一个对偶问题与对偶性质

本文对非可微凸规划问题建立了一个新的对偶问题 ,并证明其对偶性质 ,如弱对偶性 ,强对偶性及逆对偶性。     

泛函中的两个对偶定理

本文利用＊隔离定理,证明了Ｍａｚｕｒ定理和凸集的最佳逼近元存在性定理的对偶定理．     

存贮问题的优化算法

本文根据经济模型的特殊结构,利用对偶线性规划的理论和其它技巧,简化求解过程,有利于模型的普及应用.     

Optimal DB-PAYGO pension management towards a habitual contribution rate

In this paper, we propose a new objective function, which reflects the costs of unstable contribution risk and discontinuity risk in DB-PAYGO pension system. The problem is to minimize the quadratic deviation between the actual contribution rate and a habitual target and the quadratic proportional deviation of the pension accumulation. A modified non-negative constraint of the contribution rate is added, which together with a stochastic habitual target process, causes difficulty in solving the minimization problem by Lagrange dual method. The results are split into two cases which depend on the habit-adjusted adequacy of the pension budget. In the inadequate case, the optimal contribution rate reveals a hump shape curve with respect to time, which is different from the exponential growth curve of the model with a fixed target. By moderately raising the contribution rate in the initial phase, it helps to increase the accumulation and reduce the contribution burden of the follow-up policyholders. Notably, the hump shape curve is a more practical policy, because of that the exponential growth curve raises anxiety about the unlimited growth of the contribution rate and harms the confidence in the sustainability of the pension fund. We also study the impacts of the certain trend in demography, and the uncertain fluctuations in salary and investment on the optimal control policies.     

Development of a capillary electrophoresis method for the determination of the chiral purity of dextromethorphan by a dual selector system using quality by design methodology

Dextromethorphan is a centrally acting antitussive drug, while its enantiomer levomethorphan is an illicit drug with opioid analgesic effects. As capillary electrophoresis has been proven as an ideal technique for enantiomer analysis, the present study was conducted in order to develop a capillary electrophoresis‐based limit test for levomethorphan. The analytical target profile was defined as a method that should be able to determine levomethorphan with acceptable precision and accuracy at the 0.1 % level. From initial scouting experiments, a dual selector system consisting of sulfated β‐cyclodextrin and methyl‐α‐cyclodextrin was identified. The critical process parameters were evaluated in a fractional factorial resolution IV design followed by a central composite face‐centered design and Monte Carlo simulations for defining the design space of the method. The selected working conditions consisted of a 30/40.2 cm, 50 μm id fused‐silica capillary, 30 mM sodium phosphate buffer, pH 6.5, 16 mg/mL sulfated β‐cyclodextrin, and 14 mg/mL methyl‐α‐cyclodextrin at 20°C and 20 kV. The method was validated according to ICH guideline Q2(R1) and applied to the analysis of a capsule formulation. Furthermore, the apparent binding constants between the enantiomers and the cyclodextrins as well as complex mobilities were determined to understand the migration behavior of the analytes.     

基于模糊博弈视角的企业联盟“双循环”合作对策研究

企业合作在“双循环”新发展格局下呈现出更多的模糊特征,能否形成稳定的模糊合作格局及持续合作的收益再分配策略成为合作联盟的关注点。将广义模糊超量博弈和模糊凸博弈及其广义解集应用到“双循环”新发展格局下企业联盟合作与收益再分配中,提出最大广义模糊超量博弈模型及其广义模糊谈判集,并基于最大广义模糊超量博弈均衡性的视角,对模糊凸博弈下广义模糊谈判集与核心的等价性质进行论证。研究结果不仅满足了“双循环”新发展格局下合作企业以部分资源参与合作的意愿,及企业联盟模糊凸合作博弈下再分配方案等价性证明需求,而且实现了保留部分收益用于联盟再发展的策略。     

基于对偶四元数的卫星信息一致性控制

为了解决航天器控制信息一致性问题,提出了利用对偶四元数来描述对象的位置及姿态信息,实现位置与姿态的统一表述。同时利用信息一致性理论,通过设计航天器间的信息传递模型来解决分布式航天器间的状态同步问题。采用对偶四元数及信息一致性理论为工具,分别给出了位姿同步及跟踪两种控制方法并针对两种信息拓扑模型,以空间交会对接问题进行仿真实验,实验结果表明,在500s以内,卫星的位置及姿态实现了同步及跟踪控制。     

双耦合B类激光器的混沌动力学行为

提出并研究了双耦合Ｂ类激光器的动力学行为。发现该系统可在稳定连续、自脉冲和混沌输出。还发现该系统是以倍周期分岔由周期解进入混沌。     

关于Z-空间的对偶空间的讨论

本文以自然的方式定义了从Z-空间X到Z-空间Y的有界线性算子的和以及它们的数乘.从而得到了与赋范空间的对偶空间理论类似的一系列结论.     

EQ 1 rot nonconforming finite element method for nonlinear dual phase lagging heat conduction equations

EQ rot 1 nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h2 ) one order higher than its interpolation error O(h), the superclose results of order O(h2 ) in broken H1 -norm are obtained. At the same time, the global superconvergence in broken H1 -norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h4 ) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ rot 1 element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.