Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.     

无信号控制路口行人过街行为特征及博弈模型分析

过城市实地行人问卷调查及过街行为分析,描述了行人过街重要行为特征,在此基础上,引入了交通工程相关结果,针对无信号控制路口行人过街问题,构建了行人先行和车辆先行的扩展式行人过街冲突博弈模型。纳什均衡分析结果揭示了行人过街冲突的机理,并给出了各种冲突情况下相应参数临界分析。预期结果对行人过街设施的管理与建设也具有意义。     

低碳经济下环境NGO参与企业碳减排的演化博弈分析

针对我国经济可持续发展中不可回避的碳排放问题,构建了企业碳减排过程中企业、政府和环境NGO的三方演化博弈模型及其动态复制方程,解出了该模型的10个均衡点并对均衡点的局部稳定性进行了分析,最后运用Matlab工具对企业、政府和环境NGO的交互行为演化过程进行数值仿真,分析各参数变动对系统演化结果的影响,探究影响系统演化至理想状态的影响因素及其影响机理。研究结果表明:影响企业是否采取低碳生产方式的主要影响因素是企业低碳生产所需付出的成本;政府是否调控主要取决于政府对企业的罚款和政府的调控成本;环境NGO是否监督主要取决于政府和公众对其的资助与监督成本的大小。     

基于Moran过程的消费者众筹策略演化动态

考虑混合均匀的N个消费者众筹策略演化动态,每个消费者可选择参与众筹或者不参与众筹两个策略。基于Moran过程的扎根概率,计算出有限消费者群体中,参与众筹策略和不参与众筹策略成功入侵的概率。比较个体扎根的概率和中性入侵的概率大小,分别得到两策略在强选择性和弱选择性强度下占优的条件。研究发现,强选择性条件下,消费者数量小于某个数值时,不参与众筹策略演化稳定侵占整个种群,众筹融资失败。弱选择性条件下,消费者依据净收益和支出成本两因素决定是否参与众筹,净收益大于支出成本三倍,演化稳定于众筹成功,净收益小于支出成本二分之三倍,演化稳定于众筹失败。     

Measuring the interactions among variables of functions over the unit hypercube

By considering a least squares approximation of a given square integrable function f:n[0,1]→R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize several properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of f or, under certain natural conditions on f, as an expected value of the derivatives of f. Finally, we discuss a few applications of the interaction index in aggregation function theory.     

篮球持球突破技术运用分析

篮球持球突破是一项应用十分广泛的个人进攻技术。通过对篮球持球突破技术的运用以及在训练和教学中如何使这一个人技术融于整体的战术中提出一些思考和分析,以期为教学和训练提供参考。     

Quasi-Equilibrium Problems and Constrained Multiobjective Games in Generalized Convex Space

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＸａｎｄＹｂｅｎｏｎｅｍｐｔｙｓｅｔｓａｎｄ2 ＸｂｅｔｈｅｆａｍｉｌｙｏｆａｌｌｓｕｂｓｅｔｓｏｆＸ .ＬｅｔＴ :Ｘ→Ｙｂｅａｓｉｎｇｌｅ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,Ａ :Ｘ→ 2 Ｘｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,ψ :Ｘ×Ｙ×Ｘ→Ｒ∪ ±∞ ａｎｄｆ:Ｘ×Ｙ→Ｒ∪ ±∞ ｂｅｔｗｏｆｕｎｃｔｉｏｎｓ.Ｔｈｅｇｅｎｅｒａｌｑｕａｓｉ＿ｅｑｕｉｌｉｂｒｉｕｍｐｒｏｂｌｅｍＧＱＥＰ (Ｔ ,Ａ ,ψ)ｉｓｔｏｆｉｎｄ ^ｘ∈Ｘｓｕｃｈｔｈａｔ^ｘ∈Ａ( ^ｘ) ,ψ( ^ｘ ,Ｔ^ｘ ,ｙ)≤ 0…     

LINEAR QUADRATIC NONZERO-SUM DIFFERENTIAL GAMES WITH RANDOM JUMP

The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.     

三方非对称进化博弈行为分析

随着政府涉入领域以及社会合作谈判领域的增多,三方非对称进化博弈越来越多地出现在现实生活中.但目前国内外对该类型的进化博弈研究甚少,这显然不利于正确地解释和预测该类型的博弈行为.基于此,运用进化博弈论中的“复制动态”思想,对三方非对称的2×2×2进化博弈进行了渐进稳定性分析,完整地给出了其定性行为的等价定量分类和各参与主体不同情况下的稳定性策略,并且用三维立体图演示了不同策略组合的渐进趋势,从而为研究现实生活中该类型的博弈行为提供了一种理论依据.     

人力资本培训投资的博弈分析

针对人力资本组合投资模式仅定性分析职员和企业对人力资本投资行为的特点,应用博弈论进行了相应的定量分析,将贝克尔投资模式与组合投资模式相结合,建立了确定企业投资比率的计算公式,为企业进行人力资本培训投资提供了定量的决策依据。