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关键词： Λ-Ω微分系统   弱中心   复合中心   中心条件  

摘要： 运用Poincaré方法及独特的变换技巧,研究一类高次Λ-Ω微分系统的弱中心问题,给出了这类系统以原点为中心的充要条件,解决了该高次微分系统的Poincaré中心-焦点问题.

关键词： 半无限规划   KKT充要条件   Greenberg-Pierskalla次微分   本质拟凸   Slater约束规范  

摘要： 最优性条件是最优化理论的一个重要研究方向,为优化算法的研究提供了重要的理论基础,且近几十年来在凸规划中已经获得丰富的理论成果。然而,拟凸函数的性质导致KKT条件在拟凸规划中很少被表示,尤其是半无限情形。考虑半无限拟凸规划,利用Greenberg-Pierskalla次微分的并集的凸包来刻画约束集的法锥,得到相应的KKT充分必要条件。本文定理4和5将文献[1]中定理5拓展到半无限拟凸规划。最后将本文定理5应用到半无限凸规划情形。

关键词： Differential evolution (DE)   Symbiotic organisms search (SOS)   Hybrid differential evolution and symbiotic   organisms search algorithm (HDS)   Shape and size optimization   Truss  

摘要： Although a large number of metaheuristic algorithms and their variants have been proposed for many engineering optimization problems, no paradigms hybridized by differential evolution (DE) and symbiotic organisms search (SOS) to concurrently improve the optimal solution quality and the convergence speed have been published thus far, especially for size and shape optimization of truss structures with multiple frequency constraints. Therefore, this article aims to propose a novel optimization algorithm as a cross-breed of the DE and the SOS, named HDS, for such problems. This algorithm can simultaneously and effectively enhance both global and local searching abilities by utilizing newly developed operators hybridized from the DE and SOS. An automatically adapted parameter is suggested for a better trade-off between those two capabilities. Furthermore, an elitist scheme is used in the selection phase to extract the best solutions for the next generation. As a consequence, the proposed methodology results in high-quality optimal solutions with a lower computational effort in comparison with two original methods, even many other optimization paradigms available in the literature. 26 benchmark mathematical functions are examined first. 5 numerical examples of shape and size optimization of truss structures are then investigated to validate the feasibility of the current paradigm.

关键词： 导数   隐零点   单调性   最值   不等式   范围  

摘要： 导数"隐零点"问题十分常见,探究学习需要掌握"隐零点"的含义与确定方法,以及问题突破的方法策略.文章剖析导数"隐零点",归纳解法,并结合实例加以探究,提出相应的建议.

关键词： 函数   恒成立   参变分离   导数   不等式  

摘要： 参变分离是求解不等式恒成立取值问题的常用方法,可有效规避分类讨论,部分情形中需引入洛必达法则,同时参变分离法求解时会涉及不同阶求导情形.文章对一道试题加以探究,并深刻剖析参变分离法,提出相应的学习建议.

关键词： 脉冲延迟微分方程   高阶数值方法   block-by-block方法   收敛性  

摘要： 针对一类非线性脉冲延迟微分方程,首先将其转化为等价的积分方程,然后利用修正的block-by-block方法对其离散化,得到了求解问题的高阶数值方法.最后利用数学归纳法证明了该数值方法是4阶收敛的,数值试验的结果验证了所获理论的正确性.

关键词： 张量   空间协变微分   时间协变微分   空间域上的协变微分学   时间域上的协变微分学  

摘要： 本文聚焦于张量分析学中两类对称性破缺现象。一是基础性概念的对称性破缺:我们有张量对坐标的协变微分(简称空间协变微分),然而,没有明确定义过如下概念--张量对时间的协变微分(简称时间协变微分)。二是基本理论的对称性破缺:我们有空间域上张量的协变微分学,但没有时间域上张量的协变微分学。本文致力于弥补破缺的对称性。基于近年来的研究进展,回顾协变性思想的拓展历史,展示张量的时间协变微分概念的抽象过程,综述时间域上张量的协变微分学的构建历程,揭示空间域上的协变微分学与时间域上的协变微分学之间的对称性。

关键词： 双渠道供应链   主从微分对策   定价分析  

摘要： 采用微分动态下的主从对策模型,构建市场动态需求函数和动态目标泛函。研究了制造商和零售商的均衡价格及利润,分析了市场份额比例、潜在市场需求量、双渠道交叉价格弹性系数等因素对供应链成员均衡价格及其利润的影响。最终研究结果表明,市场份额对供应链定价起到至关重要的作用。

关键词： 定积分   概率论   错误   剖析  

摘要： 定积分在概率论计算中发挥着极其重要的作用,但是学生在涉及相关定积分的计算中经常出现错误。为了消除这些错误,结合具体计算实例,分别列举分布函数、概率密度函数、数学期望求解过程中经常出现的错误,对产生错误的原因进行具体剖析,找出产生错误的根源并给出详细的解答,同时指出了教学注意事项,为教师在概率论教学中更加有效地处理涉及定积分的问题提供参考。

关键词： Impulsivity   Estrous cycle   Sigma-1 receptor   Impulsive action   Aripiprazole   MK-801  

摘要： Impulsive action can be defined as the inability to withhold a response and represents one of the dimensions of the broad construct impulsivity. Here, we characterized a modified differential reinforcement of low rates of responding (DRL) task developed in our laboratory, in which impulsive action is measured in ad libitum fed/ watered subjects. Specifically, we first determined the effects of both sex and estrous cycle on impulsive action by systematically comparing male and estrous-synchronized female subjects. In addition, we evaluated the convergent validity of this modified DRL task by testing the effects of the D2R/5HT2AR antagonist, aripiprazole, and the noncompetitive NMDAR antagonist, MK-801. Finally, we tested the effects of the selective antagonist BD1063 and agonist PRE-084 of Sigma-1 receptor (Sig-1R) on impulsive action using this modified DRL task. We found that female rats showed and increased inability to withhold a response when compared to males, and this effect was driven by the metestrus/diestrus phase of the estrous cycle. In addition, aripiprazole and MK-801 fully retained their capability to reduce and increase impulsive action, respectively. Finally, the selective Sig-1R antagonist, BD-1063 dose-dependently reduced the inability to withhold a response in both sexes, though more potently in female rats. In summary, we show that impulsive action, as measured in a modified DRL task which minimizes energy-homeostatic influences, is a function of both sex and estrous cycle. Furthermore, we validate the convergent validity of the task and provide evidence that Sig-1R antagonism may represent a novel pharmacological strategy to reduce impulsive action.