解析函数的几个等价命题及其应用

解析函数是复变函数论研究的主要对象,它具有重要的性质和广泛应用。本文在教材内容的基础上,进一步探讨解析函数的几种等价条件,文章首先给出了解析函数的四种不同的定义,然后运用柯西积分定理、泰勒定理及递推的方法,证明了这四种不同定义彼此相互等价;探讨了它们的一些应用,从而使学生能够用从多种方法判断函数是否解析,为以后应用解析函数打下了坚实的基础。     

凸函数的等价证明及判定

凸函数是微积分学习中的一个重要内容,在微积分中占有重要地位,其定义、性质经常用来判断一个函数是否为凸函数,凸性是函数的一种重要性质,具有这种性质的函数在近代分析和优化两大领域中起着重要的作用,本文深入地讨论了凸函数的几种不同定义的等价性,判定定理及凸函数的应用,给出比较全面判断一个函数是否为凸函数的方法。     

与有弹性钉住通货膨胀相一致的货币政策规则

在与有弹性钉住通货膨胀相一致的货币政策动态优化问题中，本文将货币政策工具对不同目标变量影响的时滞引入损失函数，并分别在确定性等价条件下，以及模型参数不确定性条件下给出了最优的利率反应函数，进而讨论了模型参数以及模型参数不确定性对最优利率反应函数的影响。     

中国工业部门生产函数的参数估计

生产函数表示投入与产出关系的特定技术关系,用于说明一组生产要素投入所能得到的最大产出量。在每一种既定的技术条件下,都存在着一个生产函数。 一、函数选择 函数选择是参数估计的前提。在对生产函数进行估计之前,必须作出几项选择。 第一个选择我们需要确定,究竟是选择基本的生产函数还是对偶的成本函数。给定总成本的定义和生产者均衡的必要条件,就可以把总成本表示为所有投入价格和产出水平的函数,即成本函数、成本函数是生产函数的对偶,也是对于生产单位技术的等价描述。正是因为在描述生产技术方面这两种函数不分高低,所以…     

辅助函数的构造方法及其在等式证明中的应用

证明不等式的方法有很多,构造辅助函数就是转化问题的重要方法之一。辅助函数的构造就是在所要证明的命题与需要应用的已知定理之间,如果缺少一个一个条件,就可以构造一个具备所缺条件和所证结论相联系的辅助函数,从而达到证明不等式等内容。微分中值定理在微积分中占有非常重要的地位,微分中值定理是连接导数与应用的桥梁。通过研究了几种构造辅助函数的方法证明不等式,并给出相应的证明过程,最后总结相应的构造技巧。     

李嘉图等价定理在中国的验证

本文通过对1984-2013年税收、公债和收入对消费的影响程度来论证李嘉图等价定理在中国的适用性。结果证实:李嘉图等价定理因其严格的假设条件在中国不成立,并在实证的基础上,提出了政府在运用宏观调控手段时要注意公债与税收带来不同方面影响的建议。     

招标支付等价性及最优保留价博弈分析

维克里(Vickrey,1961)提出了拍卖中的收益等价性定理,梅耶森(Myerson,1981)、赖利和萨缪尔森(Riley and Samuelson,1981)几乎同时证明了在一般性的条件下维克里提出的拍卖中的收益等价性定理是成立的.本文从招标的角度出发,对招标中支付等价性以及招标人的最优保留价进行博弈分析,给出了招标支付等价性定理和最优保留价公式,并加以应用和分析.     

关于中值定理应用中辅助函数的构造

根据微分中值定理的证明及应用，给出了如何根据已知条件和结论巧妙地构造辅助函数两种有效方法，解决了微积分学中一些有关中值定理应用的证明问题，并列举了几个例子。     

均值方差偏好和下方风险控制下的动态投资组合决策模型

本文在均值方差框架下，研究了下方风险控制下的动态投资组合问题。在目标函数中考虑了投资组合的最坏结果，利用标准的期权定价理论，给出了最优投资策略的解析式。该投资策略等价于一个关于“资产”最小二阶矩组合的欧式看跌期权和无风险资产的组合，而且两基金分离定理仍然成立。     

一个新数论函数及其均值

对任意正整数n,设h(kn)表示不大于n的最大k次幂,以及h(kn)=n-IK(kn),利用初等方法和解析方法,研究了新定义的数论函数h(kn)的均值性质;并给出了一个较强的均值渐近公式。     

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces.     

环保工程项目管理中的供应商评选研究

层次分析法因其简洁明晰,使用方便而得到广泛应用,但在环保工程项目领域的研究应用相对较少,基于环保工程项目的特点,本文建立有针对性的符合项目实际需求的指标体系,利用层次分析法求解,从而为工程项目采购一线的管理者提供一种快速有效的科学决策方法,评选出可靠的供应商,降低潜在的风险,对环保工程项目采购管理而言是一个很重要的环节。     

无穷远点留数的一个重要性质及应用

利用无穷远点留数的性质,给出了复变函数中一类周线积分∫C(fz)dz计算的简单方法。     

Estimators without moments: The case of the reciprocal of a normal mean

The appropriateness of using an estimator which has no moments depends very much on the loss function. This is illustrated by an example. In this paper the properties of various estimates of the reciprocal of a normal mean are analyzed with respect to different kinds of loss functions.     

利用构造函数的思想探究罗尔定理的一些应用

罗尔定理在一元微分学处于很重要的地位,本文通过构造函数的思想来探究罗尔定理的应用。     

Universal Pareto dominance and welfare for plausible utility functions

We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents’ preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto undominated if there is no other lottery that Pareto dominates it for all plausible utility functions. We show that, under fairly general conditions, a lottery is universally Pareto undominated iff it is Pareto efficient for some vector of plausible utility functions, which in turn is equivalent to affine welfare maximization for this vector. In contrast to previous work on linear utility functions, we use the significantly more general framework of skew-symmetric bilinear (SSB) utility functions as introduced by Fishburn (1982). Our main theorem generalizes a theorem by Carroll (2010) and implies the ordinal efficiency welfare theorem. We discuss three natural classes of plausible utility functions, which lead to three notions of ordinal efficiency, including stochastic dominance efficiency, and conclude with a detailed investigation of the geometric and computational properties of these notions.     

Autocorrelation Functions

We explain the connection between autocorrelation functions of stationary continuous time processes and real characteristic functions, and review sufficient conditions for a function to be an autocorrelation function. We also give probabilistic constructions for time series reformulations of Pólya’s (1949) Theorem on characteristic functions, and Young’s (1913) classical theorem in Fourier analysis. Our constructions allow the marginal distribution of the process to be any infinitely divisible distribution with finite variance.     

Mean value theorem for convex functions

Closed proper convex functions have many properties in common with differentiable functions such as continuity and one-sided directional derivatives. In this paper it is shown that there exists a mean value theorem for such functions with the gradient vector in the differentiable case replaced by an element of the subdifferential in the convex case.Under compactness of the isoquant sets, (minus) the cost functions are convex and with the theorem above it is easy to show that under incomplete specialization and constant returns to scale the prices of international goods determine uniquely the prices of domestic goods if the isoquant sets are linearly independent.     

Locating the competitive relation of global logistics hub using quantitative SWOT analytical method

Evaluating the competitive position of location develops global logistics hub (GLH) is a multiple criteria decision-making (MCDM) problem and it is important for governor to implement suitable strategies appropriate its environment. SWOT analysis is very important in the process of strategic formulation. Under many conditions, the evaluative criteria (indicators) are mixed with quantitative/qualitative values and the values for qualitative criteria are often imprecisely defined for decision-makers. A quantified SWOT analytical method, that integrates the method of fuzzy Analytic Hierarchy Process (AHP) method, was proposed to provide more detailed and quantified data for SWOT environmental analysis to assess the competitive relation for locations develop different types’ GLH in Pacific–Asian region. Integrating the concept of Grand Strategy Matrix (GSM), a suitable competing strategy could be suggested for location developing GLH in accordance with its competitive position.