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一道以群的定义为背景的高考试题赏析 总被引:2,自引:0,他引:2
每一年的高考数学试卷中都有一些以高等数学背景立意的好题目,如2006年四川卷理科第16题,是一道以近世代数中群的定义为背景立意的填空题,这样的试题能够有效考查学生的学习能力、思维能力和数学创新意识,这为高校选拔学习潜质好的学生创造了条件.…… 相似文献
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备课是教师的一项基本功,是教师对教材进行再创造的过程,是集教学内容,教学方式,教学艺术于一体的一项关键设计.备课质量的高低,不仅影响着教学计划的实施和教育方针的落实,更潜在地制约着课堂教学的效率. 相似文献
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2011年高考已经落幕,笔者有意关注了湖北数学试卷,解读理科数学试卷,两道立体几何试题给我留下了很深的印象.小题的背景和问题设置让人耳目一新;大题的解法入口宽,方法多,涉及的知识面广,打破了单纯考查立体几何的常规,建立了立体几何与函数、三角、向量、解几的密切联系.这两道试题充分体现了源于教材,略高于教 相似文献
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有限混合模型的Log极大似然比统计量极限分布不是平常x2分布,1985年已为Hartigan指出.在这篇文章我们限制了混合比大于一正数下,讨论了两个含单个未知参数混合模型的Log极大似然比统计量的极限分布,它是零与x2分布的混合分布. 相似文献
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We consider networks where at each node there is a single exponential server with a service rate which is a non-decreasing
function of the queue length. The asymptotic profile of a sequence of networks consists of the set of persistent service rates,
the limiting customer-to-node ratio, and the limiting service-rate measure. For a sequence of cyclic networks whose asymptotic
profile exists, we compute upper and lower bounds for the limit points of the sequence of throughputs as functions of the
limiting customer-to-node ratio. We then find conditions under which the limiting throughput exists and is expressible in
terms of the asymptotic profile. Under these conditions, we determine the limiting queue-length distributions for persistent
service rates. In the absence of these conditions, the limiting throughput need not exist, even for increasing sequences of
cyclic networks.
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We show via simulation and counterexamples that the Mantel-Haenszel estimator of a common odds ratio, adapted for complex survey designs using survey weights, is inconsistent for sparse-data limiting models. We also propose an alternative estimator that is consistent for sparse-data limiting models satisfying a positivity condition, but not for large-strata limiting models. 相似文献
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William W. S. Wei Daniel O. Stram 《Annals of the Institute of Statistical Mathematics》1988,40(1):101-110
Many time series variables such as rainfall, industrial production, and sales exist only in some aggregated forms. To see the implication of time series aggregation it is important to know the limiting behavior of the time series aggregates. From the relationship of autocovariances between the underlying time series variable and its aggregates, we show that the limiting behavior of time series aggregates is closely related to the eigenvalues and the eigenvectors of the aggregation operator. Specifically, the vector of admissible autocorrelations of the limiting model for the time series aggregates is the eigenvector associated with the largest eigenvalue of the aggregation transformation. This provides an interesting and simple method for deriving the limiting model for time series aggregates. Systematic sampling of time series can be treated similarly. The method is illustrated with an empirical example. 相似文献
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We consider the small mass asymptotic (Smoluchowski–Kramers approximation) for the Langevin equation with a variable friction coefficient. The friction coefficient is assumed to be vanishing within certain region. We introduce a regularization for this problem and study the limiting motion for the 1-dimensional case and a multidimensional model problem. The limiting motion is a Markov process on a projected space. We specify the generator and the boundary condition of this limiting Markov process and prove the convergence. 相似文献
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Two preferential attachment-type graph models which allow for dynamic addition/deletion of edges/vertices are considered. The focus of this paper is on the limiting expected degree of a fixed vertex. For both models a phase transition is seen to occur, i.e. if the probability with which edges are deleted is below a model-specific threshold value, the limiting expected degree is infinite, but if the probability is higher than the threshold value, the limiting expected degree is finite. In the regime above the critical threshold probability, however, the behaviour of the two models may differ. For one of the models a non-zero (as well as zero) limiting expected degree can be obtained whilst the other only has a zero limit. Furthermore, this phase transition is seen to occur for the same critical threshold probability of removing edges as the one which determines whether the degree sequence is of power-law type or if the tails decays exponentially fast. 相似文献
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We study the limiting behavior of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that under certain assumptions the limiting dynamics is given by a McKean–Vlasov evolution equation. Moreover, we show that the evolution of the cumulative distribution function under the limiting dynamics is governed by the generalized porous medium equation with convection. The implications of the results for rank-based models of capital distributions in financial markets are also explained. 相似文献
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Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very general theorem that can be used to establish compound Poisson distributions in many other settings. 相似文献