面向横截面数据的灰色关联度

针对横截面数据的灰色关联度分析问题,研究了常用灰色关联度在横截面数据的适用性.提出具有放射变换保序性的灰色距离关联度,实例说明距离关联度的实用性与有效性.将灰色距离关联度推广到系统因素为矩阵的矩阵范数关联度,且在多属性群决策问题的成功应用证明了其合理性.     

一个点面距离问题的多角度审视

空间距离的求法是立体几何的重点和热点，由于两异面直线的距离、直线到平面的距离、两平行平面的距离都可以转化为点到平面的距离来解决，因此点面距离的求法必须掌握，下面通过2007年一道高考题多角度审视探求点面距离的常用方法．     

空间中的距离和角

1　空间中的距离1)对于空间距离 ,我们主要研究异面直线的距离、点到平面的距离、直线和平面的距离以及两个平行平面的距离 .其中核心问题是点到直线、点到平面的距离 .2 )对于点面、线面、面面距离的计算 ,既要掌握其概念 ,又要能进行它们之间的转化 ,还要能通过作辅助图形及应用解三角形的方法求出这些距离 .3)异面直线的距离的计算是一个难点 ,常用的方法有直接法、转化法、极值法等 .4 )体积法是求距离的一种间接方法 ,也是一种常用的方法 ,要注意灵活运用 .2　空间中的角1)空间中的角主要有 :异面直线所成的角、直线与平面所成的角以及…     

面面垂直——作角与距离的重要切入点

求点到平面的距离、直线和平面所成的角与二面角等是高考常考的主要问题之一,用综合法解答这些计算题的关键之一是要先准确作出所求的距离与角,而利用面面垂直作距离与角是常用方法和重要切入点之一.     

面面垂直——作角与距离的重要切入点

求点到平面的距离、直线和平面所成的角与二面角等是高考常考的主要问题之一,用综合法解答这些计算题的关键之一是要先准确作出所求的距离与角,而利用面面垂直作距离与角是常用方法和重要切入点之一.     

求空间的角与距离的最小化策略

求空间中直线与平面所成的角、二面角、点到直线的距离以及点到平面的距离有几种方法,其中最常用的有定义法、转化法和法向量法等.本着“回归自然,回归基础”的宗旨,经过研究,笔者发现了另外一种简捷可行的方法———最小化法,它借助于向量,运用最小化策略比较方便地解决了这类     

再入飞行器的最大飞行距离的似然比鉴定(Ⅰ)

当无验前信息可用时,本文导出了再入飞行器最大飞行距离的似然比检验统计量,由此构造出的置信区间优于由非中心t分布构造的对称截尾置信区间.最后,对两个常用的最大飞行距离的概率水平.0.95和0.99.以及对不同的子样数和置信水平,列出了构造这种似然比置信区间所需要的常系数,c_1和c_2的取值表.     

递推阻尼最小二乘法的收敛性与稳定性

递推最小二乘法是参数辨识中最常用的方法,但容易产生参数爆发现象,因此对一种更稳定的辨识方法－－递推阻尼最小二乘法进行了收敛特性的分析,在使用算法之前先旭一化测量向量,结果表明,参数化距离收敛于一个零均值随机变量并且在持续激励条件下,适应增益矩阵的条件数有界。参数化距离的方差有 。     

函数域中的L1范数堆积

讨论方体中的堆积(packing), 即如何在方体中放置n个点,使得它们之间的最短距离最大. 使用的距离是由L₁范数诱导出来的, 这正类似于纠错码中常用的Hamming距离. 利用函数域中关于除子类群等的研究成果, 给出了两个具有合理参数的堆积的构造方法, 同时还给出了这两个堆积的一些近似结果.     

再入飞行器的最大飞行距离的似然比鉴定（1）

当无验前信息可用时，本文导出了再入飞行器最大飞行距离的似然比检验统计量，由此构造出的置信区间优于由非中心ｔ分布构造的对称截尾置信区间。最后，对两个常用的最大飞行距离的概率水平，０．９５和０．９９。以及对不同的子样数和置信水平，列出了构造这种似然比置信区间所需要的常系数，ｃ１和ｃ２的取值表。     

Locally restricted colorings

We consider the following problem: given suitable integers χ and p, what is the smallest value ρ such that, for any graph G with chromatic number χ and any vertex coloring of G with at most χ+p colors, there is a vertex v such that at least χ different colors occur within distance ρ of v? Let ρ(χ,p) be this value; we show in particular that ρ(χ,p)?⌈p/2⌉+1 for all χ,p. We give the exact value of ρ when p=0 or χ?3, and (χ,p)=(4,1) or (4,2).     

An estimation method for the Neyman chi-square divergence with application to test of hypotheses

We propose a new definition of the Neyman chi-square divergence between distributions. Based on convexity properties and duality, this version of the χ² is well suited both for the classical applications of the χ² for the analysis of contingency tables and for the statistical tests in parametric models, for which it is advocated to be robust against outliers.We present two applications in testing. In the first one, we deal with goodness-of-fit tests for finite and infinite numbers of linear constraints; in the second one, we apply χ²-methodology to parametric testing against contamination.     

Limit distributions of the χ 2 statistic of K. Pearson in a sequence of independent trials

We study the χ ² statistic of K. Pearson in a sequence of independent and, generally, inhomogeneous trials with a fixed number of outcomes. It is assumed that the probabilities of occurrence of outcomes of the trials satisfy certain conditions. This problem statement embraces familiar results for the χ ² statistic in the case of multinomial trials. We obtain explicit expressions and estimates for the expectation and the variance of the χ ² statistic. For the χ ² statistic centered and normalized in a suitable way, we find limit distributions (the normal one, the distribution of the sum of the squares of normal random variables and, in particular, the χ ² distribution). Conditions for the convergence to the corresponding limit distributions are given.     

张量对称类上诱导算子的y-数值半径(英文)

本文研究了诱导矩阵K(A)的y-数值半径ry(K(A))、y-可分数值半径ryχ(K(A))与范数A2、广义矩阵函数dχG(A)之间的关系问题.利用ry(K(A))及ryχ(K(A))的概念,得到了ry(K(A))、ryχ(K(A))、‖A‖2、dGχ(A)它们之间的两个不等式.     

On the mean square average of special values of L-functions

Let χ be a Dirichlet character and L(s,χ) be its L-function. Using weighted averages of Gauss and Ramanujan sums, we find exact formulas involving Jordan?s and Euler?s totient function for the mean square average of L(1,χ) when χ ranges over all odd characters modulo k and L(2,χ) when χ ranges over all even characters modulo k. In principle, using our method, it is always possible to find the mean square average of L(r,χ) if χ and r?1 have the same parity and χ ranges over all odd (or even) characters modulo k, though the required calculations become formidable when r?3. Consequently, we see that for almost all odd characters modulo k, |L(1,χ)|<Φ(k), where Φ(x) is any function monotonically tending to infinity.     

About the Schur Index for Ambivalent Groups

An ambivalent group is a finite group all of whose irreducible characters are real valued. By Brauer–Speiser theorem, if G is an ambivalent group, then the absolute Schur index m _Q (χ) = m(χ) ≤2. In this note we shall prove that this property is true also for the derived subgroups of ambivalent groups. Also we will prove that there is a relation between the number of conjugacy classes of 2-regular cyclic subgroups of an ambivalent group and the irreducible characters with absolute Schur index 1.     

圈的多重联图的邻点可区别E-全染色的一些结果

记χ_(at)~e(C_n_i)为n_i阶的圈C_n_i的邻点可区别E-全色数.若n_i≡0(mod 2)(i=1,2,3…,t),则χ_(at)~e(C_n_1+C_n_2+…+C_n_t)=2t;若n_i≡0(mod 2)(i=1,2,3…,r,l相似文献   

Properties of the probability density function of the non-central chi-squared distribution

In this paper we consider the probability density function (pdf) of a non-central χ² distribution with arbitrary number of degrees of freedom. For this function we prove that can be represented as a finite sum and we deduce a partial derivative formula. Moreover, we show that the pdf is log-concave when the degrees of freedom is greater or equal than 2. At the end of this paper we present some Turán-type inequalities for this function and an elegant application of the monotone form of l'Hospital's rule in probability theory is given.     

完全二部图K_(1,n),K_(2,n)和K_(3,n)的点强可区别全染色

设f是图G的一个正常全染色.对任意x∈V(G),令C(x)表示与点x相关联或相邻的元素的颜色以及点x的颜色所构成的集合.若对任意u,v∈V(G),u≠v,有C(u)≠C(v),则称.f是图G的一个点强可区别全染色,对一个图G进行点强可区别全染色所需的最少的颜色的数目称为G的点强可区别全色数,记为X_(vst)(G).讨论了完全二部图K_(1,n),K_(2,n)和L_(3,n)的点强可区别全色数,利用组合分析法,得到了当n≥3时,X_(vst)(K_(1,n)=n+1,当n≥4时,X_(vst)(K_(2,n)=n+2,当n≥5时,X_(vst)(K_(3,n))=n+2.