重复囚徒困境博弈中的社会行为仿真

大多数经济行为都可以看作博弈论的一个特殊案例.本文通过计算机仿真对重复囚徒困境博弈的特点进行了分析,建立基于累积期望差异评价策略的重复囚徒困境博弈模型,并对仿真结果进行了分析.分析结果表明,它能够对社会群体行为随着时间的推移提供动态描述,同时对于重复博弈问题的研究有着重要的辅助作用.     

根据动力学-光谱数据解析高锰酸钾氧化草酸钠的反应过程

通过在线测量硫酸介质中高锰酸钾氧化草酸钠反应过程的光谱变化，获得了动力学—光谱二维数据。借助主成分分析法，确定了高锰酸钾的单信息区，并确认反应过程中产生了一种有吸收的中间体。根据最小二乘回归等化学计量学方法，结合相关组分间存在等吸收点这一光谱特征及质量平衡原理，成功地解折出反应体系中相关组分的实际动力学谱及纯光谱。根据Savitsky-Golay求导法，获得了各组分的速率曲线。对解析结果的进一步研究表明，该反应符合自催化模式。     

Multivariate curve resolution in liquid chromatography—resolving two-way multi-component data using a Varimax extended rotation

The Varimax extended rotations (VER) have been proposed as a new method to mathematically resolve severely overlapped peaks in chromatographic experiments that produce bilinear data. VER employs a four-step procedure to determine the relative concentration and identity of the components that comprise a severely overlapped chromatographic peak. In the first step, the data are pre-processed to ensure that they are in a form suitable for multivariate curve resolution. The second step involves principal component analysis, which reduces the dimensionality of the data matrix while simultaneously retaining the information present in the data. In the third step, a new coordinate system is developed for the data using a Varimax rotation followed by a so-called extended rotation, which assists in identifying the so-called pure regions in the peak. Identifying these regions is crucial to rotating the concentration and spectral matrices towards a solution. The fourth step utilizes alternating least squares (ALS) to improve the estimates of the concentration and spectral profiles of each component. Results from real and simulated data are used to illustrate the efficacy and simplicity of the proposed method.     

Construction of conservative test for change-point problem in two-dimensional random fields

This paper is concerned with a change-point problem in random fields. Tests for detecting a change-structure in a two-way table are constructed. Solutions to this problem require calculations of multiple integrals, but the calculations become difficult as the table gets large. To overcome this difficulty, the tube method is developed in differential geometry. It is shown by simulations that the proposed method is superior to other available methods.     

On extremal pure Nash equilibria for mixed extensions of normal-form games

In this paper we derive conditions under which mixed extensions of normal-form games have least and greatest Nash equilibria in pure strategies, and either of them gives best utilities among all mixed Nash equilibria when strategy spaces are complete separable metric spaces equipped with closed partial orderings, and the values of utility functions are in separable ordered Banach spaces. The obtained results are applied to supermodular normal-form games whose strategy spaces are multidimensional.     

未知动力学模型的化学反应过程的解析

采用迭代目标转换因子分析法(ITTFA)解析动力学模型未知的化学反应过程中的动力学-光谱数据矩阵,获得了各组分的动力学谱.基于体系中各组分间的等吸收点等光谱特征,提出并建立了一种新的初始迭代矢量的方法.利用该方法解析了动力学模型未知且各组分均有吸收的两步连续反应的模拟数据矩阵,并对最终产物无吸收的水杨酸水溶液电降解反应过程中测得的数据矩阵进行解析,获得了可靠的结果.     

基于近红外特征光谱的番茄苗氮含量快速测定方法研究

为了提高近红外光谱技术快速测定番茄苗氮含量的准确度和稳健性, 比较分析竞争自适应重加权采样法(CARS)、蒙特卡罗无信息变量消除法(MCUVE)、向后间隔偏最小二乘法(BiPLS )和组合间隔偏最小二乘法(SiPLS)四种特征波长挑选方法, 筛选与番茄苗氮含量相关的特征光谱。在十种不同氮素处理水平下(尿素溶液浓度0～120 mg·L-1), 培育60株番茄苗样本(每个处理6株), 使其分别处于不同程度的过量氮素、氮素适度、缺氮素和无氮素状态。分别采集每株番茄苗样本的叶片, 扫描其12 500～3 600 cm-1波段的近红外光谱。比较四种方法所建立的番茄苗氮素定量分析模型可知: CARS和MCUVE挑选的特征变量所建定标模型的性能比BiPLS和SiPLS挑选的特征变量所建定标模型的性能更优, 但是预测性能远低于后者。其中, 基于BiPLS建立的番茄苗氮素含量预测模型性能最佳, 相关系数(r)、预测均方根误差(RMSEP)和性能对标准差之比(RDP)分别为0.952 7, 0.118 3和3.291 0。因此, 近红外光谱技术结合特征谱区筛选可以有效地提高番茄苗叶片氮素含量的定量分析模型指标, 使模型更实用化。但是, 特征波长挑选方法不具有普适性。基于单个波长变量筛选的方法所建立的模型较为敏感, 更适用于样本状态较为均匀的待测对象;而基于波长区间筛选的方法所建的模型相对抗干扰性更强, 更适用于样品状态不均匀, 重现性较差的待测对象。因此, 特征光谱筛选只有与样本状态及建模指标结合, 才能使其在建模过程中发挥更好的作用。     

Zero-sum stochastic games with stopping and control

We study a zero-sum stochastic game where each player uses both control and stopping times. Under certain conditions we establish the existence of a saddle point equilibrium, and show that the value function of the game is the unique solution of certain dynamic programming inequalities with bilateral constraints.