运用辩证思维优化解题过程

辩证思想适用于世间万物,也适用于各门学科.任何事物都存在着对立与统一的两个方面,数学问题也不例外.因而科学地认识辨证思想,并合理地将其运用于数学解题中,往往能够起到意想不到的效果.     

Optimal harvesting for an age-dependent <Emphasis Type="Italic">n</Emphasis>-dimensional food chain model

This paper is concerned with optimal harvesting policy for an age-dependent n-dimensional food chain model. The existence and uniqueness of non-negative solution of the system are proved using the fixed point theorem. By Mazur＇s theorem, the existence of optimal control strategy is demonstrated and optimality conditions derived by means of normal cone.     

部分线性变系数模型的Profile Lagrange乘子检验

对于部分线性变系数模型附有约束条件时的估计与检验问题,基于Profile最小二乘方法给出了参数部分以及非参数部分的约束估计并研究了它们的渐近性质,并针对约束条件构造了Profile Lagrange乘子检验统计量,证明了该统计量在原假设下的渐近分布为χ2分布,从而将Lagrange乘子检验方法推广到了半参数模型上.     

Max-Lukasiewicz复合推理下的模糊图灵机

研究max-Lukasiewicz复合推理下的模糊图灵机.形式化定义了模糊图灵机--确定型模糊图灵机、非确定型模糊图灵机、带部分转移函数的非确定型模糊图灵机和多带模糊图灵机,研究了这几类模糊图灵机的关系.进而定义模糊图灵机上的模糊递归可枚举语言和模糊递归语言.得出结论:当接受模糊递归可枚举语言时 ,非确定型模糊图灵机和确定型模糊图灵机不等价;而接受模糊递归语言时,它们等价.     

毛细管电泳非接触电导分离检测金属氧化物纳米粒子

采用毛细管电泳非接触电导检测技术,以碳酸钠-碳酸氢钠为缓冲体系,同时分离测定了纳米二氧化钛和三氧化二铝两种金属氧化物的悬浮粒子.考察了缓冲溶液种类、浓度及pH对分离效果的影响,探讨了激发频率、激发电压对检测信号信噪比的影响.在最佳分离检测条件下,不同粒径的二氧化钛和三氧化二铝悬浮粒子在8 min内可实现完全分离.所选择的最佳条件为:① pH 10.5缓冲溶液为5 mmol·L-1碳酸钠和碳酸氢钠混合溶液;②分离电压20 kV;③进样条件20 kV,6 s;④激发频率460 kHz;⑤交流激发电压4 V(给出最高的S/N比值).     

Simulation Analysis of the Optimal Storage Resource Alloction for Large HENP Databases

Large High Energy and Nuclear Physics(HENP)databases are commonly stored on robotic tape systems because of cost considerations.Later,selected subsets of the data are cached into disk caches for analysis or data mining.Because of the relatively long time to mount,seek,and read a tape,it is important to minimize the number of times that data is cached into disk.Having too little disk cache will force files to be removed from disk prematurely,thus reducing the potential of their sharing with other users .Similarly,having too few tape drives will not make good use of a large disk cache,as the throughput from the tape system will form the bottleneck.Balancing the tape and disk resources is dependent on the patterns of the requests to the data.In this paper,we describe a simulation that characterizes such a system in terms of the rsources and the request patterns.We learn from the simulation which parameters affect the performance of the system the most.We also observe from the simulation that,there is a point beyond which it is not worth investing in additional resources as the benefit is too marginal.We call this point the “point-of -no-benefit“(or PNB),and show that using this concept we can more easily discover the relationship of various parameters to the performance of the system.     

热力学第二定律的非对称性

热力学第二定律揭示了自然界中存在着的非对称性。     

Chay模型混沌节律的非稳定周期轨道

在描写神经放电的理论模型（Cahy模型）中发现有位于加周期分岔过程中的混沌节律。利用So的非稳定周期轨道检测算法研究了位于周期2和周期3之间的混沌节律的非稳定周期轨道。结果发现，靠近周期2的混沌节律中只能检测出显著的非稳定周期2轨道，而靠近周期3的混沌节律中不仅可以检测出非稳定周期2轨道，还可以检测出非稳定周期3轨道；并且该非稳定周期2轨道位置与稳定周期2位置相似，非稳定周期3位置与稳定周期3位置类似。这表明，非稳定周期轨道在神经混放电节律的动力学起着重要作用；非稳定周期轨道的结构决定着混沌节律的特征，可以用来区分混沌节律。