Maximum Shannon Entropy, Minimum Fisher Information, and an Elementary Game

We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no solution based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

基于目标信息系统学习的多准则决策方法

给出目标信息系统学习的多准则决策方法，建立多准则决策的规则学习模型，讨论该模型的性质。该模型优于Z．Pawlak方法，将规则提取与信息融合为一体。也优于AHP等模型，具有简洁性．通过实例计算，取得了满意结果。     

An Informational Approach to the Sinusoidal Law of Photon Polarization

The photon polarization law po ＝ sin2θ is derived from a simple informational consideration by twomethods: The first is via an intuitive principle of mininum Fisher information, the second is via a symmetry andinvariance argument. The results demonstrate that in photon polarization, Nature has a tendency to hide herselfas deepas possible while obeying some regular conditions.     

Hypothesis testing for the generalized multivariate modified Bessel model

In this paper, we consider hypothesis testing problems in which the involved samples are drawn from generalized multivariate modified Bessel populations. This is a much more general distribution that includes both the multivariate normal and multivariate-t distributions as special cases. We derive the distribution of the Hotelling's T²-statistic for both the one- and two-sample problems, as well as the distribution of the Scheffe's T²-statistic for the Behrens–Fisher problem. In all cases, the non-null distribution of the corresponding F-statistic follows a new distribution which we introduce as the non-central F-Bessel distribution. Some statistical properties of this distribution are studied. Furthermore, this distribution was utilized to perform some power calculations for tests of means for different models which are special cases of the generalized multivariate modified Bessel distribution, and the results compared with those obtained under the multivariate normal case. Under the null hypothesis, however, the non-central F-Bessel distribution reduces to the central F-distribution obtained under the classical normal model.     

劳动力供给带弹性的Solow模型

本文给出了在劳动力供给带弹性条件下的Ｓｏ１ｏｗ增长模型，给出了经济增长的黄金律和均衡处资本稳定性的证明，并且与不带弹性的Ｓｏｌｏｗ模型作了比较．     

二价金属离子萃取速率常数与软硬酸碱规则

用上升液滴法测定了２－乙基己基膦酸单（２－乙基己基）酯－正辛烷从硝酸介质中萃取镁、钙、锌、镍、铜和铅等二价金属离子的正向初始速率，建立了速率方程，计算出正向萃取反应的速率常数、活化能及活化熵，首次将软硬酸碱规则与金属溶萃取速率常数关联。结果表明，在萃取机理相同时，萃取速率常数的大小与金属离子的软硬酸碱标度一致，即萃取过程中，作为酸的被萃取金属离子，其硬度越大，萃取速率常数亦越大，萃取反应的活化能…     

关于渐近中位无偏估计的渐近效率(英文)

本文在几种重要的分布族中,给出了渐近中位无偏估计的渐近效率的一种定义。给出了如下一些结果：在单参数族中,提出了构造渐近有效的渐近中位无偏估计的一种方法,在具有共同支撑集的分布族中,论证了渐近中位无偏有效估计与ＢＡＮ估计之间的等价值;而在非共同支撑集的截断族中,对一般的参数向量函数构造了它们的渐近中位无偏估计,并且计算出了它们的渐近效率。     

果糖-水混合溶液中多组分电解质热力学

恒定混合溶液总离子强度I=1.0000 mol•kg－1,改变果糖-水混合溶液中果糖的质量分数w=2.5％、5.0％和7.5％的条件下,应用电动势方法测定下列无液体接界电池(A)和(B)在278.15、283.15、288.15、293.15、298.15、303.15、308.15、313.15、318.15 K等9个温度下的电动势: Pt, H2 (105 Pa)│HCl(m), C6H12O6(w), H2O(1－w)│AgCl-Ag (A) Pt, H2 (105 Pa)│HCl(mA), NaCl(mB), C6H12O6(w), H2O(1－w)│AgCl-Ag (B) 根据测得电池的电动势,计算出混合溶剂中AgCl-Ag电极的标准电极电势和HCl的标准迁移吉布斯自由能、迁移熵和迁移焓; 求出四元混合溶液中HCl的活度系数γA.结果表明在溶液中总离子强度I保持恒定,HCl的活度系数服从Harned规则,进一步讨论了混合物中HCl的介质效应.     

Net information measures for modified Yukawa and Hulthén potentials

The dimensional analyses of the position and momentum variances‐based quantum mechanical Heisenberg uncertainty measure, as well as the entropic information measures given by the Shannon information entropy sum and the product of Fisher information measures are carried out for two widely used nonrelativistic isotropic exponential‐cosine screened Coulomb potentials generated by multiplying the superpositions of (i) Yukawa‐like, ?Z(e^?μr/r), and (ii) Hulthén‐like, ?Zμ(1/(e^μr ? 1)), potentials by cos(bμr) followed by addition of the term a/r², where a and b ≥ 0, μ are the screening parameters and Z, in case of atoms, denotes the nuclear charge. Under the spherical symmetry, all the information measures considered are shown to be independent of the scaling of the set [μ, Z] at a fixed value of μ/Z, a, and b and the other parameters defining the superpositions of the potentials. Numerical results are presented, which support the validity of the scaling properties. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007