The hierarchical approach to modeling knowledge and common knowledge

One approach to representing knowledge or belief of agents, used by economists and computer scientists, involves an infinite hierarchy of beliefs. Such a hierarchy consists of an agent's beliefs about the state of the world, his beliefs about other agents' beliefs about the world, his beliefs about other agents' beliefs about other agents' beliefs about the world, and so on. (Economists have typically modeled belief in terms of a probability distribution on the uncertainty space. In contrast, computer scientists have modeled belief in terms of a set of worlds, intuitively, the ones the agent considers possible.) We consider the question of when a countably infinite hierarchy completely describes the uncertainty of the agents. We provide various necessary and sufficient conditions for this property. It turns out that the probability-based approach can be viewed as satisfying one of these conditions, which explains why a countable hierarchy suffices in this case. These conditions also show that whether a countable hierarchy suffices may depend on the “richness” of the states in the underlying state space. We also consider the question of whether a countable hierarchy suffices for “interesting” sets of events, and show that the answer depends on the definition of “interesting”.     

傅立叶变换近红外光谱法快速评价涪陵榨菜品质

应用傅立叶变换近红外光谱技术,建立了评价涪陵榨菜品质的定量分析模型.测定了58份涪陵榨菜的近红外光谱数据,通过光谱预处理方法消除噪声,以偏最小二乘法(PLS)建立回归模型.最终得到评价其品质的水分、总酸(以乳酸计)和氨基酸含量近红外光谱分析模型的决定系数(R2)依次为0.957 8、0.975 4、0.950 4,交叉...     

黑膜厚度与膜表面张力关系的研究

用微干涉测量技术直接测定楔压等温线,研究了电解质浓度对阳离子表面活性剂TTAB在浓度大于cmc时形成黑膜厚度的影响及膜表面张力与溶液表面张力之间的差别.结果显示,黑膜厚度取决于楔压和电解质浓度,随着楔压的增加,液膜厚度减少至一定程度后几乎保持不变,表明黑膜类型的转化是阶跃式的,而电解质屏蔽了液膜两个表面电荷层间的排斥作用,故电解质浓度增加,液膜厚度变小.由楔压等温线得出的膜表面张力的结果说明一般黑膜的表面张力与溶液的表面张力并无明显差别.     

Common fixed points of two maps in cone metric spaces

We prove the existence of points of coincidence and common fixed points of a pair of self-mappings satisfying a generalized contractive condition in cone metric spaces. Our results generalize several well-known recent and classical results.      

Common supercyclic vectors for a path of operators

We examine common supercyclic vectors for a path of operators. In particular, we show that the path consisting of convex combinations of two arbitrary unilateral weighted backward shifts has a dense Gδ set of common supercyclic vectors. Moreover, we show there exists a path with a dense Gδ set of common supercyclic vectors between a unilateral weighted backward shift which satisfies the Supercyclicity Criterion, and an operator which does not. Lastly, we provide an example of a path of unilateral weighted backward shifts that fails to have a common supercyclic vector.     

茵陈挥发油GC-MS指纹图谱分析

建立了茵陈挥发油GC-MS指纹图谱,将正交投影算法用于不同样本中共有峰的提取,提高了共有峰的识别能力,降低了由于保留时间的漂移、质谱检索匹配度不高以及色谱峰重叠而引起的共有峰识别的难度.采用共有峰率、变异率及相似度等几个指标对4个不同产地的茵陈挥发油成分进行了评价,从共性、差异和整体性等多个方面全面表征茵陈挥发油的化学模式特征.结果表明,不同产地的茵陈挥发油成分大致相同,该指纹图谱可用于茵陈中挥发油成分的质量控制.     

A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving

In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are allowed to evolve in a recursive manner, and dependence is incorporated in the specification of these factors using a common shock approach.We consider factors that evolve across accident years in conjunction with factors that evolve across calendar years. This two-dimensional evolution of factors is unconventional as a traditional evolutionary model typically considers the evolution in one single time dimension. This creates challenges for the estimation process, which we tackle in this paper. We develop the formulation of a particle filtering algorithm with parameter learning procedure. This is an adaptive estimation approach which updates evolving factors of the framework recursively over time.We implement and illustrate our model with a simulated data set, as well as a set of real data from a Canadian insurer.     

Determination of common anions in oxalate by ion chromatography coupled with UV photolysis pretreatment

A new and simple method was developed to determine anions in oxalate of analytical reagent grade.After UV photolysis with optimal 1%H₂O₂ in 10,000 mg/L oxalate in the fabricated photoreactor,sample was directly injected into IC system.Satisfactory linearity,detections limits,good repeatability and spiked recovery were obtained.The method was successfully applied to determine anions in two commercial oxalate samples.     

Optimal estimates of common remainder for the robust Chinese Remainder Theorem

Common remainder is significant to the estimation of the robust Chinese Remainder Theorem (CRT). This paper presents two optimal estimates of common remainder for the robust CRT. The two different optimal estimates are obtained based on different definitions of circular distance. Both of the two estimations are more effective with lower computational complexity than the existing searching method. Simulation results show that the two estimations have nearly the same performance, however, the second optimal estimation has less computation than the first one. These optimal estimates can improve the performance of the estimation of the robust CRT.     

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized(φ, ψ)-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.