Matrix Padé Approximation of rational functions

In many applications it is of major interest to decide whether a given formal power series with matrix-valued coefficients of arbitrary dimensions results from a matrix-valued rational function. As the main result of this paper we provide an answer to this question in terms of Matrix Padé Approximants of the given power series. Furthermore, given a matrix rational function, the smallest degrees of the matrix polynomials which represent it are not necessarily unique. Therefore we study a certain minimality-type, that is, minimum degrees. We aim to obtain all the minimum degrees for the polynomials which represent the function as equivalents. In addition, given that the rational representation of the function for the same pair of degrees need not be unique, we have obtained conditions to study the uniqueness of said representation. All the results obtained are presented graphically in tables setting out the above information. They lead to a number of properties concerning special structures, staired blocks, in the Padé Table.     

基于差异化产品动态寡头博弈的系统动力学分析

以寡头企业具有有限理性和简单理性的产量调整行为和非线性成本函数为基础,论证了当横向产品差异度在一定范围内时,纳什均衡可作为稳定的动态均衡而实现.当超过一定范围时,利用数值模拟可观测到系统出现的周期性和混沌的复杂现象.在企业具有二次成本的假设条件下,研究了产品差异程度对纳什均衡稳定性的影响,得到了产品差异度越大,或市场竞争程度越低,系统的纳什均衡越不稳定的结论,表明了经济周期波动产生于非线性系统的内生性.与线性成本的对比说明,非线性成本缩小了纳什均衡的稳定域,增加了寡头市场的复杂性.研究也表明规模不经济的寡头厂商想通过增加产品差异度来减少竞争是有一定难度的.     

市场自治与低碳认证情形下企业低碳生产行为研究

消费者愿意为产品支付低碳溢价的低碳消费趋势及政府环境政策驱动企业审视自身的低碳生产决策问题。通过将影响企业低碳生产决策的因素纳入有限理性的博弈框架,分析市场自治与政府介入低碳认证情形下企业群体低碳生产行为。结果表明,企业低碳生产决策受低碳收益及公平效用影响;市场初始阶段,低碳成本较高,具备低碳知识的理性消费者较少,企业与消费者关于低碳信息的不对称导致企业不能获得合适的低碳溢价收益,在完全自治的市场情形下,仅靠企业自身决策很难达到主动进行低碳生产的良性状态;低碳认证作为政府介入手段,当市场中低碳认证的产品达到一定比例,能够加速推动市场向企业进行低碳生产的良性状态转化。     

Calabi–Yau Threefolds and Moduli of Abelian Surfaces I

We describe birational models and decide the rationality/unirationality of moduli spaces A _d (and A _d ^lev ) of (1, d)-polarized Abelian surfaces (with canonical level structure, respectively) for small values of d. The projective lines identified in the rational/unirational moduli spaces correspond to pencils of Abelian surfaces traced on nodal threefolds living naturally in the corresponding ambient projective spaces, and whose small resolutions are new Calabi–Yau threefolds with Euler characteristic zero.     

化学课堂教学有效性的评价研究

依据系统科学理论,探讨了课堂教学基元系统有效性(EfPrS)的含义;运用项目分析、探索性因素分析和验证性因素分析方法,开发了EfPrS的评价量表,并得到了影响EfPrS的5个最主要因素,分别为:"时间利用的合理性(RUT)" "教学行为链的实施质量(QTBC)" "匹配度(MD)" "资源和手段的使用质量(QUR&T)"和"基元内容的合理性(RPrC)";运用回归分析方法建立了EfPrS与5个影响因素之间的线性回归方程,并得出QTBC是影响EfPrS的最主要因素;运用聚类分析和判别分析方法得到了课堂教学基元系统高效、中效和低效的边界值。     

An impossibility result for housing markets with fractional endowments

The housing market setting constitutes a fundamental model of exchange economies of goods. House allocation with fractional endowments of houses was considered by Athanassoglou and Sethuraman (2011) who posed the open problem whether individual rationality, efficiency, and weak strategyproofness are compatible for the setting. We show that the three axioms are incompatible.     

Punishment in optional public goods games

In this work,the optional public goods games with punishment are studied.By adopting the approximate best response dynamics,a micro model is given to explain the evolutionary process.Simultaneously,the magnitude of rationality is also considered.Under the condition of bounded rationality which provides a light to interpret phenomena in human society,the model leads to two types of equilibriums.One is the equilibrium without punishers and the other is the equilibrium including only punishers and cooperators.In addition,the effects of rationality on equilibriums are briefly investigated.     

Complete reducibility,Külshammer’s question,conjugacy classes: A D4 example

Let k be a nonperfect separably closed field. Let G be a connected reductive algebraic group defined over k. We study rationality problems for Serre’s notion of complete reducibility of subgroups of G. In particular, we present a new example of subgroup H of G of type D₄ in characteristic 2 such that H is G-completely reducible but not G-completely reducible over k (or vice versa). This is new: all known such examples are for G of exceptional type. We also find a new counterexample for Külshammer’s question on representations of finite groups for G of type D₄. A problem concerning the number of conjugacy classes is also considered. The notion of nonseparable subgroups plays a crucial role in all our constructions.     

Convergence of aspirations and (partial) cooperation in the prisoner's dilemma

This paper proposes an aspiration-based dynamic model for cooperation where a large population of agents are matched afresh every period to play a Prisoner's Dilemma. At each point in time, agents hold a common aspiration level which is updated on the basis of some “population statistic”, i.e. a certain scalar summary (e.g. average payoff) associated to the current state. On the other hand, those agents who feel “dissatisfied” (relative to current aspiration) switch actions at a rate which is increasing in the magnitude of the dissatisfaction. The resulting process is shown to converge in the long run under quite general conditions. Moreover, if agents are responsive enough, the long-run social state displays some extent of cooperation, with a constant positive fraction of the population (always less than half) choosing to cooperate in every period. Received: January 1998/Revised version: October 1998     

The structure of social decision functions

This paper investigates possible extensions of the Arrow Impossibility Theorem by relaxing the collective rationality condition from transitivity to acyclicity. It is shown that some elements of dictatorship must persist even when two of Arrow's conditions are dropped (namely the Pareto principle and transitivity of social preferences).