Using the Semantic Information G Measure to Explain and Extend Rate-Distortion Functions and Maximum Entropy Distributions

In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual Information (MMI) distributions and ME distributions are expressed by Bayes-like formulas, including Negative Exponential Functions (NEFs) and partition functions. Why do these non-probability functions exist in Bayes-like formulas? On the other hand, the rate-distortion function has three disadvantages: (1) the distortion function is subjectively defined; (2) the definition of the distortion function between instances and labels is often difficult; (3) it cannot be used for data compression according to the labels’ semantic meanings. The author has proposed using the semantic information G measure with both statistical probability and logical probability before. We can now explain NEFs as truth functions, partition functions as logical probabilities, Bayes-like formulas as semantic Bayes’ formulas, MMI as Semantic Mutual Information (SMI), and ME as extreme ME minus SMI. In overcoming the above disadvantages, this paper sets up the relationship between truth functions and distortion functions, obtains truth functions from samples by machine learning, and constructs constraint conditions with truth functions to extend rate-distortion functions. Two examples are used to help readers understand the MMI iteration and to support the theoretical results. Using truth functions and the semantic information G measure, we can combine machine learning and data compression, including semantic compression. We need further studies to explore general data compression and recovery, according to the semantic meaning.     

Entropy production and viscosity of a dilute gas

It is known that the viscosity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by using two entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy production (MEP) principle. The known result is reproduced in a similar form.     

爆轰法合成碳包覆镍纳米颗粒的研究

 采用自制的负氧平衡复合炸药前驱体,在密闭容器中充氮气保护下爆轰合成了碳包覆镍纳米颗粒。利用X射线衍射、X射线荧光、透射电镜和拉曼光谱等技术,对爆炸产物的组成成分、结构形貌等进行了观测。结果表明,爆轰产物主要由具有面心立方结构的镍晶核和碳元素构成,此外还含有其它微量元素;合成的纳米颗粒呈球形或椭球形状,颗粒尺寸主要分布在10~25 nm范围,包覆的碳壳厚度约1~2 nm,核壳结构完备。结合观测结果,对爆轰法合成碳包覆纳米颗粒的形成机制进行了简单的讨论。     

黄浦江上游遥感监测溶解氧模型与时空变化

溶解氧含量是反映水体有机污染的重要水质指标。文章选择黄浦江上游水源中的典型水质参数——溶解氧为研究对象,利用地面高光谱遥感数据、多光谱遥感数据和现场水质监测数据来研究水体反射光谱特征与水质参数浓度之间的关系,发现溶解氧含量与641 nm波段的光谱反射率相关性最高,由Landsat5 TM第3和4波段的遥感反射率比值变量所建立的对数模型相关性最高,达到0.829。在此基础上,基于多时相遥感影像对溶解氧模型的通用性和准确性进行验证,并探讨了溶解氧的时空变化规律。结果表明,该模型具有较高精度,估测值与地面实测值在时间变化规律上保持一致,同时根据该模型得出的黄浦江上游溶解氧含量空间分布规律与该区域的有机污染实际分布情况是相互吻合的。     

一阶线性模糊微分方程的解

利用文[8]中的扩展原理求解了一阶线性模糊微分方程,给出了解可表示的条件,讨论了同其他求解方法之间的关系,最后给出了具体算例。     

Investigation on PVDF-HFP microporous membranes prepared by TIPS process and their application as polymer electrolytes for lithium ion batteries

Poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) microporous membranes were prepared via thermally induced phase separation (TIPS) process. Then they were immersed in a liquid electrolyte to form polymer electrolytes. The effects of polymer content in casting solution on the morphology, crystallinity, and porosity of the membranes were studied by scanning electron microscopy (SEM), differential scanning calorimetry (DSC), X-ray diffraction (XRD), and a mercury porosimeter, respectively. Ionic conductivity, lithium-ion transference number, and electrochemical stability window of corresponding polymer electrolytes were characterized by AC impedance spectroscopy, DC polarization/AC impedance combination method, and linear sweep voltammetry, respectively. The results showed that spherulites and “net-shaped” structure coexisted for the membranes. Polymer content had no effect on crystal structure of the membranes. The maximum transference number was 0.55. The temperature dependence of ionic conductivity followed the Vogel–Tammann–Fulcher (VTF) relation. The maximum ionic conductivity was 2.93 × 10⁻³ Scm⁻¹ at 20 °C. Electrochemical stability window was stable up to 4.7 V (vs. Li⁺/Li).     

基于样本协方差矩阵的多维随机数生成方法

对于概率模型未知的多维数据样本容量扩充问题,根据主成分分析原理以及多维正态分布的性质,讨论并给出了与已知多维样本数据有相同协方差结构的模拟数据生成算法,并在此基础上给出了变量的离散化处理方法。实现了在小样本数据基础上不改变变量间协方差结构的样本容量扩充,为小样本条件下的数学建模、检验和分析提供样本数据支撑。     

Analytic solutions of a reducible strain gradient elasticity model for solid cylinder with a cavity and its application in zonal failure

In this work, the reducibility condition of the fourth-order equilibrium equation in the strain gradient elasticity (SGE) model for solid cylinder with a cavity is obtained. When the reducibility condition is satisfied, the analytic displacement, generalized radial stress, and generalized angular stress can be solved out, and according to the higher-order coefficients, internal length scale, and Lamé constants, the displacement, generalized radial stress, and generalized angular stress are classified into four types: (1) conventional elasticity solution, (2) quasiperiodic SGE solution, (3) monotonous SGE solution, and (4) non-real-number solution. Quasiperiodic generalized radial stress and generalized angular stress are used to explain the occurrence of zonal failure of surrounding rock of a circular roadway. Numerical analysis with MATLAB is applied to study the influence of loading on zonal failure of surrounding rock of a circular raodway.     

n阶线性模糊微分方程的结构元解法

研究了n阶线性模糊微分方程的模糊初值问题,将n阶线性模糊微分方程转化成一阶线性模糊微分方程组,利用结构元方法将模糊线性微分方程组转化成两个分明的线性微分方程组,通过分明的线性微分方程组的解构造出原n阶线性模糊微分方程的解.最后,给出了具体的算例.     

一种求解半定规划的邻近外梯度算法

本文提出了一种求解半定规划的邻近外梯度算法.通过转化半定规划的最优性条件为变分不等式,在变分不等式满足单调性和Lipschitz连续的前提下,构造包含原投影区域的半空间,产生邻近点序列来逼近变分不等式的解,简化了投影的求解过程.将该算法应用到教育测评问题中,数值实验结果表明,该方法是解大规模半定规划问题的一种可行方法.