“无穷大”及其相关事实浅析

本文基于无穷大和无穷小的数学定义,通过x→∞,1/x→0的逻辑分析,指出将趋于无穷大定义为无穷大存在逻辑严密性不高的问题。通过对导数与广义导数、概率、希尔伯特无穷旅馆问题的分析,指出它们无不涉及0、无穷小和无穷大,有重要的逻辑关联性。通过对极值收敛性、0与负值的关系等问题的讨论,阐述了0、无穷大与宇宙的内在关系,指出无穷大与0等价,是宇宙存在的状态。     

《礼记·学记》中歧义断句的语法视角考证

《礼记·学记》中的“大学之教”部分,各家在断句和注解方面都存在歧见。对于任何文献而言,其语言必定刻有其所处时代的烙印,对其作语言层面的分析不能离开其所处历史时期的语言面貌。据此,以《礼记》、《孟子》和《春秋繁露》为语料,结合《礼记·学记》的内容和篇章结构特点对该句作出重新标注,可使各家的对错得失得到一个较为公正的评判。     

A likelihood ratio test of quasi-independence for sparse two-way contingency tables

We consider a likelihood ratio test of independence for large two-way contingency tables having both structural (non-random) and sampling (random) zeros in many cells. The solution of this problem is not available using standard likelihood ratio tests. One way to bypass this problem is to remove the structural zeroes from the table and implement a test on the remaining cells which incorporate the randomness in the sampling zeros; the resulting test is a test of quasi-independence of the two categorical variables. This test is based only on the positive counts in the contingency table and is valid when there is at least one sampling (random) zero. The proposed (likelihood ratio) test is an alternative to the commonly used ad hoc procedures of converting the zero cells to positive ones by adding a small constant. One practical advantage of our procedure is that there is no need to know if a zero cell is structural zero or a sampling zero. We model the positive counts using a truncated multinomial distribution. In fact, we have two truncated multinomial distributions; one for the null hypothesis of independence and the other for the unrestricted parameter space. We use Monte Carlo methods to obtain the maximum likelihood estimators of the parameters and also the p-value of our proposed test. To obtain the sampling distribution of the likelihood ratio test statistic, we use bootstrap methods. We discuss many examples, and also empirically compare the power function of the likelihood ratio test relative to those of some well-known test statistics.     

从三堂街话中古全浊声母字读音看喻母的来源

中古声母中的全浊音到了《中原音韵》时代全部变读为相应的清音声母。其规律是,原全浊塞音与塞擦音平声字归同部位的次清音、仄声字归同部位的全清音、擦音多清化为同类清音。这一规律在浊音发生清化的方言中大都适用,但在湘方言三堂街话中,中古全浊声母多读为零声母。这与浊音清化的规律不符,也与湘方言其他地方读音相异。这是声母受主元音或介音的影响,或同化或异化的结果。这一特殊音读现象有助于我们重新探讨中古喻母的来源。     

Improved estimation of the stable laws

Fitting general stable laws to data by maximum likelihood is important but difficult. This is why much research has considered alternative procedures based on empirical characteristic functions. Two problems then are how many values of the characteristic function to select, and how to position them. We provide recommendations for both of these topics. We propose an arithmetic spacing of transform variables, coupled with a recommendation for the location of the variables. It is shown that arithmetic spacing, which is far simpler to implement, closely approximates optimum spacing. The new methods that result are compared in simulation studies with existing methods, including maximum-likelihood. The main conclusion is that arithmetic spacing of the values of the characteristic function, coupled with appropriately limiting the range for these values, improves the overall performance of the regression-type method of Koutrouvelis, which is the standard procedure for estimating general stable law parameters.     

Behavior of agreement measures in the presence of zero cells and biased marginal distributions

Kappa and B assess agreement between two observers independently classifying N units into k categories. We study their behavior under zero cells in the contingency table and unbalanced asymmetric marginal distributions. Zero cells arise when a cross-classification is never endorsed by both observers; biased marginal distributions occur when some categories are preferred differently between the observers. Simulations studied the distributions of the unweighted and weighted statistics for k=4, under fixed proportions of diagonal agreement and different patterns off-diagonal, with various sample sizes, and under various zero cell count scenarios. Marginal distributions were first uniform and homogeneous, and then unbalanced asymmetric distributions. Results for unweighted kappa and B statistics were comparable to work of Muñoz and Bangdiwala, even with zero cells. A slight increased variation was observed as the sample size decreased. Weighted statistics did show greater variation as the number of zero cells increased, with weighted kappa increasing substantially more than weighted B. Under biased marginal distributions, weighted kappa with Cicchetti weights were higher than with squared weights. Both statistics for observer agreement behaved well under zero cells. The weighted B was less variable than the weighted kappa under similar circumstances and different weights. In general, B's performance and graphical interpretation make it preferable to kappa under the studied scenarios.     

标点符号的衔接性及其在英汉翻译中的应用

标点符号在语言表达中有很强的衔接力, 是文字语言不可或缺的辅助手段。在英汉翻译过程中,标点的正确应用不仅有助于读者理清源语的句子结构层次,辨明逻辑关系,而且有助于译者准确转达译入语的含义,突显信息焦点,使译文衔接紧密,更加自然流畅。根据不同语境对标点的使用作不同的处理,从而更加简洁而有效地传达信息。     

如何由图像确定函数у= A sin(ωx Ψ)的解析式

已知ｙ＝Ａｓｉｎ（ωｘ＋）（Ａ＞０，ω＞０）的图像求解析式有多种方法，如利用图像上各点对应的相 应或相位范围列方程组求解等方法，大家都已熟悉。本文介绍几种新的、快捷的解题方式。     

一类微分差分方程解的有界性和指数稳定性

通过构造函数和利用推广的Halanay一维时滞微分不等式,研究一类中立型微分差分方程解的有界性和零解的全局指数稳定性,给出其判定的充分性条件.     

对我国循环经济研究若干观点的述评

对中国理论界关于循环经济的概念、意义、研究现状、技术领域、政策等方面的观点进行了述评。指出循环经济不仅是一种全新的经济发展模式 ,也是一场物质变换的革命 ,更是一种新型的人与自然的关系。这必将引发产业升级、产业结构的大调整和经济增长方式的根本性改变。实现循环经济必须经历废物回收利用、逐步减少排放和全新的封闭式的零排放的资源利用方式最终确立三个阶段。中国目前仍处于第一阶段