Perfect Packings of Squares Using the Stack-Pack Strategy

Abstract. We consider the problem of packing an infinite set of square tiles into a finite number of rectangular boxes. We introduce a simple packing strategy that we call stack-pack. Using this strategy, we prove that if 1/2 < t < 2/3, then the squares of side n ^-t , for positive integers n , can be packed into some finite collection of square boxes of the same area ζ(2t) as the total area of the tiles.     

Perfect Packings of Squares Using the Stack-Pack Strategy

   Abstract. We consider the problem of packing an infinite set of square tiles into a finite number of rectangular boxes. We introduce a simple packing strategy that we call stack-pack. Using this strategy, we prove that if 1/2 < t < 2/3, then the squares of side n ^-t , for positive integers n , can be packed into some finite collection of square boxes of the same area ζ(2t) as the total area of the tiles.     

有限理性双寡头博弈模型的复杂性分析

以Bowley博弈模型为核心,将寡头的调整速度作为企业的竞争策略,并对该模型Nash均衡点的稳定域进行分析;通过数值仿真把双寡头的策略区域分为均衡区、周期区和混沌区。研究发现双寡头博弈市场中,寡头为了获得更大的利润而不断改变自身产量策略,这是市场出现周期波动、甚至陷入混沌的根本内因.     

基于博弈论混合策略下的路径选择模型

为了缓解交通拥挤的状况,预测出行者路径选择行为是一项值得研究的工作.在混合策略下,根据出行者之间的博弈关系,定义了混合策略下的得益函数,并引入求解混合策略纳什均衡的一种新方法,即极值法,对出行者的路径选择博弈模型进行了求解,有效弥补了传统划线法的不足,最终得到每个出行者的最优选择,实现了博弈各方的平衡.通过算例,有效地说明了混合策略下出行者最可能做出的路径选择.     

基于Stackelberg博弈均衡的双寡头企业竞争策略

在具有网络外部性的Hotelling模型中,放松厂商定位必须局限于消费者空间的假设,运用Sackelberg博弈来研究产品具有不同边际成本结构的企业竞争策略。相比较于传统的Nash博弈价格均衡结果,当不局限厂商定位空间时,两厂商通过Sackelberg价格博弈可以选择更大的产品差异性。如果边际成本相等,两厂商在Stackelberg博弈均衡中都获得比在Nash博弈均衡中更大的市场利润,当不局限厂商定位空间时,市场先进人者获得先动优势,当局限厂商定位空间时,市场后动者获得后动优势。     

非营利组织财务开发策略的博弈分析——与政府和营利组织合作视角

政府和市场双双失灵之时,产生了非营利组织,构筑了现代三元社会结构.作为第三部门的非营利组织,为社会提供公共产品和服务配送,在中国的转型社会中肩负着太多的责任,其发展状况是中国社会能否成功转型的关键.然而,资金瓶颈制约着中国非营利组织的生存和发展.迄今为止,系统研究非营利组织财务开发的文献甚少.尝试借助利益相关者、关系契约、信号等理论,建构了一个博弈分析的框架,基于非营利组织与政府和营利组织合作视角,对非营利组织财务开发策略的理论支撑进行了探索性研究,并提出了一系列财务开发策略,试图缓解或解决其所面临的主要困境,以实现非营利组织健康可持续发展.     

剔除相关性的最小二乘研究

本文提出了一种新的回归模型,剔除相关性的最小二乘,它有效的克服了变量间的相关性,兼顾到变量的筛选。并与最小二乘、向后删除变量法、偏最小二乘比较分析。发现剔除相关性的最小二乘能很好的处理自变量间多重相关性,对变量进行有效的筛选,克服了回归系数反常的现象。     

汽车生产厂家的定价策略博弈模型

讨论了企业在经营管理中的最优化问题,构建了汽车行业在寡头垄断市场中各厂商之间的定价博弈模型.利用统计学中的多元线性回归模型给出两种不同型号汽车的销售量和价格的经验的需求函数关系式,检验了此模型的拟合优度,对其整体显著性的进行了F检验,并对偏回归系数的显著性进行了t检验,探讨了两寡头垄断企业的产品的需求函数为二元线性函数的伯特兰德模型,获得了其纳什均衡解的一般结论,并给出了某两型号汽车的定价博弈的具体均衡结果.     

转让定价视角下的我国企业对外投资战略博弈

我国企业通过对外投资可以拥有在分处国内外的两个实体间开展转让定价的机会,以此来对抗跨国公司在华通过转让定价谋求战略竞争优势,获取公平竞争机会.以单市场双寡头古诺竞争下的转让定价决策模型为基础,构建了我国企业对外投资后在国内和国外两个市场与跨国公司进行战略性转让定价博弈模型,发现无论我国企业与跨国公司相比是否具有成本优势,都应该通过对外投资获取开展战略性转让定价机会,与跨国公司进行公平竞争.     

Latin Squares, Partial Latin Squares and Their Generalized Quotients

A (partial) Latin square is a table of multiplication of a (partial) quasigroup. Multiplication of a (partial) quasigroup may be considered as a set of triples. We give a necessary and sufficient condition for a set of triples to be a quotient of a (partial) Latin square. Received: April, 2003     

The Complexity and Effectiveness of Prediction Algorithms

The problem of predicting an arbitrary sequence x₁x₂x₃ · · · is considered with x_{t + 1} being predicted from an analysis of the word x₁x₂ · · · x_t. There are no presumptions concerning the probability structure on this process. The relation between prediction effectiveness and Kolmogorov complexity is established. Then the Hausdorff dimension of sets of sequences for which effective methods of prediction exist is estimated. The prediction method which is asymptotically superior to other arbitrary ones realized by finite automata is constructed.     

The Complexity of Gene Placement

We focus on algorithmic problems related to deriving gene locations on DNA sequences of closely related species by using comparative mapping data. Conventional genetic mapping generates intervals on the DNA sequence of given species for potential gene positions. The simultaneous analysis of gene intervals in related species, e.g., human and mouse, may eliminate some of the ambiguities and lead to better estimates of gene locations. We address the problem of eliminating the ambiguities in gene orders by means of minimizing the number of conserved regions among the species. This is equivalent to the problem of choosing gene coordinates (gene placement) that satisfy the genetic mapping constraints and minimize the breakpoint distance between genomes. We first show that the gene ordering problem is hard: there is no polynomial-time approximation scheme unless P = NP, even under the restrictions that: (1) the order of genes in one of species is known, or (2) at most two intervals overlap at any location on the map of any of the species. Then we provide two polynomial-time algorithms under restriction (1) above; the first approximates the problem within a factor of 3, and the second exactly solves the problem under the additional restriction that (3) no more than O((log n)/(log log n)) intervals overlap at a location on the map of any of the species. We also prove the tractability of the general problem when there is a single conserved region (i.e., when there exists a gene placement resulting in identical gene orders).     

Smash积的复杂度

给定任意一个有限维代数A,记其复杂度为C（A）.本文的主要结果是：如果有限维Hopf代数H和H是半单的,则对任意有限维H-模代数A,有C（A#H）=C（A）.利用此等式,可以计算一些代数的复杂度.     

The Complexity of Stratification Computation

This paper investigates the complexity of stratification computation for semialgebraic sets. An upper bound for the computation of canonical stratifications is given for a wide class of stratifying conditions called here admissible. For such conditions, the stratifying process is at most doubly exponential in the depth of the stratification. Usual conditions of regularity like Whitney conditions (a) and (b) or Bekka condition (C) are admissible. A useful criterion and tools are given in order to prove easily other admissibilities. Received February 15, 1995, and in revised form January 29, 1997 and May 6, 1997.     

二人零和连续对策上的判断与最优策略间的关系

引进了二人零和连续对策上的判断，判断块以及在判断下的最优策略等概念．研究了判断下的最优策略集与经典最优策略集之间的关系，得到了一些在理论上有趣而且有用的结果．     

贷款市场中基于最优博弈策略的激励契约

信贷风险是商业银行主要的信用风险,信贷风险分为企业的经营风险和企业违约赖账的道德风险.本文运用相关知识建立了双方的博弈模型,讨论了均衡状态下双方的最优博弈策略,通过制定合理的利率水平和惩罚力度来激励借款人按合同规定投资某项目而不去投资高风险项目,以达到有效控制道德风险的目的.     

Squares and their centers

We study the relationship between the size of two sets B, S ? R², when B contains either the whole boundary or the four vertices of a square with axes-parallel sides and center in every point of S. Size refers to cardinality, Hausdorff dimension, packing dimension, or upper or lower box dimension. Perhaps surprisingly, the results vary depending on the notion of size under consideration. For example, we construct a compact set B of Hausdorff dimension 1 which contains the boundary of an axes-parallel square with center in every point in [0, 1]², prove that such a B must have packing and lower box dimension at least 7/4, and show by example that this is sharp. For more general sets of centers, the answers for packing and box counting dimensions also differ. These problems are inspired by the analogous problems for circles that were investigated by Bourgain, Marstrand and Wolff, among others.