Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term

Necessary and sufficient conditions are established in this paper for the existence of positive- and/or negative-definite solutions to the algebraic Riccati equation with indefinite coefficient. An iterative procedure is also given for computing such a solution.Project supported by the National Science Foundation of China and by the special program of the State Education Commission of China under grant 9033507.     

Chip-Firing Games on Directed Graphs

We consider the following (solitary) game: each node of a directed graph contains a pile of chips. A move consists of selecting a node with at least as many chips as its outdegree, and sending one chip along each outgoing edge to its neighbors. We extend to directed graphs several results on the undirected version obtained earlier by the authors, P. Shor, and G. Tardos, and we discuss some new topics such as periodicity, reachability, and probabilistic aspects.Among the new results specifically concerning digraphs, we relate the length of the shortest period of an infinite game to the length of the longest terminating game, and also to the access time of random walks on the same graph. These questions involve a study of the Laplace operator for directed graphs. We show that for many graphs, in particular for undirected graphs, the problem whether a given position of the chips can be reached from the initial position is polynomial time solvable.Finally, we show how the basic properties of the probabilistic abacus can be derived from our results.     

Phenomenology of nonlocal cellular automata

Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting edge-of-chaos nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled selectors or multiplexers. It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.     

黑龙江省篮球裁判员培养现状调查与对策研究

采用文献资料法、问卷调查法、访谈法和数理统计法,对黑龙江省篮球裁判员的基本现状进行了调查研究,旨在加强黑龙江省篮球裁判员的队伍建设.     

企业并购决策的非合作博弈

在经济全球化背景下,企业并购活动越发频繁,如以外资渗入中国化工行业为例.在企业并购活动中,科学合理的并购决策无疑是企业并购成功的关键.基于非合作博弈理论,建立了二阶段三人非合作博弈模型,对企业并购活动中的均衡、战略、报价以及期望收益进行了详尽的分析,为科学决策的做出提供理论指导.     

模糊信息静态伯特德双寡头博弈分析

在分析了厂商的市场信息具有模糊性的基础上,分别给出了2个模糊信息静态伯特德双寡头博弈模型,并运用模糊数学理论及方法,分别求出了这两种情形下博弈的均衡解.     

在技术训练中培养运动员的"篮球意识"

结合篮球技术训练，加强对运动员篮球意识的培养，能够明显提高运动员的篮球技战术水平，以适应现代篮球比赛高速度、高强度和强对抗的要求。采用理论阐述和现状分析的方法，对影响运动员篮球意识的相关因素和培养方法与途径做了较详细的介绍。     

浅析篮球运动在高校学生休闲体育中的价值

休闲体育是因终身教育思想而兴起的一种体育形式。篮球运动无论从场地设施、环境条件、学生休闲体育观念还是体育文化个性等方面都是比较适合高校学生进行休闲活动的体育项目之一，其价值和意义更为突出。     

篮球运动中的假动作

从技术的角度,对篮球运动中假动作进行分析,提出篮球假动作的运用方法.     

渠道管理中的厂商与分销商的博弈分析

分销渠道管理中生产厂商与分销商的良好合作是进行优势互补、提高渠道竞争力和适应市场变化的有效手段。通过对生产厂商与分销商合作交易特征介绍和交易条件的假设，基于相互之间合作的关系建立混合博弈模型，并进行分析，找出影响双方合作关系的因素和实行稳定作的条件；然后，进一步对生产厂商与分销商的长期合作进行有限次重复博弈分析，找出影响双方合作关系的条件，最后，根据推论分析的结果，指出生产厂商与分销商建立良好的合作关系应采用的策略。