Imitation, local interaction, and coordination

This paper analyzes players’ long-run behavior in evolutionary coordination games with imitation and one-dimensional local interaction. Players are assumed to interact with their two neighbors and to imitate actions with the highest average payoffs. We find that the payoff-dominant equilibrium survives in the long run with positive probability. The results derive the conditions under which both risk-dominant-strategy and payoff-dominant-strategy takers co-exist in the long run. The risk-dominant equilibrium is the unique long-run equilibrium for the remaining cases. This study extends and complements the analyses of Eshel et al. (Am Econ Rev 88:157–179, 1998) and Vega-Redondo (Evolution, games, and economic behaviour, 1996). Combining Alós-Ferrer and Weidenholzer’s (Econ Lett 93:163–168, 2006; J Econ Theory 14:251–274, 2008) and our results, we conclude that players’ long-run behavior varies with imitation rules and information collecting modes. Finally, we show the convergence rate to all the long-run equilibria.     

聚氨酯的热分解研究进展

介绍了有关聚氨酯热性能研究的状况,着重阐述了聚氨酯在不同气氛下的热解机理及热解动力学的内容,同时也阐述了聚氨酯今后热解研究的发展方向。     

锑在酸、碱溶液中的极化行为Ⅰ.锑在酸、碱溶液中的阳极氧化

本文用经典极化曲线的方法和交流电测定电极表面状态的方法,对锑在氢氧化钾、硫酸和盐酸中的阳极过程进行研究,获得如下的结果:1.锑的阳极电位φ与极化电流密度i及pH之间的关系可由公式表示:φ=a+blogi-b'pHo在1-13.4N氢氧化钾溶液中,b=116毫伏,b'=115毫伏;在1-14N硫酸中,b=24毫伏,b'=48毫伏;在1-12N盐酸中,b=24毫伏,b'=-48至-54毫伏。a为常数。2.溶液pH对锑的阳极溶解速度的关系,λ=(∂logi/∂pH)_φ,在氢氧化钾溶液中,λ=1;在硫酸中,λ=2;在盐酸中λ'=(∂logi/∂pH)_φ=+2:即溶解速度在氢氧化钾或盐酸中随浓度增长而加速;在硫酸中则相反。3.假设锑在这些介质中的阳极反应具共同的基本步骤:Sb+O^-→SbO_吸+e^-,在氢氧化钾溶液中,过程的进行依靠类似的步骤,使SbO继续氧化而逐步形成Sb₂O₃,Sb₂O₄;后者在溶液中因不稳定而歧化为Sb_O3及Sb₂O₅。O^-假定通过如下步骤形成:OH^-→OH_吸+e^-,OH_吸+OH^-→O^-+H₂O。前者如为控制步骤则与实验数据相符合。在硫酸中则以共同步骤形成的中间物SbO失去电子而成SbO⁺为控制步骤。在盐酸中因氧化膜SbO被氯离子破坏而生成络离子SbCl₄^-为控制步骤。在酸中,O^-假定是由水分子的单电子放电产生:H₂O→O^-+2H⁺+e^-。4.由于氧化产物(Sb₂O₃,Sb₂O₅及吸附氧原子)在电极表面的积累,不论在酸或碱中,形成3-5个分子层,才导致表面钝化。氧的逸出发生在稳定钝化区的电位,这可能是O^-在钝化表面继续放电的结果。     

Kishner-Wolff改良法——X.数种C20羰基甾体化合物的还原

在螺旋内酯甾的结构与疗效关系研究中,我们准备用17α-羟基-17β-醛基化合物(Ⅰ)为原料以合成具反式构型的螺旋内酯甾(Ⅱ).Ⅰ系未知体.为证明其结构曾用改良的Kishner-Wolff还原法处理.Ⅰ还原后得一混合物,经氧化铝层析获得化合物(Ⅲ)及(Ⅳ),其纯品得率分别为13%及45%,两者均为已知体.Ⅳ经Oppenauer氧化成17β-甲基异睾丸素(Ⅴ);Ⅲ经微量臭氧氧化生成甲醛,因而得到进一步的证明.α-酮醇在用改良的Kishner-Wolff法还原时,α位置的羟基往往易被除去,而现在含α-羟基的醛基化合物(Ⅰ)经还原则主要生成羟基保留之物(Ⅳ).     

5-羟基嘧啶——Ⅳ.5-烷氧基-5-烷基-2-硫代巴比酸和有关化合物的合成

自烷氧基乙酸乙酯的乙氧草酰化,继以热裂去羰化反应,合成了一系列烷氧基丙二酸二乙酯(Ⅵ,R=n-C₃H₇,n-C₄H₉,iso-C₄H₉,iso-C₅H₁₁和C₆H₅CH₂);进一步烷基化,得到烷氧基烷基丙二酸二乙酯(Ⅶ,R'=CH₃,C₂H₅,n-C₃H₇和n-C₄H-9)。烷氧基烷基丙二酸二乙酯(Ⅶ)与脲、硫脲和与胍的缩合的容易程度相差颇巨。除苯甲氧基乙基丙二酸二乙酯曾与脲缩合生成相应的5,5-二取代巴比酸(I,Y=O)外,其他的各烷氧基烷基丙二酸二乙酯(Ⅶ)均未能与脲顺利地发生缩合。各烷氧基烷基丙二酸二乙酯(Ⅶ)与硫脲的缩合效果较佳,但其中仍有若干未能得到所期望的2-硫代巴比酸(I,Y=S)。两个系列的烷氧基烷基丙二酸二乙酯(Ⅶ,R=n-C₃H₇和C₆H₅CH₂;R'=CH₃,C₂H₅,n-C₃H₇,和n-C₄H₉)与胍的缩合非常顺利,生成相应的5,5-二取代-2-亚氨基巴此酸(I,Y=NH)。5-苯甲氧基-5-烷基-2-亚氨基巴比酸还进行了氢解,得到相应的5-羟基-5-烷基-2-亚氰基巴比酸(I,R=H,R'=烷基,Y=NH)。     

聚氨酯的FTIR光谱与热分析研究

采用原位傅里叶变换红外光谱法,研究了聚酯型聚氨酯和聚醚型聚氨酯在空气气氛中从室温到400 ℃之间的热解反应,实时考察了其在不同温度条件下分解残留物的基团特性。利用热分析技术考察了它们在不同气氛下从室温到700 ℃之间的热解反应。探讨了在有氧条件下的热解反应机理。结果表明聚酯型聚氨酯在空气中存在硬段和软段先后分解的两个阶段,而聚醚型聚氨酯则是硬段与软段同时分解。热分解结果也显示,硬段相同的聚氨酯,聚酯型聚氨酯的起始失重温度高于聚醚型聚氨酯,显示聚酯型的热稳定性强于聚醚型。同时聚氨酯在空气中的起始失重温度比在氮气中提前,说明氧气的存在能促进聚氨酯主链上C—C和C—O键的断裂。     

On the convergence rate of a recursively defined sequence

Consider the following recursively defined sequence: $\tau _1 = 1,\sum\limits_{j = 1}^n {\frac{1} {{\sum\nolimits_{s = j}^n {\tau _s } }}} = 1forn \geqslant 2, $ , which originates from a heat conduction problem first studied by Myshkis (1997). Chang, Chow, and Wang (2003) proved that $\tau _n = \log n + O(1) for large n.$ . In this note, we refine this result to $\tau _n = \log n + \gamma + O\left( {\frac{1} {{\log n}}} \right). $ . where γ is the Euler constant.     

Allee effects in a Ricker-type predator–prey system

We study a discrete host–parasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the host–parasitoid interaction are completely analysed. If the host's intrinsic growth rate is large, then the interaction may support multiple interior steady states. Linear stability of these steady states is provided.     

Dynamics of a system of three interacting populations with Allee effects and stocking

A model of three interacting populations where two populations engage in competition and two populations are in predator–prey type interaction is proposed and analysed. One of the two competing populations is subject to Allee effects and is also a pest population. The other competing population is regarded as a control agent and is the host for the predator population. There is a constant level of the external control agents released into the interaction at each generation after parasitism. We provide asymptotic dynamics of the competition subsystem and prove that a Neimark–Sacker bifurcation occurs for the host–parasitoid subsystem when the unique interior steady state loses its stability. The three interacting populations are impossible to persist for all positive initial conditions. Sufficient conditions based on the initial population size of the population with Allee effects are derived for persistence of the three populations.     

Dynamics of a population in two patches with dispersal

A two-dimensional discrete system of a species in two patches proposed by Newman et al. is studied. It is shown that the unique interior steady state is globally asymptotically stable if the active population has a Beverton–Holt type growth rate. If the population is also subject to Allee effects, then the system has two interior steady states whenever the density-independent growth rate is large. In addition, the model has period-two solutions if the symmetric dispersal exceeds a critical threshold. For small dispersal, populations may either go extinct or eventually stabilize. However, populations are oscillating over time if dispersal is beyond the critical value and the initial populations are large.