Price competition in the Hotelling model with uncertainty on costs

For the linear Hotelling model with firms located at the boundaries of the segment line, we study the price competition in a scenario of incomplete information in the production costs of both firms. We introduce the bounded uncertain costs (BUC) condition in the production costs and we prove that there is a local optimum price strategy if and only if the BUC condition holds. We compute explicitly the local optimum price strategy and we prove that it does not depend upon the distributions of the production costs of the firms, except on their first moments. We prove that the ex-post profit of a firm is smaller than its ex-ante profit if and only if the production cost of the other firm is greater than its expected cost.     

Flexibility in a Stackelberg leadership with differentiated goods

We study the effects of product differentiation in a Stackelberg model with demand uncertainty for the first mover. We do an ex-ante and ex-post analysis of the profits of the leader and of the follower firms in terms of product differentiation and of the demand uncertainty. We show that even with small uncertainty about the demand, the follower firm can achieve greater profits than the leader, if their products are sufficiently differentiated. We also compute the probability of the second firm having higher profit than the leading firm, subsequently showing the advantages and disadvantages of being either the leader or the follower firm.     

Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities

In this paper, the problem of chaos synchronization between two different uncertain chaotic systems with input nonlinearities is investigated. Both master and slave systems are perturbed by model uncertainties, external disturbances and unknown parameters. The bounds of the model uncertainties and external disturbances are assumed to be unknown in advance. First, a simple linear sliding surface is selected. Then, appropriate adaptive laws are derived to tackle the model uncertainties, external disturbances and unknown parameters. Subsequently, based on the adaptive laws and Lyapunov stability theory, a robust adaptive sliding mode control law is designed to guarantee the existence of the sliding motion. Two illustrative examples are presented to verify the usefulness and applicability of the proposed technique.     

不确定非自治混沌陀螺仪在非线性输入下的有限时间稳定性

陀螺仪是一个非常有趣,又是永恒的非线性非自治动力系统课题,它可以显示出非常复杂的动力学行为,如混沌现象.在一个给定的有限时间内,研究非线性非自治陀螺仪鲁棒稳定性问题.假设陀螺仪系统受到模型不确定的外部扰动而摄动,系统参数并不知道,同时考虑了非线性输入的影响.为未知参数提出了适当的自适应律.以自适应律和有限时间控制理论为基础,提出非连续有限时间控制理论,来研究系统的有限时间稳定性.解析证明了闭循环系统的有限时间稳定性及其收敛性.若干数值仿真结果表明,该文的有限时间控制法是有效的,同时验证了该文的理论结果.     

最大度不小于3的图的星全色数的一个上界

对圈、扇和轮作了简单的剖分,得到了其剖分图的星全色数,并运用Lovasz局部引理证明了若G(V,E)是一个最大度为△≥3的简单无向图,则Χ_(st)(G)≤22Δ~2.     

不确定环境下服务资源配置优化

在服务资源配置过程中,按维修状态将服务对象分成三类:完全维修、部分维修及最小维修.由于维修服务的特性,服务成本与服务时间均是一个模糊数,并且维修对象在服务时所处的维修状态也具有一定的不确定性.针对这类情况下的服务资源配置问题,提出了同时考虑模糊服务成本和模糊服务时间及不确定维修状态的最小化服务成本为优化指标的服务资源配置模型.在模型的求解过程中采用多粒子群算法,通过仿真计算表明了该方法的可行性和有效性.     

空气下无配体钯催化二苯胺和卤代芳烃的C—N偶联

研究了空气下无配体Pd(OAc)2在弱碱碳酸钾存在下催化二苯胺和溴代芳烃的C—N偶联合成三苯胺类化合物.与传统合成方法相比,该反应可以在无配体存在下在空气和温和的条件下进行,即,无需无水无氧操作条件,操作特别方便.催化剂用量、碱、溶剂、反应温度、反应时间等因素对反应的影响均做了考察.优化的反应条件是:在Pd(OAc)2(3 mol%)和K2CO3(1.5 equiv.)存在下,二苯胺和溴代芳烃在DMSO中在空气下在90℃加热24 h.溴代芳烃上的吸电子基团和二苯胺上的给电子基团有利于该偶联反应的进行,其中4-硝基三苯胺的产率高达93%.     

大学物理实验中A类不确定度探究

由于许多大学物理实验教材对A类不确定的估算方法不够明了透彻,给大学物理实验教学带来不便,也影响了学生的数据处理,本文对大学物理实验中A类不确定度的估算进行了探究.     

利用广义不确定关系计算Reissner-Nordstrm-de Sitter黑洞的统计力学熵

利用广义不确定关系修正的态密度方程并采用Wentzel-Kramers-Brillouin(WKB)近似方法,计算了Reissner-Nordstrm-de Sitter(RNdS)黑洞时空中标量场的统计力学熵.结果表明,由这种方法得到的黑洞熵与它的内、外视界面积和宇宙视界面积之和成正比,这与采用其他方法所得的结果一致,从而揭示了黑洞熵与视界面积之间的内在联系,也进一步表明了黑洞熵是视界面上量子态的熵,是一种量子效应.     

基于测量不确定度评定的数据处理方法

中利用直接测量量和间接测量量的测量不确定度评定方法,根据误差理论的教学经验与实践,给出了直接测量量和间接测量量的实验数据处理的具体方法步骤,并结合实际的测量数据,举例说明了如何运用直接测量量和间接测量量的实验数据处理方法,既便于学生理解又利于他们更好地掌握。