论《红楼梦》结构的对称艺术

曹雪芹创作的《红楼梦》在故事情节的布局、人物关系的配置以及回目句法的创制等方面巧妙地运用了对称艺术手法,使《红楼梦》这部中国古典文学名著从内容到形式达到了完美的统一,具有恒久不衰的艺术魅力。     

论对称性方法视野中的技术性幸福感

在技术性幸福感学说提出的初期,由于传统人文理论对幸福感已经进行了较为系统地界定,加上人们受技术性产品副作用的心理影响较大,同时,技术性幸福感学说自身也存在着发展不完善等因素,导致了人们最初对其产生了否定的思维模式.但客观地从技术性幸福感的存在规律出发,借助于自然科学广泛应用的对称性方法,恰当地揭示技术性幸福感的诸多特征,我们就能够为技术性幸福感搭建一个平台,使其得到充分地讨论,从而能够更深一步地诠释人类的幸福感理论问题.     

Comparing two dependent groups via quantiles

This paper considers two general ways dependent groups might be compared based on quantiles. The first compares the quantiles of the marginal distributions. The second focuses on the lower and upper quantiles of the usual difference scores. Methods for comparing quantiles have been derived that typically assume that sampling is from a continuous distribution. There are exceptions, but generally, when sampling from a discrete distribution where tied values are likely, extant methods can perform poorly, even with a large sample size. One reason is that extant methods for estimating the standard error can perform poorly. Another is that quantile estimators based on a single-order statistic, or a weighted average of two-order statistics, are not necessarily asymptotically normal. Our main result is that when using the Harrell–Davis estimator, good control over the Type I error probability can be achieved in simulations via a standard percentile bootstrap method, even when there are tied values, provided the sample sizes are not too small. In addition, the two methods considered here can have substantially higher power than alternative procedures. Using real data, we illustrate how quantile comparisons can be used to gain a deeper understanding of how groups differ.     

Estimation of the scale parameter after a pre-test for homogeneity in a mis-specified regression model

The risk properties of estimators of the scale parameter after a pre-test for homogeneity of the error variances in the two sample linear regression model has received quite an amount of attention in the literature. This literature typically assumes normal disturbances and a properly specified model. In this paper we consider that both equations may be mis-specified by the omission of relevant regressors and that the error distributions may belong to a wider class than the normal distribution. We derive and analyse the exact risk (under quadratic loss) of the pre-test estimator of the scale parameter for the first sub-sample.     

文化符号的数学思维

本文从科学的视角研究探讨数学及其对称原理和理论,并应用数学作为方法论,研究中西方传统文化和艺术中所蕴含的数学观.人们在创造和使用一切文化世界的符号过程中,时常蕴藏着人类智慧的另一个重要内容,即数学.我们将其称之为"文化符号的数学思维",即文化符号在构筑过程中同时所蕴含着某种数学原理、理论及思想.探讨艺术如何遵循数学"法则"进行创作活动,其动机不在于数学本身,而在于唤醒人们重视科学对艺术的影响作用.研究数学与文化的另一主要目的是,希望人们能从全方位的和文化的视角欣赏数学的全貌和魅力,同时阐明一个基本观点:数学不仅仅是一种抽象的思想,同时也在艺术的创作方法和工具中具备重要价值.     

Partitioning chi-squape in contingency tables: A teaching approach

A representation of sums and differences of the form 2n log n, the lnn function, is introduced to express likelihood-ratio chi-square test statistics in contingency table analysis. This is a concise explicit form to display when partitioning chi-square statistics in accordance with hierarchical models. The lnn representation gives students insights into the construction of test statistics, and assists in relating identical forms under differing model sets. Hierarchies are presented for independence and equi-probability in two-way tables, for symmetry in correlated square tables, for independence-and-homogeneity of two-way responses across levels of a factor, and for mutual independence in three-way tables, along with relevant partitions of chi-square.     

一个(3 1)维可积Sinh-gordon-MKdV方程

利用MKdV方程的递推算子的遗传性，构造了一个（3＋1）维的Sinh-Gordon－MKdV型的可积模型。该模型是（1＋1）维Sinh－Gordon方程和（1＋1）维MKdV方程的推广。同时给出了该模型的丰富的对称性。     

共同支配地位反垄断法规制“企业因素”界定

企业间的诸多因素,如企业数量、企业对称性、生产能力、以及结构联系,对它们达成或维持协调行为或一致行动很重要。因此,在判定企业是否具有共同支配地位时,必须充分考虑到这些因素,方能确保判断的准确性。目前我国反垄断执法尚未完全掌握这一考察方法,因而今后应充分借鉴相关国家的成熟经验,尽早探寻出一套契合我国国情的共同支配地位判定方法。     

Measure of departure from symmetry for the analysis of collapsed square contingency tables with ordered categories

For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper considers the symmetry model for collapsed square contingency tables and proposes a measure to represent the degree of departure from symmetry. The proposed measure is defined as the arithmetic mean of submeasures each of which represents the degree of departure from symmetry for each collapsed 3×3 table. Each submeasure also represents the mean of power-divergence or diversity index for each collapsed table. Examples are given.     

A class of exact UMP unbiased tests for conditional symmetry in small-sample square contingency tables

Testing conditional symmetry against various alternative diagonals-parameter symmetry models often provides a point of departure in studies of square contingency tables with ordered categories. Typically, chi-square or likelihood-ratio tests are used for such purposes. Since these tests depend on the validity of asymptotic approximation, they may be inappropriate in small-sample situations where exact tests are required. In this paper, we apply the theory of UMP unbiased tests to develop a class of exact tests for conditional symmetry in small samples. Oesophageal cancer and longitudinal income data are used to illustrate the approach.