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1.
W.E.Denting(1940),Discussion of Professor Hottelling's Paper "The Teaching of Statistics"(Ann.Math.Stat.Vol.11,457-470): Above all,a statistician must be a scientist. 最重要的是,统计学家应该是科学家.  相似文献   

2.
本文考虑部分自回归模型 X_t=X_(t-1)β g(U_t) ε_t,t≥1.这里g是一未知函数,β是一待估参数,ε_j是具有0均值和方差σ~2的i.i.d.误差,U_t i.i.d.服从[0,1]上均匀分布.本文首先给出了相合估计的收敛阶和Takeuchi意义下渐近有效界.同时给出了β最小二乘估计是有效的充要条件.最后证明了MLE是渐近有效的.  相似文献   

3.
环$R$称为是半clean的, 是指环中的每个元素都是一个单位与一个周期元的和. clean环是半clean的. 刻画半clean群环的一般情形是不容易的. 我们的目的是考虑如下问题:若$G$ 是局部有限群或者是阶是3的循环群, 群环$RG$何时是semiclean的. clean群环上的一些已有结果被推广.  相似文献   

4.
相反数和绝对值是两个非常重要的基础概念,有着广泛的应用.不少学生在学习时觉得不好理解,应用时经常出问题,下面就和同学们一起学习相反数和绝对值.1.理解相反数的概念要注意"只有符号不同"的含义,及零的相反数是零的这个规定.2.互为相反数指的是一对数,甲、乙两数互为相反数包括甲是乙的相反数,乙也是甲的相反数.  相似文献   

5.
九年义务教育新教材《几何》第三册第44页有这样一道例题:已知○.O1和○.O2外切于点A,BC是○.O1和○.O2的公切线,B、C为切点,求证:AB⊥AC.图1这是一道直线与圆及圆与圆的位置关系的综合题,目的是复习与巩固上述位置关系的知识点.这也是一道典型例题.我们还可以从多种角度探讨、  相似文献   

6.
我历来认为数学教学的目的是培养学生逻辑思维的能力.一定要彻底摆脱机械记忆.要努力让学生学习有兴趣.运用从特殊到一般的方法是很重要的.下面随意举几个例子.……  相似文献   

7.
孙太祥 《数学年刊A辑》2006,27(5):645-648
设T是个有限树,f是T上的连续映射.证明了f是分布混沌的当且仅当它的拓扑熵是正数.一些已知结论得到了改进.  相似文献   

8.
有界线性算子的不变Gauss测度   总被引:2,自引:0,他引:2  
设E是一个复的可分的自反Banach空间,T是E上的可逆有界线性算子,μ是E上的复的Gauss测度且μ的支集张成E.本文证明了若E是Cotype-2空间,且μ关于T是不变的.那么T的模为1的特征向量全体张成E.上述结论推广了E.Flytzanis的结果.  相似文献   

9.
研究K-本原环.证明了素环R是K-本原环当且仅当R含有一个非零理想I是K-本原环,当且仅当eRe是K-本原环,其中e是R的非零幂等元.并证明了GPI素环是K-本原环.推广了文献中的相应结果.  相似文献   

10.
数学家哈尔莫斯(P.P.Hal mos)说:数学的真正组成部分应该是问题和解,解题才是数学的心脏.而解题教学是高三数学复习的重要组成部分.从某种意义上说,解题教学是否高效决定了高三复习的成  相似文献   

11.
A new fractal dimension: The topological Hausdorff dimension   总被引:1,自引:0,他引:1  
We introduce a new concept of dimension for metric spaces, the so-called topological Hausdorff dimension. It is defined by a very natural combination of the definitions of the topological dimension and the Hausdorff dimension. The value of the topological Hausdorff dimension is always between the topological dimension and the Hausdorff dimension, in particular, this new dimension is a non-trivial lower estimate for the Hausdorff dimension.  相似文献   

12.
In this article,we introduce and study the concept of countably generated dimension,which is a Krull-like dimension extension of the concept of DCC on countably generated submodules.We show that some of the basic results of Krull dimension are true for countably generated dimension.It is shown that an R-module M has Krull dimension if and only if it has countably generated dimension,and its Krull dimension and countably generated dimension coincide.  相似文献   

13.
Following our previous work about quasi-projective dimension [11], in this paper, we introduce quasi-injective dimension as a generalization of injective dimension. We recover several well-known results about injective and Gorenstein-injective dimensions in the context of quasi-injective dimension such as the following. (a) If the quasi-injective dimension of a finitely generated module M over a local ring R is finite, then it is equal to the depth of R. (b) If there exists a finitely generated module of finite quasi-injective dimension and maximal Krull dimension, then R is Cohen-Macaulay. (c) If there exists a nonzero finitely generated module with finite projective dimension and finite quasi-injective dimension, then R is Gorenstein. (d) Over a Gorenstein local ring, the quasi-injective dimension of a finitely generated module is finite if and only if its quasi-projective dimension is finite.  相似文献   

14.
In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that: for Г as a non-empty set in R^n with Lebesgue measure |Г| = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.  相似文献   

15.
沈忠环 《数学杂志》2008,28(2):145-149
本文研究了填充维数与上盒维数的关系.利用Cantor-Bendixson定理的方法,得到了由上盒维数给出的填充维数的等价定义.并证明了齐次Moran集对上盒维数和填充维数的连续性.  相似文献   

16.
The dimension print is a concept which contains more detailed information than the usual Hausdorff dimension. So, for example, a sphere and the surface of a cube have same dimension but different dimension prints. Can anything be said about the dimension print of most convex surfaces (in the Baire category sense)?  相似文献   

17.
We effect a stabilization formalism for dimensions of measures and discuss the stability of upper and lower quantization dimension. For instance, we show for a Borel probability measure with compact support that its stabilized upper quantization dimension coincides with its packing dimension and that the upper quantization dimension is finitely stable but not countably stable. Also, under suitable conditions explicit dimension formulae for the quantization dimension of homogeneous Cantor measures are provided. This allows us to construct examples showing that the lower quantization dimension is not even finitely stable. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

18.
In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimension 5. We then show that the dimension of the adjacency poset of an outerplanar graph is at most 5. From below, we show that there is an outerplanar graph whose adjacency poset has dimension 4. We also show that the dimension of the adjacency poset of a planar bipartite graph is at most 4. This result is best possible. More generally, the dimension of the adjacency poset of a graph is bounded as a function of its genus and so is the dimension of the vertex-face poset of such a graph.  相似文献   

19.
We define a classical probability analogue of Voiculescu's free entropy dimension that we shall call the classical probability entropy dimension of a probability measure on Rn. We show that the classical probability entropy dimension of a measure is related with diverse other notions of dimension. First, it can be viewed as a kind of fractal dimension. Second, if one extends Bochner's inequalities to a measure by requiring that microstates around this measure asymptotically satisfy the classical Bochner's inequalities, then we show that the classical probability entropy dimension controls the rate of increase of optimal constants in Bochner's inequality for a measure regularized by convolution with the Gaussian law as the regularization is removed. We introduce a free analogue of the Bochner inequality and study the related free entropy dimension quantity. We show that it is greater or equal to the non-microstates free entropy dimension.  相似文献   

20.
We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite Gorenstein AC-projective dimension. This lets us give some general techniques for computing complete cohomology of complexes with finite Gorenstein AC-projective dimension. As a consequence, the classical relative cohomology for modules of finite Gorenstein AC-projective dimension is extended. Finally, the relationships between projective dimension and Gorenstein AC-projective dimension for complexes are given.  相似文献   

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