留数定理求逆z变换时的极点选择

得当地使用留数定理可改变所需参与运算的极点,从而简化求逆z变换的过程。本文就此讨论了两种方法的依据和实际运用,并指明了它们的思想实质。     

On the nonexistence of Blackwell's theorem-type results with general preference relations

A well-known theorem of Blackwell states that, when quantity of information is properly defined, every expected utility decision maker prefers more information to less; for more general preferences, however, the theorem is no longer true. In this article, we investigate the extent to which Blackwell's Theorem does not hold and describe conditions, and situations, under which information is still valuable. We also show that, for many types of additions of information, there exists a decision maker who will reject this information.We thank Niv Ahituv, Larry Epstein, Uzi Segal, and an anonymous referee for their helpful comments. This article was partially financed by the Israel Institute of Business Research.     

罗尔中值定理的推广研究

高等数学中微分学占有很大比重,相对来说微分学中的基础理论比较重要也比较基本,微分学的科学价值在于逻辑运用。其中罗尔中值定理是最基本也是应用最为广泛,在应用过程中有着"钥匙"、"桥梁"的作用。充分利用开区间、闭区间以及半开半闭区间条件的转换,来运用罗尔中值定理的推广及其证明,并得出不同条件下的结论。     

Exercising Property Rights to Pollute: Do Cancer Risks and Politics Affect Plant Emission Reductions?

This paper examines whether firms' decisions about reductions in toxic emissions depend on the magnitude of dangers arising from their pollution and on who bears pollutant risks. Controlling for the quantity of air toxics released in 1988, this article finds that plants whose emissions generated higher numbers of expected cancer cases did reduce their emissions more between 1988 and 1991. The nature of the community bearing the pollution risk also affected firm decisions. The higher the voter turnout in the area, a proxy for residents' likelihood of collective action, the greater the reductions in a plant's release of air carcinogens.     

Inhomogeneous Markov Chains and Ergodicity Coefficients: John Hajnal (1924–2008)

In 1958, a paper by John Hajnal, a demographer and mathematical statistician, was fundamental in the revival of the theory of inhomogeneous Markov chains. Hajnal made his contribution by the development of tools for the analysis of weak ergodicity, and proofs of fundamental theorems. This article reviews Hajnal's career, and then focuses on the four topics: 1. ergodicity coefficients and the weak ergodicity theorem; 2. scrambling matrices; 3. the coupling theorem; and 4. non-negative matrix products. Related work by other authors, especially Wolfgang Doeblin, is mentioned in context. Attention is given to some recent surveys and applications of ergodicity coefficients, including the Google matrix.     

古代中印勾股测望术之比较

勾股测量法是勾股定理的实际应用,在古代中国和印度都曾出现过,而且两国的许多数学著作与天文学著作中都有勾股测量法的记载。两国的勾股测量法由测量太阳高度和晷影长度发展起来,并随着实际问题的需要日益提高。由于社会生活和生产需求的一致,中印两国勾股测量方法存在很多的共性,但都是在各自的本土文化中发展起来的,没有受到外来文化的影响。     

关于含参变量无穷积分的绝对一致收敛的注记

本文从一个反例 ,证明了即使∫∞af(x ,t)dt绝对收敛且一致收敛 ,但不能推出∫∞a |f(x ,t) |dt一致收敛。     

Folk theorems for the observable implications of repeated games

The fact that infinitely repeated games have many different equilibrium outcomes is known as the Folk Theorem. Previous versions of the Folk Theorem have characterized only the payoffs of the game. This paper shows that over a finite portion of an infinitely repeated game, the concept of perfect equilibrium imposes virtually no restrictions on observable behavior. The Prisoner's Dilemma is presented as an example and discussed in detail.I would like to thank an anonymous referee, Sushil Bikhchandani, David Hirshleifer, David Levine, Thomas Voss, and participants in the UCLA Game Theory Seminar for helpful comments.     

Approximate Identifiability, Moments and Censored Data

It is well known that the joint distribution of a pair of random variables ( X,Y ) is not identifiable on the basis of the joint distribution of the function (min ( X,Y ), 1[ X < Y ]). This paper introduces the concept of approximate identifiability and studies its relevance to the function (min ( X,Y ), Y ). It shows that the distribution of ( X,Y ) is approximately identifiable on the basis of the distribution of (min ( X,Y ), Y ). The identification is explicitly executed by a method of moments. The method is applied to the analysis of censored distributions arising in the theory of clinical trials and is compared to the standard method of Kaplan and Meier.     

Estimating a covariance function having an un unknown scale kakameter

The structure of a family ρ of measures corresponding to a zero-mean Gaussian process with covariance αR(s,t) is discussed. When R itself is known (R and T completely arbitrary), it is shown that ρ is either homogeneous or composed of singular measures, depending on whether the reproducing kernel Hilbert space H(R,T) is finite- or infinite-dimensional. For the case dim H < ∞ the MLE α is given; when dim H = ∞ an almost sure discriminator is constructed. More generally, it is shown that when R itself depends upon a parameter θ (not necessarily a scalar) and certain broad assumptions are met, one may describe the orthogonal decomposition of P and estimate both a and θ.