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关于协方差、相关系数与相关性的关系 总被引:12,自引:1,他引:11
本文利用最小二乘法,导出了协方差与相关系数这两个概念的由来,说明了人们总是用相关系数而不用协方差来判断两个随机变量线性相关程度的原因,阐明了两个普通变量与两个随机变量存在线性关系时,它们的根本区别,并用直观图形展示了两个随机变量线性相关的概率意义。 相似文献
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H. Legind Larsen 《BIT Numerical Mathematics》1983,23(3):303-307
As a modification of a system earlier developed by Selmer, this note describes a system for checking decimal numerals by using two modulus 11 check digits. In addition to the error detection obtained by using one check digit, this system achieves full detection of errors of the following types: wrong digit in two arbitrary positions, and transposition of two 2-digit component numerals. 相似文献
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Terje O. Espelid 《BIT Numerical Mathematics》2003,43(2):319-337
In this paper we test two recently published Matlab codes, adaptsim and adaptlob, using both a Lyness–Kaganove test and a battery type of test. Furthermore we modify these two codes using sequences of null rules in the error estimator with the intention to increase the reliability for both codes. In addition two new Matlab codes applying a locally and a globally adaptive strategy respectively are developed. These two new codes turn out to have very good properties both with respect to reliability and efficiency. Both algorithms are using sequences of null rules in their local error estimators. These error estimators allow us both to test if we are in the region of asymptotic behavior and thus increase reliability and to take advantage of the degree of precision of the basic quadrature rule. The new codes compare favorably to the two recently published adaptive codes both when we use a Lyness–Kaganove testing technique and by using a battery test. 相似文献
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The general solution of the non homogeneous matrix difference system is established in terms of two fundamental matrix solutions by using the variation of parameters formula. Uniqueness of solution to two point boundary value problem is established by using modified QR algorithm and Barterls—Stewart algorithm. 相似文献
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Catherine Rainer 《Applied Mathematics and Optimization》2007,56(1):131-144
We make the link between two approaches to Nash equilibria for nonzero-sum stochastic differential games: the first one using
backward stochastic differential equations and the second one using strategies with delay. We prove that, when both exist,
the two notions of Nash equilibria coincide. 相似文献
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介绍了一种求解TSP问题的算法改进的混合型蚁群算法,该算法在近邻法构造初始解的基础上,使用2-opt局部搜索法对当前解进行改进,在更新全局信息素时采用基于排序的蚂蚁系统对排在前2名的蚂蚁更新全局信息素,且为全局信息素设置最大值和最小值,并使用Matlab仿真求解了kroa200等13个经典tsp问题,得到的结果和最优解的误差很小,并和两种最新改进的蚁群算法以及两种自组织算法进行比较,比较结果充分证明了该改进算法的有效性. 相似文献
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《Mathematical and Computer Modelling》1995,21(9):49-54
A systematic methodology for risk assessment of environmental pollutants is outlined. The methodology, based on multivariate quantitative structure-activity modelling, consists of six consecutive steps which are reviewed and illustrated using two examples. The two examples discussed refer to polychlorinated dibenzofurans and halogenated aliphatic hydrocarbons. The benefits of using this approach based on multivariate data analysis and statistical experimental design is discussed. 相似文献
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In this paper, we first prove the strict quasi-concavity of maximizing functions, and next, using a generalization of the KKM theorem, we prove two maximum theorems without assuming the upper semicontinuity. As an application, using a common fixed point theorem, the existence theorem of social equilibrium is obtained. Finally, we shall give two illustrative examples of systems of constrained optimization problems. 相似文献
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研究具有巢寄生行为的两种群模型,两个种群都具有阶段结构.利用微分方程比较定理得到该系统持续生存的充分性条件,进一步利用Liapunov函数方法,证明了在适当的条件下,周期解及概周期解的全局渐近稳定性. 相似文献
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In this paper, both analytical and semi-analytical solutions for Green’s functions are obtained by using the image method which can be seen as a special case of method of fundamental solutions (MFS). The image method is employed to solve the Green’s function for the annular, eccentric and half-plane Laplace problems. In addition, an analytical solution is derived for the fixed-free annular case. For the half-plane problem with a circular hole and an eccentric annulus, semi-analytical solutions are both obtained by using the image concept after determining the strengths of two frozen image points and a free constant by matching boundary conditions. It is found that two frozen images terminated at the two focuses in the bipolar coordinates for the problems with two circular boundaries. A boundary value problem of an eccentric annulus without sources is also considered. Error distribution is plotted after comparing with the analytical solution derived by Lebedev et al. using the bipolar coordinates. The optimal locations for the source distribution in the MFS are also examined by using the image concept. It is observed that we should locate singularities on the two focuses to obtain better results in the MFS. Besides, whether the free constant is required or not in the MFS is also studied. The results are compared well with the analytical solutions. 相似文献
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A new computational method for solving two‐dimensional Stratonovich Volterra integral equation 下载免费PDF全文
This paper presents a method for computing numerical solutions of two‐dimensional Stratonovich Volterra integral equations using one‐dimensional modification of hat functions and two‐dimensional modification of hat functions. The problem is transformed to a linear system of algebraic equations using the operational matrix associated with one‐dimensional modification of hat functions and two‐dimensional modification of hat functions. The error analysis of the method is given. The method is computationally attractive, and applications are demonstrated by a numerical example. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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The dynamic behaviors of two beams connected by a joint with clearance are investigated. A new equivalent joint model using the transverse and torsion spring systems is developed to describe the dynamics of two jointed beams with clearance. Based on the finite element method (FEM), the equations of motion of the two jointed beams with clearance are established using Hamilton's principle. A modified numerical solution method is presented based on the Newmark integration method to solve the equations with the nonlinearity due to clearance. The contributions of the clearance size and stiffness on the amplitude-frequency response are discussed. The effects of the clearance on the vibration transfer between the two connected beams and the impact force of the joint are investigated. 相似文献