On non-linear extensions of the Perron-Frobenius theorem

The note provides bounds for eigenvalues of non-negative, homogeneous mappings, which need not be linear. It also gives a simple proof of the result, that repeated iterations of a primitive mapping take any semipositive vector to the positive eigenvector.     

A theorem on the additivity of the quasi-concave closure of an additive convex function

In this paper a necessary and sufficient condition for the additivity of the quasi-concave closure of an additive convex function is given.     

An equilibrium existence theorem without complete or transitive preferences

The Walrasian equilibrium existence theorem is reproved without the assumptions of complete of transitive preferences.     

The Frobenius theorem, its Solow-Samuelson extension and the Kuhn-Tucker theorem

In economics, the Frobenius theorem and its extension are often used in the theory of linear models and the theory of balanced growth. In these contexts optimization does not appear explicitly. Our proof by the Kuhn-Tucker theorem may lead to some interesting economic reinterpretations of the Frobenius root and eigenvectors in these models. As for economic applications, see, for example, Morishima (1964); the extended bibliography of Debreu and Herstein (1953) is also useful.     

Maxmin expected utility with additivity on unambiguous events

This paper provides a model of beliefs representation in which ambiguity and unambiguity are endogenously distinguished in the maxmin expected utility model of Gilboa and Schmeidler (1989). Specifically, I first extend it by getting a representation of beliefs such that the probabilistic beliefs over each ambiguous event are represented by a nondegenerate interval, while the ones over each unambiguous event are represented by a number. I then suggest a behavioral definition of ambiguity. It provides a choice theoretical foundation for the Knightian distinction between ambiguity and unambiguity.     

A reexamination of additivity of power in randomized social preference

We show that Barberá and Sonnenscheins (1978) power function becomes additive if we replace the Paretian condition by nonimposition and monotonicity. Since these conditions are very much in the spirit of Arrow (1951), our result sharpens the analogy to Arrows theorem.Received: 29 November 2001, Accepted: 4 May 2003, JEL Classification: D71Shasikanta Nandeibam: I would like to thank Professor Prasanta Pattanaik for very helpful discussions. I have also benefitted from the comments and suggestions of an associate editor. The usual disclaimer applies.     

无故障管理

无故障管理是在采矿生产特定的环境下,分析、把握系统运行规律,并通过对安全、成本、质量、工艺、设备、人力资源等要素的不断优化配置,设置预定途径,实现有效控制,保证采矿系统一直顺利运行的管理模式.     

The mean-standard deviation efficient set theorem: A note

This note is concerned with the proof of a revised version of the mean-standard deviation efficient set theorem. Given only risky securities, it is irrational to hold the global boundary portfolio, whereas when a riskless security exists a finitely risk-averse investor does not invest exclusively in such a security.     

Stochastic utility theorem

This paper analyzes individual decision making. It is assumed that an individual does not have a preference relation on the set of lotteries. Instead, the primitive of choice is a choice probability that captures the likelihood of one lottery being chosen over the other. Choice probabilities have a stochastic utility representation if they can be written as a non-decreasing function of the difference in expected utilities of the lotteries. Choice probabilities admit a stochastic utility representation if and only if they are complete, strongly transitive, continuous, independent of common consequences and interchangeable. Axioms of stochastic utility are consistent with systematic violations of betweenness and a common ratio effect but not with a common consequence effect. Special cases of stochastic utility include the Fechner model of random errors, Luce choice model and a tremble model of [Harless, D., Camerer, C., 1994. The predictive utility of generalized expected utility theories. Econometrica 62, 1251–1289].     

The Walras core of an economy and its limit theorem

The Walras core of an economy is the set of allocations that are attainable for the consumers when their trades are constrained to be based on some agreed price system, such that no alternative price system exists for any sub-coalition that allows all members to trade to something better. As compared with the Edgeworth core, both coalitional improvements and being a candidate allocation for the Walras core become harder. The Walras core may even contain allocations that violate the usual Pareto efficiency. Nevertheless, the competitive allocations are the same under the two theories, and the equal-treatment Walras core allocations converge under general conditions to the competitive allocations in the process of replication.     

没有舞台的歌舞剧--土族婚俗

土族婚礼是世间最奇特、最热闹、最壮观的婚礼,整个婚礼犹如一出精彩美妙的歌舞剧,演义着土族独特的婚礼风俗。 土族婚礼作为一出大型歌舞剧,大致可分为四场,前两场在女方家举行。迎娶新娘的前一日,女方家设嫁女宴,将新娘的嫁妆及新娘准备抬进男方亲朋的“针线”一一摆开,供人观赏,新娘在至亲女宾的陪伴下,唱起《哭嫁歌》……     

定理证明自动化的实现

在计算机上实现逻辑推理和定理证明的自动化,是人们探索很久的问题.本文从基本概念出发,较系统地分析了定理证明自动化的实现问题,并通过实例说明定理证明自动化的实现过程.     

Discrete fixed point theorem reconsidered

The aim of this note is to indicate an example that demonstrates the incorrectness of Iimura’s discrete fixed point theorem [Iimura, T., 2003. A discrete fixed point theorem and its applications. Journal of Mathematical Economics 39, 725–742] and to present a corrected statement using the concept of integrally convex sets.     

Discrete fixed point theorem reconsidered

The aim of this note is to indicate an example that demonstrates the incorrectness of Iimura’s discrete fixed point theorem [Iimura, T., 2003. A discrete fixed point theorem and its applications. Journal of Mathematical Economics 39, 725–742] and to present a corrected statement using the concept of integrally convex sets.     

VaR准确性检验的贝叶斯方法

文章对VaR准确性检验的失败检验法进行了分析,提出了一种新的失败检验法,即贝叶斯检验法。并与传统的正态近似法和Kupiec检验法进行了比较,说明了贝叶斯检验法的合理之处。     

A strict expected multi-utility theorem

This paper integrates two key approaches to the representation of incomplete preferences over lotteries. The main result strengthens the conclusion of the expected multi-utility theorem in Dubra, Maccheroni, and Ok (2004) by ensuring that all utility indices involved are Aumann utilities (i.e., yield a strictly increasing expectation). The advantages of the method are demonstrated by parametrizing maximal elements and by providing a novel characterization of Aumann utilities.     

“等效电源定理”的教学设计

为了培养学生的认知能力、应用能力和创新能力,从教学目标、学情、教学方法、教学组织、教学效果等5个方面对《等效电源定理》这一课的教学设计进行说明。