两个不同的费尔马定理

数论是历史最悠久的数学分支之一,两个费尔马定理是数论领域的两个有一定代表性的著名定理,其中费尔马小定理在密码技术方面起了关键性的作用.     

Nondictatorial social welfare functions with different discrimination structures

In societies where agents distinguish imperfectly among the alternatives, a necessary and sufficient condition for the existence of an Arrovian Social Welfare Function is the presence of an agent who only distinguishes two groups of alternatives or of two agents with complementary discrimination patterns. This result is based on the observation that differences in discrimination structures may lead to the absence of free triples, thus providing a way to escape Arrow's impossibility result.     

When are two step estimators efficient?

Kruskal's theorem is used to provide simple and elegant alternative derivations of the efficiency of some two step estimators (2SE) for models containing anticipated and unanticipated variables. Several new results are established: 2SE is not efficient for a structural equation with current and lagged values of both anticipated and unanticipated variables; 2SE is always efficient for the parameter associated with the current unanticipated variable, and for the parameter associated with the lagged unanticipated variable if there is no lagged dependent variable in the expectations equation; the inclusion of additional regressors in the structural equation and contemporaneous correlation of the structural and expectations errors can both be analysed in a straightforward manner; the single-equation generalized least squares estimator can be as efficient as the systems maximum likelihood estimator.     

探寻Desargues定理之美

本文从Ｄｅｓａｒｇｕｅｓ定理在公理系统中的地位，Ｄｅｓａｒｇｕｅｓ定理的证法及应用，Ｄｅｓａｒｇｕｅｓ构形特征等方面论述了该定理的美。     

ON THE GLOBAL ASYMPTOTIC STABILITY OF THE EQUATION +f+h+g(x)=0

This paper gives a sufficient criterion of the global asymptotic stability of the zerosolution of the equation(?)+f((?))+h((?))+g(x)=0     

Wolstenholme定理的进一步推广

Ｗｏｌｓｔｅｎｈｏｌｍｅ定理巳被推广过．本文再作进一步推广，得到一般性的结果和几个重要的同余关系式．     

村民自治的程序民主与实质民主——基于社会选择理论对村支“两委”选举的案例分析

本文分析了投票悖论与阿罗不可能定理是个人理性决策与集体一致性行动的冲突在社会选择领域的表现,并结合森对悖论的解答,引入信息基础的理性扩张、合约成本和作为契约的程序、制度,以农村村支“两委”选举为例,探讨村民自治过程中不同经济发展水平和结构特征的农村中个人理性走向集体一致性社会选择实现路径,在此基础上提出村民自治中实现程序民主与实质民主统一的对策建议.     

The generalized fluctuation test: A unifying view

In this paper, a general principle of constructing tests for parameter constancy without assuming a specific alternative is introduced. A unified asymptotic result is established to analyze this class of tests. As applications, tests based on the range of recursive and moving estimates are considered, and their asymptotic distributions are characterized analytically. Our simulations show that different tests have quite different behavior under various alternatives and that no test uniformly dominates the other tests.     

周线上复积分的几种算法

通过典型例题,恰当运用复变函数论中有关复积分的基本理论与方法,系统地给出了周线上的复积分的八种不同的计算方法.     

文化经济学的视野:“私有化”与“市场化”反思——兼论“广义科斯定理”和产权公平

西方主流经济学一直把自由市场作为理论的重要起点之一,亦影响到我国经济改革的私有化和市场化走向。另一方面,却是国家在国企垄断和诸如楼市调控中显示出来的强势计划性市场倾向。本文从人类学的经济学或说文化经济学的视角,探讨了上述经济改革中的两难困境:自由市场还是计划性市场?本文由文化群体动力学的信号灯法则引出问题,论证了中国的经济改革不应以私有化和自由市场为方向,也不能回归计划性市场,而应寻找自由市场和计划性市场两端中间的合适平衡态。(1)本文首先指出了自由市场和计划性市场的原初逻辑均是来自人类初民社会,把自由市场归为资本主义或把计划性市场归为社会主义因而争论主义的思维模式存在误区;(2)通过论证广义科斯定理,探讨了自由市场和计划性市场两端论的观点,强调了产权表达的公平秩序是市场的本质。产权改制的核心不是私有化和自由市场之类,而应该是公平配置共有产权(民权基础)和个有产权(人权基础)、合理安排自由市场和计划性市场两端中间的平衡状态。公有制和私有制的意识形态争论是一个伪问题。(3)由两端论的观点讨论了国家角色,指出国家既不可能超脱于自由市场之外,亦不应操控计划市场。它应该正视自己是市场的一部分并为其在国企转制和市场改革...