老庄之道与言意之辨

老庄之道主要指宇宙本体及其永恒存在的规律 ,而意是人们对宇宙本体及其运行规律的认识 ,言又是意的表现形式。由于道本身的复杂性、精微性和玄妙性、无限性 ,人们不可能完全认识它 ,更不可能用语言完美地表现它。因此 ,言不尽意是绝对的 ,言能尽意是相对的。老庄明知道不可言却又连篇累牍言道的行为并不矛盾 ,他们在宇宙的伟力前感到了自身的渺小 ,因而在无法完美描绘彼岸世界之道的大前提下 ,勉为其难地对此岸世界之道进行了详尽描述 ,文章认为这是领会老庄之心的关键所在     

孤立点集及其导集的性质

归纳出孤立点集及其导集的6个性质;还通过几个实例讨论了孤立点集之导集的可数性问题.     

论人的超越性本质

人既具有现实性,又具有超越性.人的超越性是人的主体性和生命本质力量的发挥与确证,是人之为人所不可或缺的内在生命特质.人的超越性是由人本身具有的能动性、创造性、意义性、精神性和无限性决定的,它主要表现为四个方面:创造对适应的超越;意义对现实的超越;无限对有限的超越;精神对物质的超越.现实性是人存在的基础,超越性是人存在的升华.否定人的现实性,超越性便成为空中楼阁;忽视或放弃了超越性,人之为人的高贵性便无从彰显.     

Countable Additivity and the Foundations of Bayesian Statistics

At a very fundamental level an individual (or a computer) can process only a finite amount of information in a finite time. We can therefore model the possibilities facing such an observer by a tree with only finitely many arcs leaving each node. There is a natural field of events associated with this tree, and we show that any finitely additive probability measure on this field will also be countably additive. Hence when considering the foundations of Bayesian statistics we may as well assume countable additivity over a σ-field of events.     

丘奇-图灵论点与人类认知能力和极限

丘奇-图灵论点是论述人类认知能力及其极限的一个重要背景。在此背景下,人类认知的无限性是 一种可数无限性,人的认知能力受递归规律的限制,并且只能在递归的意义上认知事物。对于非递归结构或非递 归性质的事物,人只能做递归性的认知。计算神经科学为计算主义认知观提供了一定的证据。     

Geometric Ergodicity and Moment Conditions for a Seasonal GARCH Model with Periodic Coefficients

A seasonal GARCH process with periodic coefficients is considered and conditions for periodic stationarity, geometric ergodicity, β-mixing property with exponential decay rate, and existence of higher-order moments are obtained.     

艺术解释的向度

主观性、历史性、对话性、无限性是艺术解释活动中的四个重要向度,它们决定着解释的方向、结论以及解释的广度和深度。在此向度上进行艺术解释活动,可以使主观与客观、传统与现代、自我与他者、现实创造性以及未来指向性之间的张力或冲突,得到相应的缓解或解决。     

Power periodic threshold GARCH model: Structure and estimation

Abstract

In this paper, we introduce and study the Power Periodic Threshold GARCH Model (PPTGARCH). We give the necessary and sufficient conditions for the existence of the unique strictly periodically stationary solution of the model and the necessary and sufficient conditions for the existence of moments. A sufficient condition for the periodic geometric ergodicity and β – mixing property using the uniform countable additivity condition is given. We prove the consistency and asymptotic normality of the Quasi-Maximum Likelihood estimator (QMLE) of the parameters. Simulation studies to illustrate consistency and asymptotic normality of the estimators for different underlying error distributions are presented.     

Perspectives on a Pair of Envelopes

The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue).     

实函数间断点的某些特性

本文给出了几类常见函数间断点及一般实函数第一类间断点的某些特性,并指出它们在实际问题中的应用.