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1974年,Neal根据Kac和Siegert的思想,给出了一个在电子工程、海洋工程、建筑工程、航空工程、自动控制的随机振动中有重要应用的二阶Volterra非线性系统对平稳正态输入的统计响应的表示定理.1984年,Naess对此定理又给出了一个数学证明.经过研究后发现,他们对定理条件的叙述都是模糊的,而且其数学证明都是有问题的.本文重新讨论了这个表示定理,给出了明确的定理条件及严格的数学证明,为它的广泛应用奠定了理论基础. 相似文献
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In this paper we obtain a linear predictor and its error for a multidimensional,discrete parameter, full-rank and regular stationary stochastic process (S.P.) having a spectral density matrix f(λ), which mets some conditions. An example which shows that Szeg(?)-Kolmogorov's Theorem for the prediction error with lag 1 in terms f(λ): (1) ean't be formally kept true in matrix form is given. 相似文献
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关于量子力学基础的一个质疑 总被引:1,自引:3,他引:1
本文对量子力学的基础提出了质疑,以一个常见的例子说明量予力学三个基本假设是不相容的. 相似文献
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《工科数学》九五年第一期《随机向量独立性的一个充要条件)一中提出了一个不需要通过求边缘密度函数即可判定连续型随机向量独立性的一个充要条件,即如下的定理。 相似文献
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Starting from Voe Neumann's axiomatic system of quantum mechanics, this paper calculates the probability distributions of the kinetic and potential energy of the one-dimensional harmonic oscillator and the particle in one-dimonsional infinitely deep square potential well. The results are compared with the classical cases, and it is shown that their relation conforms to Bohr's correspondence principle.Then we put forward a new viewpoint:it seems that the concept of the total energy of the particle in quantum mechanics should be deliberated again; the two basic hypotheses in quantum mechanics--"Bohr's probabilistic interpretation" and "the postulate that the particle's energy eguals the eigenvalue in the energy eigenstate" ars not logically harmonious. At the same time, the limitation of von Neumann's axiomatic system is pointed out. 相似文献
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本文指出用概率方法与用泛函方法定义量子力学中“可观察量在态中的平均值”是有区别的,而唯一正确的方法应为采用概率的方法从而澄清了绝大多数量子力学文献中对于“平均值”概念的某些误解 相似文献
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Starting from Voe Neumann's axiomatic system of quantum mechanics, this paper calculates the probability distributions of the kinetic and potential energy of the one-dimensional harmonic oscillator and the particle in one-dimensional infinitely deep square potential well. The results are compared with the classical cases, and it is shown that their relation conforms to Bohr's correspondence principle. Then we put forward a new viewpoint: it seems that the concept of the total energy of the particle in quantum mechanics should be deliberated again; the two basic hypotheses in quantum mechanics-"Bohr's probabilistic interpretation" and "the postulate that the particle's energy eguals the eigenvalue in the energy eigenstate" ars not logically harmonious. At the sametime, the limitation of von Neumann's axiomatic system is pointed out. 相似文献
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In this pape we obtain a linear predictor and its error for a multidimensional, discrete parameter, full-rank and regular stationary stochastic process (S. P.) having a spectral density matrix f(λ), which mets some conditions. An example which shows that Szego-Kolmogorov's Theorem for the prediction error with lag l in terms f(λ):σ12=2πexp{1/(2π)∫-xxlogf(λ)dλ},(1) can't be formally kept true in matrix form is given. 相似文献