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1.
Complete and partial diallel cross designs are examined as to their construction and robustness against the loss of a block of observations. A simple generalized inverse is found for the information matrix of the line effects, which allows evaluation of expressions for the variances of the line-effect differences with and without the missing block. A-efficiencies, based on average variances of the elementary contrasts of the line-effects, suggest that these designs are fairly robust. The loss of efficiency is generally less than 10%, but it is shown that specific comparisons might suffer a loss of efficiency of as much as 40%.  相似文献   
2.
本文借助于SU(1.1)代数找出了二维氢原子与二维谐振子的能量本征值。能基本征态、角动量以及能级简并度间的关系.  相似文献   
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Several procedures have been proposed for testing the hypothesis that all off-diagonal elements of the correlation matrix of a multivariate normal distribution are equal. If the hypothesis of equal correlation can be accepted, it is then of interest to estimate and perhaps test hypotheses for the common correlation. In this paper, two versions of five different test statistics are compared via simulation in terms of adequacy of the normal approximation, coverage probabilities of confidence intervals, control of Type I error, and power. The results indicate that two test statistics based on the average of the Fisher z-transforms of the sample correlations should be used in most cases. A statistic based on the sample eigenvalues also gives reasonable results for confidence intervals and lower-tailed tests.  相似文献   
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通过分析左定与右定问题的关系,应用谱曲线和高阶右定问题的谱,研究了一类高阶左定问题谱的特性及谱对给定参数的可微性.  相似文献   
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In this paper we study the sampling properties of a test statistic which has important applications in the area of linear stochastic control systems with multi-inputs and multi-outputs. The statistic is the ratio of a partial sum of the eigenvalues of a sample covariance matrix and its trace. It turns out that using a method due to Sugiura we may derive a useful approximation for its distribution up to and including terms of order l/n, where n denotes the appropriate size. Numerical illustrations using real data are given.  相似文献   
6.
A new method for constructing interpretable principal components is proposed. The method first clusters the variables, and then interpretable (sparse) components are constructed from the correlation matrices of the clustered variables. For the first step of the method, a new weighted-variances method for clustering variables is proposed. It reflects the nature of the problem that the interpretable components should maximize the explained variance and thus provide sparse dimension reduction. An important feature of the new clustering procedure is that the optimal number of clusters (and components) can be determined in a non-subjective manner. The new method is illustrated using well-known simulated and real data sets. It clearly outperforms many existing methods for sparse principal component analysis in terms of both explained variance and sparseness.  相似文献   
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研究了一类微分方程系统解的渐近行为和零解的稳定性问题;讨论了利用特征值的符号及运用解对初值的连续依赖性和一些变换算法,该算法优点是不需求出解的解析表达式,就能判断方程解的渐近行为和零解的稳定性态,其推理过程较清晰严密并有一定的参考价值。  相似文献   
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The Craig-Sakamoto theorem establishes a sufficient and necessary condition for the independence of two quadratic forms in normal variates, fascinating many statisticians and mathematicians, who continuously seek for simple and better proofs of the theorem and its extensions. In this article, we present a simple proof of a unified theorem on the independence of linear and quadratic functions in general normal variates.  相似文献   
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