计方程解的增长性,这种估计比级,超级更为精确. 相似文献
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首次用解析的方式给出了Euler-Bernoulli梁后屈曲与非线性弯曲问题的高阶二次摄动解答.假定梁的中线不可伸长,用精确曲率公式与能量变分原理导出了非线性Euler-Bernoulli梁的模型.通过与精确解或高阶摄动解的比较,讨论了二次摄动解答的收敛性及适用域.得到主要结论如下:低阶摄动解适用于描述梁的初始后屈曲阶段及初始非线性弯曲阶段;更高阶次的摄动解适用于描述梁的深度后屈曲以及深度非线性弯曲.从这个意义上去说,该文不仅仅指出某些文献上的部分结果不精确是由于摄动解答超出了其特定的适用域,并且还进一步发展与完善了二次摄动法. 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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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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《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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Juan Elias 《Transactions of the American Mathematical Society》1999,351(10):4027-4042
For a dimensional Cohen-Macaulay local ring we study the depth of the associated graded ring of with respect to an -primary ideal in terms of the Vallabrega-Valla conditions and the length of , where is a minimal reduction of and . As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to -primary ideals. We also study the growth of the Hilbert function.
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