Conformal invariance and conserved quantities of Appell systems under second-class Mei symmetry

In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system＇s conformal invariance and Mei symmetry are discussed. And Appell system＇s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.

A Comparison of Statistics for Assessing Model Invariance in Latent Class Analysis

Latent class analysis (LCA) is a widely used statistical technique for identifying subgroups in the population based upon multiple indicator variables. It has a number of advantages over other unsupervised grouping procedures such as cluster analysis, including stronger theoretical underpinnings, more clearly defined measures of model fit, and the ability to conduct confirmatory analyses. In addition, it is possible to ascertain whether an LCA solution is equally applicable to multiple known groups, using invariance assessment techniques. This study compared the effectiveness of multiple statistics for detecting group LCA invariance, including a chi-square difference test, a bootstrap likelihood ratio test, and several information indices. Results of the simulation study found that the bootstrap likelihood ratio test was the optimal invariance assessment statistic. In addition to the simulation, LCA group invariance assessment was demonstrated in an application with the Youth Risk Behavior Survey (YRBS). Implications of the simulation results for practice are discussed.

Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry

This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry. The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given. The conformal factor in the determining equations is found. The relationship between Birkhoff system＇s conformal invariance and second-class Mei symmetry are discussed. The necessary and sufficient conditions of conformal invaxiance, which are simultaneously of second-class symmetry, are given. And Birkhoff system＇s conformal invariance may lead to corresponding Mei conserved quantities, which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.

SB模型恒稳定解的degree(英文)

研究一个非线性常微分方程系统———一个简化的Brusselator模型.证明这个模型存在一个严格的正的不变区域,在此区域内该模型存在唯一的恒稳定解,且解的degree为1.

Earthquake Barcode from a Single-Degree-of-Freedom System

Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and meanwhile investigate the response behavior from a novel theory about the dynamical system, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting with respect to time. We analyze the complex jumping behavior in a barcode and an essential property of a high percentage occupation of the first set of dis-connectivity in the barcode from four strong earthquake records: 1940 El Centro earthquake, 1989 Loma earthquake, and two records of 1999 Chi-Chi earthquake. Through the comparisons of four earthquakes, we can observe that strong earthquake leads to large percentage of the first set of dis-connectivity.

Extension of covariant derivative(Ⅲ): From classical gradient to shape gradient

This paper further extends the generalized covari ant derivative from the first covariant derivative to the sec ond one on curved surfaces. Through the linear transforma tion between the first generalized covariant derivative and the second one, the second covariant differential transformation group is set up. Under this transformation group, the sec ond class of differential invariants and integral invariants on curved surfaces is made clear. Besides, the symmetric struc ture of the tensor analysis on curved surfaces are revealed.

Successive Approximation of p-Class Towers

Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.

光伏发电系统对配电网三相电压不平衡度影响的计算方法

针对传统确定性潮流计算在对分布式光伏电站接入配电网后导致的三相电压不平衡现象进行评估时的不足,提出了一种基于多点线性化的半不变量概率潮流和重要抽样对配电网不平衡度进行评估的方法.首先,针对Beta分布描述的局限性,以自适应非参数核密度估计法对光伏出力和负荷波动的随机过程进行表征,从而提高建模精度;然后,利用分段线性化半不变量法进行随机潮流分析以降低不确定性引起的误差,构建出混合Copula函数计算公共连接点的不平衡度;最后,采取抽样方法得到不平衡度均值进行评估.通过对IEEE33节点系统进行仿真分析,验证了此方法的有效性和可行性.

群作用在复几何中的一些运用

In this article,we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020,mostly related to my own interests.

ON STRONG DENSITY OF ALGEBRAS WITH A CLASS OF MINIMAL INVARIANT OPERATOR RANGES

Ⅰ. INTRODUCTION Let be a separable infinite-dimensional Hilbert space, be the algebra of all （bounded linear） operators on, and be a subalgebra in with identity Ⅰ. Let lat (resp. lat1/2) denote the lattice of invariant subspace （resp. invariant operator ranges） of. If we do not require that is closed in any

THE REDUCTION PROPERTY AND COMPLETE UNITARY INVARIANT OF A CLASS OF OPERATORS

M. J. Cowen and R. G. Douglas studied operators in B_n(Ω) from the point of view of complex geometry (Acta Math., 141(1978), 187—261). They got some unitary invariants of operators in B_n(Ω) using the curvature of the vector bundle related to the operator. Especially, when n=1, the curvature itself is a complete unitary

现代产品几何技术规范(GPS)的数字化理论基础

现代产品几何技术规范 (generationgeometricalproductspecificationandverification ,GPS)是ISO TC2 13针对产品的设计与制造而规定的一系列宏观和微观的几何技术规范 ,它包括产品的规范过程、生产过程、认证 (检验 )过程以及不确定度的评定和控制。表面模型是ISO TC2 13GPS语言中新提出概念 ,它是实现GPS系统阶段功能的操作基础和系统关联基础 ,表面模型需要由相应的“要素”和“特征”予以定义和描述。ISO TC2 13GPS将工件 要素分为七种恒定类 ,所有的理想要素都属于七种恒定类中的一种 ,且可由其位置要素和本质特征进行定义与描述 ;位置特征则定义了要素之间的关系。第二代GPS系统通过表面模型、恒定类、恒定度、特征等概念的引入和互补应用 ,实现了几何要素从定义、描述、规范到实际检验评定过程中数字化控制功能的飞跃 ,比较有效地解决了产品在“功能描述、规范设计、检验评定”过程中数学表达统一规范的难题。

一种提高计算精度的类直流潮流算法

基于一个已知的初始稳态断面,提出了一种适用于拓扑不变而仅有注入量变化的提高计算精度的类直流潮流算法。该算法相比于标准直流潮流,只需在初始稳态断面基础上求解一组修正因子量,从而实现拓扑不变仅有注入量变化的新断面潮流计算。算例中多个IEEE标准系统和波兰实际电网的仿真结果表明,当网络注入量在-30%～60%范围内变化时,类直流潮流法比标准直流法在潮流计算精度上有70%以上的改进。

熵损失函数下刻度参数估计的不变性和本质完全类

讨论在熵损失函数下，刻度参数的可容许估计的不变性及Bayes估计的不变性，证明在熵损失函数下，刻度参数所有依赖于充分统计量T的非随机化判决构成一个本质完全类．

基于物理模型的彩色图像边缘检测与分类

提出一种基于物理模型——双色反射模型的彩色图像边缘检测与分类方法。首先在分析双色反射模型的基础上,论证了不同的色彩空间具有不同的色彩不变性特征;然后提出一种彩色图像的Sobel边缘检测算子和基于类别方差的阈值自动选取方法,并用该方法在不同颜色空间中对彩色图像进行边缘检测;最后,根据不同颜色空间的色彩不变性特征将边缘分为材质边缘、阴影边缘和高亮边缘3类。实验表明该彩色图像边缘检测与分类方法具有良好的效果和应用价值。

发电机转子轴心轨迹形状自动识别方法的研究

给出了一种自动识别轴心轨迹形状的新方法。首先将采集到的轴心轨迹线图,用边界颜色填充各区域,形成轴心轨迹图象,计算其不变矩特征向量。然后将仿真生成的各种轴心轨迹不变矩特征向量作为参考模式,将实际检测的轴心轨迹不变矩特征向量作为待识别模式,利用关联度进行识别。最后成功地识别了 MJF-30-6 型发电机在空转、并网正常运行、转子短路故障运行、A 相接地四种工况的轴心轨迹形状,并揭示了发电机电气故障对转子轴心轨迹的影响。

基于GPS的形位公差项目分析和设计

零件信息的描述是计算机辅助形位公差设计首先要解决的问题.基于GPS恒定类、特征等数字化描述理论基础,结合对零件结构和功能特征的相关分析,建立了面向CAx集成的零件特征信息模型和相应的形位公差项目生成规则;为实现形位公差信息在CAD/CAM中的集成控制奠定了基础.

基于不变矩特征和神经网络的图像模式模糊分类

提出了一种基于不变矩特征和神经网络的医学图像识别模型·所设计的识别模型包括不变矩特征提取、不变矩矢量标准化、模糊化预处理、BP网络与竞争选择·利用不变矩方法提取医学图像的特征矢量,能有效检测出具有平移、旋转和比例变化的图像,利用神经网络作为分类器对提取的特征矢量分类,使用模糊化的方法先对输入特征数据做预处理再进行识别,每一个图像模式归属于某一类是以0到1的数字代表其归属程度·实验结果验证了模型的有效性,训练好的网络有很好的分类能力·

面向非合作目标识别的大规模类属超图建模

针对大量不同成像条件下获得的多视图像,研究利用局部不变特征及其空间布局约束构建用于非合作目标识别的类属超图模型的方法.该方法首先将每一幅图像表示为使用选定的稳健SIFT特征构成的属性图,然后提出了一种属性图相似性传播聚类原理.在给定的F度量的约束下,利用该原理进行聚类,并根据熵函数最小化优化条件,可迭代得到特定目标属性图样本集合的最优聚类,进一步将所获得的聚类简化成以非冗余属性图作为节点的类属超图模型.本文用大量图像样本进行了试验测试.实验结果验证了模型的可扩展性和识别性能.

二维轴对称图象高阶胡氏不变矩快速算法的改进

提出了基于二维轴对称性目标图象矩快速算法的实用化改进方案 算法实用化改进是通过两个命题的证明实现的 一是通过轴对称目标图象质心在对称轴上的命题证明 ,实现了将二维轴对称图象矩快速算法用于轴对称性图象中心矩的计算 ;二是通过目标图象以坐标系中任意两点为圆心 ,旋转相同角度 ,结果图象具有平移性的命题证明 ,实现了算法用于对旋转不同角度的对称目标图象的中心矩的计算改进 在此基础上 ,完成了二维轴对称目标图象高阶胡氏不变矩实用化快速算法的实现 实验证明 ,该算法具有较好的实时性能 。