Natural bound in Kwiecinski's criterion for flatness

Kwiecinski has proved a geometric criterion for flatness: A morphism of germs of analytic spaces is not flat if and only if its fibre power has a vertical component, for some . We show how to bound using Hironaka's local flattener: If is not flat, then has a vertical component, where is the minimal number of generators of the ideal in of the flattener of .

     

Information patterns and Nash equilibria in extensive games: 1

In this paper we explore the relation between information patterns and Nash Equilibria in extensive games. By information we mean what players know about moves made by others, as well as by chance. For the most part we confine ourselves to pure strategies. But in Section 2 behavioral strategies are also examined. It turns out that they can be modeled as pure strategies of an appropriately enlarged game. Our results, applied to the enlarged game, can then be reinterpreted in terms of the behavioral strategies of the original game.     

The Study of Minimax Inequalities, Abstract Economics and Applications to Variational Inequalities and Nash Equilibria

In this survey, a new minimax inequality and one equivalent geometricform are proved. Next, a theorem concerning the existence of maximalelements for an LC-majorized correspondence is obtained.By the maximal element theorem, existence theorems of equilibrium point fora noncompact one-person game and for a noncompact qualitative game withLC-majorized correspondences are given. Using the lastresult and employing 'approximation approach', we prove theexistence of equilibria for abstract economies in which the constraintcorrespondence is lower (upper) semicontinuous instead of having lower(upper) open sections or open graphs in infinite-dimensional topologicalspaces. Then, as the applications, the existence theorems of solutions forthe quasi-variational inequalities and generalized quasi-variationalinequalities for noncompact cases are also proven. Finally, with theapplications of quasi-variational inequalities, the existence theorems ofNash equilibrium of constrained games with noncompact are given. Our resultsinclude many results in the literature as special cases.     

Ozone monitoring in a Mediterranean forest using diffusive and continuous sampling

Ambient ozone was measured in a forest in Castelporziano (Italy) characterised by the prevailing presence of Holm-oak trees (Quercus ilex L.) from June to November 2003. Two methods for measuring ozone were used: long-term monitoring using diffusive samplers at three heights within the canopy, and continuous monitoring at two heights using the UV method. Results for one week mean ozone levels above and below the canopy from the diffusive samplers were compared to those obtained using the automatic analyser at the same levels. A good correlation between the two sampling techniques was found. Continuous monitoring showed a daily cycle with a midday maximum and a nocturnal minimum. While the forest floor consistently had the lowest ozone concentration, there were no differences during most daytime hours. The midday maximum is clearly due to downward mixing with O₃-rich air from above. The night-time ozone decay within the canopy is the result of dry deposition of O₃ and most likely due to reaction with biogenically produced NO. AOT40 within and above the canopy mostly exceeded the critical levels.     

Borel stay-in-a-set games

Consider an n-person stochastic game with Borel state space S, compact metric action sets A ₁,A ₂,,A _n , and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state x and continuously on the actions (a ₁,a ₂,,a _n ) of the players. If the payoff to each player i is 1 or 0 according to whether or not the stochastic process of states stays forever in a given Borel set G _i , then there is an -equilibrium for every >0. AMS (1991) subject classification: 60G40, 91A60, 60E15, 46A55.     

On existence of undominated pure strategy Nash equilibria in anonymous nonatomic games: a generalization

In this paper, we generalize the exitence result for pure strategy Nash equilibria in anonymous nonatomic games. By working directly on integrals of pure strategies, we also generalize, for the same class of games, the existence result for undominated pure strategy Nash equilibria even though, in general, the set of pure strategy Nash equilibria may fail to be weakly compact. Received August 2001     

Al2O3Hx(x=1—3)分子团簇的结构与光谱研究

用密度泛函理论(DFT)的B3lyp方法在6-311++g(d,p)水平上对Al₂O₃H_x(x=1—3)分子的几何构型, 电子结构, 振动频率等性质进行了系统研究. 并给出了它们可能基态结构的总能量(E_T), 零点能(E_z), 摩尔热容(C_v), 标准熵(S), 原子化能(ΔE_m), 垂直电离能(IP)及垂直电子亲和能(E_A). Al₂O₃H和Al₂O₃H₂分子可能的基态的几何构型都为平面结构. Al₂O₃H₃的两个可能为基态的几何构型都是在立体Al₂O₃(D_3h)的几何结构基础上加三个氢原子构成. 这三个分子的能量最低结构为Al₂O₃H(²A′)C_s, Al₂O₃H₂(¹A′) C_s, Al₂O₃H₃ (²A) C₁.     

垂直电偶极子在球外侧电磁场的闭合解及验证

给出了理想导体球外侧垂直电偶极子激励电场的闭合解，解决了直接场的级数表达式的不连续性问题.同球外电磁场直接级数求和表达式的计算结果进行了比较.在相同的电磁模型下，利用闭合解对一种近似方法进行了验证：当垂直电偶极子以及场点在球体表面附近并且频率较低时，这两种方法的计算结果非常一致；当垂直电偶极子以及场点不在球体表面附近并且频率较高时，闭合解的计算结果逐渐出现了近似方法未出现的干涉现象.     

多组元化合物晶体生长过程中的双扩散对流现象

针对多组元化合物晶体的Bridgman生长过程,通过对液相区流场和浓度场的数值模拟,研究生长过程中容器内部双扩散对流与组分分布的情况.首先对比了三段场和梯度场炉壁温度设计情况下液相区的流体双扩散对流以及组分分布情况.在此基础上,针对梯度场炉壁温度条件,分析了不同参数的影响.结果表明:在溶质格拉晓夫数较大时,它的增大能够明显地削弱液相区的流体流动,从而使得界面附近的组分分布也产生变化;此外,拉晶速度的增大也能够使得液相区的双扩散对流受到抑制.     

Curvilinear smoothed particle hydrodynamics

We suggest a new set of equations to employ smoothed particle hydrodynamics (SPH) in a curvilinear space, and we refer to it as curvSPH. In classical SPH, the horizontal and vertical resolution of discretization is supposed to be equal for fluid particles. However, curvSPH makes the horizontal and vertical resolutions independent from each other. This is performed by transformation of physical space into an appropriate computational space with a different scale in horizontal and vertical directions. Solving a problem using SPH in a curvilinear space also provides capability to model curved boundaries as straight lines. In classical SPH, special care is needed to reach a uniform mass distribution along curved boundaries; however, producing uniform mass distribution along a line using curvSPH is straight forward. Different simulations, including simulation of a flip bucket are performed to demonstrate the applicability of the proposed method. Good agreement of results with experimental data and classical SPH confirms the capabilities of curvSPH. Copyright © 2016 John Wiley & Sons, Ltd.