计算知识论视域下的科学发现逻辑研究

在科学发现逻辑受制于描述性的传统研究路径，经历衰落和缓慢复苏的大背景之下，计算知识论为科学发现逻辑提供了一个全新的规范性研究框架。该框架不仅为科学发现逻辑做了系统性辩护，而且围绕发现问题的可解性做了许多规范性讨论。虽然其有关具体规范性的研究距离现实的科学发现仍然较远，但这一路径对未来发现逻辑研究走向的启发意义毋庸置疑。     

Fear of Miscoordination and the Robustness of Cooperation in Dynamic Global Games With Exit

This paper develops a framework to assess how fear of miscoordination affects the sustainability of cooperation. Building on theoretical insights from Carlsson and van Damme (1993), it explores the effect of small amounts of private information on a class of dynamic cooperation games with exit. Lack of common knowledge leads players to second guess each other's behavior and makes coordination difficult. This restricts the range of equilibria and highlights the role of miscoordination payoffs in determining whether cooperation is sustainable or not. The paper characterizes the range of perfect Bayesian equilibria as the players' information becomes arbitrarily precise. Unlike in one‐shot two‐by‐two games, the global games information structure does not yield equilibrium uniqueness.     

A solvable singular control problem driven by a jump diffusion process with applications

We consider a class of singular control problems driven by a double exponential jump diffusion process, which come from the reversible investment problem. In some interesting cases (e.g., the running cost function is given by the so-called Cobb-Douglas production function), we give the explicit solutions to the singular control problem by using the connection between singular control and optimal switching. We solve a collection of consistent optimal switching problems and yield the explicit solution for the singular control problem. We then give an application to a particular inventory control problem in a single random period.     

关于Diophantine方程x3-8=py2

在p是奇素数的假设下,证明了如果p=12r2 1,其中r是偶数,则方程x3-8=py2没有适合gcd(x,y)=1的正整数解(x,y).     

整数矩阵集上的Fermat方程

设A 是 m 阶整数矩阵,A 是由A 的全体方幂构成的集合.本文证明了:当 m > 9 时,如果A 的行列式｜ A｜ ≠0 ,而且A 的特征根不全为单位根,则A 上的Fermat 方程无解.     

关于三角数与多角数

对于正整数m、n(n≥ 3 ) ,设Sm(n)是第m个n的角数 .该文证明了 :当n >6且n -2是平方数时 ,方程Sx(n) =Sy(3 )无正整数解 (x,y) ;当n >6,2 n且n -2非平方数时 ,该方程有无穷多组正整数解 (x ,y) .     

关于Ljunggren方程

设a,b是互素的正整数,c∈{±1,±2,±4}.该文简要介绍Ljunggren方程ax4-by2=c的重要结果,并且对有关该方程的某些尚未解决的问题进行分析.     

A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements

Rationalizability is a central solution concept of game theory. Economic models often have many rationalizable outcomes, motivating economists to use refinements of rationalizability, including equilibrium refinements. In this paper we try to achieve a general understanding of when this multiplicity occurs and how one should deal with it. Assuming that the set of possible payoff functions and belief structures is sufficiently rich, we establish a revealing structure of the correspondence of beliefs to sets of rationalizable outcomes. We show that, for any rationalizable action a of any type, we can perturb the beliefs of the type in such a way that a is uniquely rationalizable for the new type. This unique outcome will be robust to further small changes. When multiplicity occurs, then we are in a “knife‐edge” case, where the unique rationalizable outcome changes, sandwiched between open sets of types where each of the rationalizable actions is uniquely rationalizable. As an immediate application of this result, we characterize, for any refinement of rationalizability, the predictions that are robust to small misspecifications of interim beliefs. These are only those predictions that are true for all rationalizable strategies, that is, the predictions that could have been made without the refinement.     

关于Diophantine方程x3-8=3py2

设p是奇素数.该文证明了:如果p=12s2 1,其中s是奇数,则方程x3-8=3py2没有适合gcd(x,y)=1的正整数解(x,y).     

“问题”及其构成要素的哲学考察

"问题",尤其是"科学问题",是科学认识论或方法论中一个十分重要的范畴。问题除了与世界相关联,还与另外四个基本概念相杂合:不理想性、注意力、困难、可解性。这四个基本概念既展示了问题的实质内容,也从概念意义上展示了问题的形成过程。文章以吉恩.阿格雷关于问题的思想为切入点,在分析评价的基础上,论述了问题的四大构成要素及其相互之间的关系。