Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.

Analytical Research of Temperature Distribution and Thermal Stresses within Circular Micro-hotplates

Micro-hotplate(MHP) technology is one key part in the manufacturing of gas sensors.The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scientific interest.In this study,analytical solutions for the temperature field,and both radial and tangential stresses and von Mises stress for circular MHP were obtained.Two geometries were considered:one had a circular heater at the center and the other had a circular heater at the center and an annular heater within the membrane part.Internal heat generation was incorporated in the energy equation for the MHP and different values of convection heat transfer coefficient were used at the upper and lower surfaces of the MHP.It has been shown that the MHP with two heaters can provide more uniform temperature field compared with the MHP with one heater.The main objective of this work is to provide an exact analytical solution for thermal stresses within the circular micro-heater with a simple geometry as a benchmark,from mathematical point of view,against which the accuracy of new numerical schemes can be checked.To make sure that the analytical procedure is correct,the analytical results are checked against numerical solutions derived from finite element simulation.Since the analytical models for the temperature field and especially for the thermal stresses of MHP are seldom investigated in the literature,the obtained results are believed to facilitate the design and performance evaluation of MHPs as well.

The Chapman-Richards Distribution and its Relationship to the Generalized Beta

Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptions of the Chapman-Richards growth function, constant mortality and recruitment into the mathematical form of the distribution. Therefore, unlike 'assumed' distribution models, it is intrinsically linked with the underlying vital rates for the forest area under consideration. Methods: It is shown that the Chapman-Richards distribution can be recast as a subset of the generalized beta distribution of the first kind, a rich family of assumed probability distribution models with known properties. These known properties for the generalized beta are then immediately available for the Chapman-Richards distribution, such as the form of the compatible basal area-size distribution. A simple two-stage procedure is proposed for the estimation of the model parameters and simulation experiments are conducted to validate the procedure for four different possible distribution shapes. Results: The simulations explore the efficacy of the two-stage estimation procedure;these cover the estimation of the growth equation and mortality-recruitment derives from the equilibrium assumption. The parameter estimates are shown to depend on both the sample size and the amount of noise imparted to the synthetic measurements. The results vary somewhat by distribution shape, with the smaller, noisier samples providing less reliable estimates of the vital rates and final distribution forms. Conclusions: The Chapman-Richards distribution in its original form, or recast as a generalized beta form, presents a potentially useful model integrating vital rates and stand diameters into a flexible family of resultant distributions shapes. The data requirements are modest, and parameter estimation is straightforward provided the minimal recommended sample sizes are obtained.

基于概率球面判别分析的说话人识别信道补偿算法

在说话人识别任务中,概率线性判别分析(PLDA)模型是目前常用的分类后端,但由于高斯PLDA模型分布假设不能准确拟合真实说话人特征分布,导致基于高斯分布假设长度归一化的信道补偿方法会破坏说话人特征类内分布的独立性,使得高斯PLDA不能充分利用上游任务提取特征所包含的说话人信息,从而影响识别结果。针对这一问题,提出基于概率球面判别分析的信道补偿算法(CC-PSDA),通过引入冯·米塞斯-费希尔(VMF)分布假设的概率球面判别分析模型(PSDA)和特征变换方法代替高斯分布假设的概率线性判别分析方法,以避免信道补偿对说话人特征类内分布独立性的影响。首先,为了使说话人特征符合VMF分布先验假设拟合后端分类模型,在特征级利用非线性转换对说话人特征进行分布变换。之后,利用基于VMF分布假设的PLDA模型不会破坏说话人特征的类内分布结构的特点,将变换后的说话人特征定义到特定维度的超球面,最大化特征类间距离。所提算法通过期望最大化(EM)算法进行求解,最终完成分类任务。实验结果表明,改进算法在三个测试集上的识别等错误率相较于对比模型PSDA、高斯PLDA均最低。由此可见,所提模型可以有效区分说话人特征,提高识别性能。

静力-随机振动复合工况下Von Mises应力的概率分布及强度评估

针对静力-高斯随机载荷复合作用下的线性结构,考察了结构Von Mises应力过程的概率分布,在此基础上,利用中心卡方分布近似研究了一定累积概率(99.73%)水平下Von Mises应力值的计算,提出了静力-随机振动复合条件下的强度评估方法。基于一个数值算例,比较了该方法与Monte Carlo模拟的结果和计算效率,结果表明,该方法具有较高的准确度和计算效率。最后,对目前常用的两种工程近似方法进行了考察,从数学上证明了工程近似方法总是偏于保守,为现有方法提供了理论依据。

Von Mises分布在陕西省保费收入中的应用

保费收入的季节波动对保险业的增长具有重要的影响。应用方向数据统计对2005~2009年陕西省保费收入进行了季节波动分析,通过假设检验及统计推断得出陕西省保费收入服从双峰Von Mises分布,具有明显的季节波动性。

一种基于Gauss von Mises分布模型的非线性量测更新方法

基于状态空间模型的许多传统滤波算法都基于Rn空间中的高斯分布模型,但当状态向量中包含角变量或方向变量时,难以达到理想的效果。针对J.T.Horwood等提出的nS?R流形上的Gauss Von Mises(GVM)多变量概率密度分布,扩展了狄拉克混合逼近方法,给出了联合分布的GVM逼近方法,推导了后验分布的GVM参数计算公式,设计了量测更新状态估计算法。将J.T.Horwood等的时间更新算法与所提出的量测更新算法相结合,可实现基于GVM分布的递推贝叶斯滤波器(GVMF)。仿真结果表明,当状态向量符合GVM概率分布模型时,GVMF对角变量的估计明显优于传统的扩展卡尔曼滤波器。

von Mises分布及其在医学中的应用

von Mises分布是圆形统计学或方向数据统计学中最重要的分布。本文简要地讨论了该分布的分布函数、参数估计、假设检验及其在确定医学正常值范围中的应用。本文(1)编制了不同正常值范围的长度表,以利应用;(2)举例说明如何较精确地拟合 vonMises 分布;(3)是《中国医学百科全书·医学统计学》中“圆形分布法”的补充.

Descriptively probabilistic relationship between mutated primary structure of von Hippel-Lindau protein and its clinical outcome

In this study, we use the cross-impact analysis to build a descriptively probabilistic relationship between mutant von Hippel-Lindau protein and its clinical outcome after quantifying mutant von Hippel-Lindau proteins with the amino-acid distribution probability, then we use the Bayes-ian equation to determine the probability that the von Hippel-Lindau disease occurs under a mutation, and finally we attempt to distinguish the classifications of clinical outcomes as well as the endocrine and nonendocrine neoplasia induced by mutations of von Hippel-Lindau protein. The results show that a patient has 9/10 chance of being von Hippel-Lindau disease when a new mutation occurs in von Hippel- Lindau protein, the possible distinguishing of classifications of clinical outcomes using mod-eling, and the explanation of the endocrine and nonendocrine neoplasia in modeling view.

光滑Cramér-von Mises统计量的分布函数的收敛速度

用光滑的经验分布函数估计总体分布函数从而得到光滑的Ｃｒａｍéｒ－ｖｏｎＭｉｓｅｓ统计量，本文考虑了这种统计量收敛于极限分布的速度。

Average projection type weighted Cramér-von Mises statistics for testing some distributions

This paper addresses the problem of testing goodness-of-fit for several important multivariate distributions: (Ⅰ) Uniform distribution on p-dimensional unit sphere; (Ⅱ) multivariate standard normal distribution; and (Ⅲ) multivariate normal distribution with unknown mean vector and covariance matrix. The average projection type weighted Cramér-yon Mises test statistic as well as estimated and weighted Cramér-von Mises statistics for testing distributions (Ⅰ), (Ⅱ) and (Ⅲ) are constructed via integrating projection direction on the unit sphere, and the asymptotic distributions and the expansions of those test statistics under the null hypothesis are also obtained. Furthermore, the approach of this paper can be applied to testing goodness-of-fit for elliptically contoured distributions.

长江和清江洪水遭遇风险分析

引入混合von Mises分布拟合了长江上游与清江年最大洪水发生时间的双峰特征,即夏汛和秋汛。随后应用Copula函数分别构造了两江年最大洪水发生时间及发生时间与其量级之间的联合分布,研究了最大洪水发生时间及发生量级遭遇的风险特征,计算得出两江洪水遭遇的两个峰值点7月15日和9月13日的风险率分别为0.02%和0.008%;并定量估算了7月15日两江洪峰流量达到荆江河段安全流量及最大防洪能力的遭遇风险,其最大风险率分别为6.0×10-5和5.8×10-6。最后,绘出了两江同频率洪水的日遭遇风险图和非同频率洪水在遭遇时间两个峰值点的风险图,可为三峡水库和隔河岩水库进行风险调度或补偿调度提供一定依据。

2型糖尿病并发脑梗死患者联合检测血浆vWF水平及血小板参数的临床价值

目的探讨2型糖尿病并发脑梗死患者联合检测血浆血管性假性血友病因子(vWF)与血小板参数的临床价值。方法选取2011年12月—2013年10月2型糖尿病并发脑梗死患者32例,设为糖尿病并发脑梗死组,同期32例2型糖尿病患者设为糖尿病组,同期健康体检者30例设为对照组。检测3组糖化血红蛋白(HbA1c)、血vWF水平及血小板各参数,观察其差异及HbA1c与血vWF水平、血小板参数的关系。结果糖尿病并发脑梗死组、糖尿病组和对照组的HbA1c、血vWF水平呈逐步下降趋势,组间比较有显著差异(P<0.01)。3组血小板计数(PLT)无显著差异(P>0.05);血小板分布宽度(PDW)及血小板平均体积(MPV)在3组中呈逐步下降趋势,组间比较具有显著差异(P<0.01);HbA1c与vWF、MPV、PDW呈正相关(P<0.01)。结论 2型糖尿病并发脑梗死患者血vWF水平显著升高,联合检测血vWF与血小板各参数可为早期诊断与治疗提供参考。

三维传播环境天线阵列空域相关性研究

针对任意三维传播环境下多天线空域相关性求解复杂的问题,提出一种基于角度域脉冲采样的高效近似计算方法。针对均匀角度谱分布,详细推导出了天线空域相关系数的闭合表达式和近似表达式;针对非均匀任意角度谱,利用有限个均匀二维采样脉冲加权叠加进行逼近,从而将天线空域相关系数等效为多个均匀采样脉冲对应相关系数的加权之和。基于实测的Von Mises Fisher角度谱,仿真结果表明,当采样间隔小于2°时,所提方法运算量仅为数值积分方法的十分之一,而绝对误差小于0.005,可以应用于多天线分集、多输入多输出系统性能评估及天线阵列流型优化等场合。

三维空间域VMF分布模型的多天线系统性能

针对城市移动通信环境,提出了散射体各向异性分布的VMF分布模型.在室外宏小区的移动通信环境下引入散射体群的概念,并结合MIMO多天线Y型阵列(UYA)和圆形阵列(UCA)拓扑结构,使得模型能够估计多径衰落信道的重要信道参数,如UYA和UCA的空间衰落相关函数(SFC)、衰落信道模型的信道容量及多天线阵列UYA和UCA对平均余纬的敏感度等,并延伸了SFC在求解信道协方差矩阵的应用.结果表明:M IM O多天线系统的性能不仅取决于天线阵列阵元间距,还与到达角度有关;所提模型的信道参数估计结果适用于实际的城市移动通信环境.针对UYA和UCA的SFC和信道容量研究,拓展了VM F分布模型在三维空间域移动通信领域的应用,对MIMO多天线阵列的信道参数评估和无线通信系统仿真提供了有力的工具.

最大值密度函数的收敛速度

{Xn,n≥1}为独立随机序列,F(x)为公共分布函数,Mn=max1≤i≤n{Xi},基于VonMises条件得到F∈D(G)时Mn的密度函数的收敛速度.

基于CST域相位与幅值信息的医学图像融合方法

为了克服传统医学图像融合方法不能高效表示待融合图像中医学特征信息的问题,提出一种基于复数剪切波变换域幅值和相位统计信息的医学图像融合方法.首先利用复剪切波变换得到待融合医学图像的低频子带和高频子带,揭示各个高频子带系数相位呈现双峰分布的特点,提出基于两状态Von-Mises分布的相位统计模型;然后将经典的图像结构相似性(structural similarity of image,SSIM)推广至复数剪切波域,给出了结合幅值和相位的SSIM新表达形式,并基于此新表达式和相位统计模型提出全局-局部的融合规则;最后通过逆变换重建得到融合结果.对实验结果进行主观视觉比较和客观量化分析表明,该方法能够得到更好的融合结果.

Rayleigh信道空间相关及其对空时码性能的影响

为了研究空间相关对空时编码性能的影响。假设散射量沿波达角的功率分布服从von Mises分布。推导出了Rayleigh衰落信道多径接收信号的角度扩展．引入近似的高斯函数型阵列空间互相关系数。构造接收等距线阵的空间相关矩阵。并证明该矩阵是正定和满秩的。其行列式取值介于0～1之间．分析表明：若空时码字的差异矩阵满秩且仅在接收端存在空间相关，只会造成空时编码传输在编码增益上的损失。而不会造成分集增益上的损失；Rayleigh空间衰落相关信道中的最优空时编码设计准则与Rayleigh空间衰落独立信道中的相同．

病人入院时间分布规律的研究

目的掌握病人入院时间分布规律,为医院管理提供决策依据。方法利用圆形分布理论,对2002-2005年医院病人入院时间分布规律进行研究。结果通过对病人入院时间分布的分析,表明我院病人人院时间高峰时点大约处于8、9月份,高峰时期大约为6月至11月。结论病人入院时间具规律性分布,即病人入院时间存在高峰时点和高峰时期。

互耦效应对不同阵列流型相关性的影响

分析了互耦机理及其对接收信号矢量的影响,详细推导了入射信号角度谱服从Von Mises分布时,任意数目线型、圆型及面型等不同流型阵列的天线空间相关系数的闭式表达式和近似表达式,并据此推导出了综合互耦因素的对应流型阵列天线的相关系数解析式。仿真结果表明:本文推导的天线空间相关系数表达式与数值积分结果非常吻合。另外,在互耦效应下,天线阵元相关性围绕着无互耦时的相关性曲线上下波动,且面型阵列具有更好的抗互耦能力。