Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

The visible and ultraviolet organic light-emitting diodes with germanium dioxide as facile solution-processed anode buffer layer

Germanium dioxide (GeO₂) aqueous solutions are facilely prepared and the corresponding anode buffer layers (ABLs) with solution process are demonstrated. Atomic force microscopy, X-ray photoelectron spectroscopy and ultraviolet photoelectron spectroscopy measurements show that solution-processed GeO₂ behaves superior film morphology and enhanced work function. Using GeO₂ as ABL of organic light-emitting diodes (OLEDs), the visible device with tris(8-hydroxy-quinolinato)aluminium as emitter gives maximum luminous efficiency of 6.5 cd/A and power efficiency of 3.5 lm/W, the ultraviolet device with 3-(4-biphenyl)-4-phenyl-5-tert-butylphenyl-1,2,4-triazole as emitter exhibits short-wavelength emission with peak of 376 nm, full-width at half-maximum of 42 nm, maximum radiance of 3.36 mW/cm² and external quantum efficiency of 1.5%. The performances are almost comparable to the counterparts with poly (3,4-ethylenedioxythiophene):poly (styrenesulfonate) as ABL. The current, impedance, phase and capacitance as a function of voltage characteristics elucidate that the GeO₂ ABL formed from appropriate concentration of GeO₂ aqueous solution favors hole injection enhancement and accordingly promoting device performance.     

一类稀疏效应下捕食┐被捕食者系统极限环的存在性和唯一性

本文研究捕食者种群具有线性密度制约的一类稀疏效应下捕食－被捕食者系统ｘ＝ｘ（ａｘ－ｃｘ３－ｂｙ），ｙ＝ｙ（－α＋βｘ－γｙ）．（＊）得到：（１）当Ａ１＜Ａ１，Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在极限环；（２）当Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在唯一极限环     

双层桥梁耦合系统的强迫振动

本文研究作为双层桥模型的梁方程耦合系统，利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理，得到了一个关于这种系统的解的存在性定理，它类似于ＭｃＫｅｎｎａ和Ｗａｌｔｅｒ文２中关于吊桥方程的一个定理。     

西部开发中能源配置模型的研究

开发西部丰富的能源资源,解决东部地区能源紧缺的矛盾,是东西部经济合作、优势互补、东西联动双赢战略研究的一项重要课题.在国家投资主体和市场经济条件下,以能源消费效益最大为目标,建立了基于边际效益均衡的能源空间配置优化模型;兼顾经济效益与环境效益的能源部门配置优化模型.结果显示,各地区、部门要获得更多的能源,就必须提高能源的使用效率,提高能源消费的边际效益,降低污染排放水平.     

Carathéodory's method for a class of dynamic games

The method of equivalent variational methods, originally due to Carathéodory for free problems in the calculus of variations is extended to investigate feedback Nash equilibria for a class of n-person differential games. Both the finite-horizon and infinite-horizon cases are considered. Examples are given to illustrate the presented results.     

烟气中Hg的氧化机理的研究

本文对Ｈｇ与Ｃｌ２在烟气中的氧化反应进行了热力平衡计算和动力学计算。平衡计算的结果表明有ＣＩ元索存在时Ｈｇ的氧化率为１００％，而在相同的条件下动力学计算纺果为Ｈｇ的氧化率在２０％～８０％之间变化，与实验结果吻合。实际的氧化反应是一种超平衡状态，不能达到理想的平衡状态。因此应采用动力学与热力平衡分析相结合的方法研究Ｈｇ在烟气中的反应机理。同时，计算结果显示Ｃｌ含量对Ｈｇ的氧化率的影响很大．     

共振下n维Lienard型方程的2π周期解

本文在跨共振点条件下证明n维Lienard型方程存在2π周期解.     

The effects of doubly excited states on ionization balance

The effects of highly doubly excited states on ionization balance are investigated. In the calculation, A Collisional-Radiative model in Detailed-Configuration-Accounting (DCA) is applied to population calculations for NLTE plasmas. Configuration-averaged rate coefficients that needed in the rate equations are obtained based on the first order perturbation theory. The Hatree-Fock-Slater self-consistent-field method is used to calculate the electron wave functions. The mean ionization stage of high-Z plasma Lu is presented. The comparison shows that the mean ionization stage increases more than 3 stages when doubly excited states 5l6l' and 5l5l' are not included in the population calculations.     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.