THE HEAT KERNEL ON THE CAYLEY HEISENBERG GROUP

The authors obtain an explicit expression of the heat kernel for the Cayley Heisenberg group of order n by using the stochastic integral method of Gaveau. Apart from the standard Heisenberg group and the quaternionic Heisenberg group, this is the only nilpotent Lie group on which an explicit formula for the heat kernel has been obtained.

Symmetry groups and Gauss kernels of Schrdinger equations

The relationship between symmetries and Gauss kernels for the SchrSdinger equation iut = uxx ＋ f（x）u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schroedinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.

HEAT KERNELS AND HARDY'S UNCERTAINTY PRINCIPLE ON H-TYPE GROUPS

This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.

含较少非线性非忠实不可约特征标的有限幂零群

有限群不可约特征标核的性质对群结构有重要的影响.刻画了非线性非忠实不可约特征标个数至多为2的有限幂零群的结构.

中国城镇居民收入分布演进特征——基于非参数Kernel密度估计方法和省域区域视角

基于城镇居民人均可支配收入分组数据,运用非参数Kernel密度估计方法和MonteCarlo模拟技术,估计了1987—2008城镇居民收入分布及其演进特征。结果发现:(1)从全国城镇居民收入分布演进特征看,城镇居民收入不平等呈扩大趋势,基尼系数由0.17上升到0.33,增长近一倍,但没有观察到普遍和持久的两极分化现象(双峰分布);(2)在12个代表性省(区、直辖市)中,以经济发展模式(经济增长—收入分配)分类,广东属于平等发达型,湖南、四川、宁夏和广西属于不平等落后型,急需调整和转变增长方式;(3)从区域经济发展特征看,东部地区和东北地区收入增长较快,但收入不平等现象十分严重,中部地区和西部地区收入增长相对较慢,不平等现象相对轻微。

面向水质分类的分组降维核朴素贝叶斯模型

为提高贝叶斯模型在实际数据中处理相关性维度时的效率、精度,并保持其可解释性,本文提出一种改进的核朴素贝叶斯模型。首先通过关联规则挖掘相关维度子集,然后对这些子集进行降维处理,利用降维后的数据构建核朴素贝叶斯模型。实际应用的结果显示,该模型减少了降维对数据的影响,在保留有效信息的同时,提高了模型的可解释性。

一类Hartogs域的Bergman核函数

利用Bergman核函数定义以及双全纯等价域之间Bergman核函数的关系,计算一类以典型域直乘积为底空间的Hartogs域的Bergman核函数的显式表达式。

Kernel(λ)之元的辛平延之积

在局部环上对辛群的生成问题进行研究,给出了辛变换的亏失数概念,将局部环上辛群的Kernel(λ)的元表示为辛平延之积.

基于KPCA和数据处理组合方法神经网络的半球谐振陀螺温度建模补偿方法

针对半球谐振陀螺(HRG)的温度建模与补偿问题,提出基于核主成分分析(KPCA)和数据处理组合方法(GMDH)神经网络的建模补偿方法.通过分析HRG的温度特性和大数据特征,初步确定网络模型的特征向量.为了去除HRG输出数据的相关性和冗余性,引入KPCA并降低特征向量维度.将特征向量代入GMDH神经网络训练,区分训练集和验证集以确定网络权值和网络结构,实现HRG温度漂移的建模与补偿.实验结果表明,单一样本预测时,所提方法预测效果明显好于传统多项式模型;多样本预测时,在4种不同训练样本下,所提方法相比传统多项式模型精度分别提升了48.5%、54.0%、56.3%、68.4%,相比GMDH模型分别提升了3.6%、5.1%、3.8%、8.8%.所提方法能够有效提高HRG在变温工况下的测量精度.

The Bergman Kernel on Cartan-egg Domains of the First Type

We obtain the Bergman kernel and holomorphic automorphism group in explicit formulas on the Cartan egg domains of the first type.

THE UNIFORMLY BOUNDEDNESS OF THE RIESZ TRANSFORMS ON THE CAYLEY HEISENBERG GROUPS

In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups.

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the L-p-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.

IMPROVED GAGLIARDO-NIRENBERG INEQUALITIES ON HEISENBERG TYPE GROUPS

Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.

Zeroes of the Bergman Kernels on Some New Hartogs Domains

We obtain the Bergman kernel for a new type of Hartogs domain.The corresponding LU Qi-Keng's problem is considered.

Size and proportion of urban and rural middle-income group in China: A comparative analysis based on CHNS and CHIP data

To enlarge the middle-income group and construct the "olivary" income distribution becomes one of the important issues of the economic development and income distribution reform in China. The income distribution function is estimated with kernel density, and the income distribution M-curve is constructed with CHNS and CHIP data to calculate the middle-income group. Furthermore, a comparative analysis is carried out for the changing trend of the size and proportion of middle-income group. Research conclusion: it is discovered according to the income distribution M-curve that the key to the enlargement of urban middle-income group lies in the lower middle-income group, while the key to the enlargement of rural middle-income group lies in the improvement of the upper middle-income group. The range of middle-income group is expanding, but due to the small scale, low proportion, and poor stability, it has not developed the "olivary" income distribution structure yet, and income inequality tends to be deepened.

基于大数据的徽州古建筑群游客热度研究

选择徽州古建筑群景点进行研究,通过网络爬虫获取景点微博数据,采用数据预处理、数据可视化、核密度分析等方法对古建筑群的讨论热度进行分析,判断各景点话题变化趋势,便于整合用户信息,筛选热门景点,促进徽州古建筑群旅游的良性发展。

Abnormality Degree Detection Method Using Negative Potential Field Group Detectors

Online monitoring methods have been widely used in many major devices, however the normal and abnormal states of equipment are estimated mainly based on the monitoring results whether monitored parameters exceed the setting thresholds. Using these monitoring methods may cause serious false positive or false negative results. In order to precisely monitor the state of equipment, the problem of abnormality degree detection without fault sample is studied with a new detection method called negative potential field group detectors（NPFG-detectors）. This method achieves the quantitative expression of abnormality degree and provides the better detection results compared with other methods. In the process of Iris data set simulation, the new algorithm obtains the successful results in abnormal detection. The detection rates for 3 types of Iris data set respectively reach 100%, 91.6%, and 95.24% with 50% training samples. The problem of Bearing abnormality degree detection via an abnormality degree curve is successfully solved.

Co-Periodicity Isomorphisms between Forests of Finite <I>p</I>-Groups

Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their automorphism groups under these isomorphisms is described with simple transformation laws. For the tree of finite 3-groups with elementary bicyclic commutator qu-otient, the information content of each coclass subtree with metabelian main-line is shown to be finite. As a striking novelty in this paper, evidence is provided of co-periodicity isomorphisms between coclass forests which reduce the information content of the entire metabelian skeleton and a significant part of non-metabelian vertices to a finite amount of data.

基于最大信息系数的分组支持向量数据描述故障检测

工业过程的众多变量之间往往存在着复杂的相关关系,传统的故障检测模型通常会忽略不同变量间相关性的差异,对不同相关关系的变量采用相同的特征提取方法,从而导致检测效果欠佳。针对以上问题,提出了一种基于最大信息系数的分组支持向量数据描述故障检测模型,首先计算变量间的最大信息系数矩阵,按照相关性的不同对变量进行分组,再通过最大信息系数为模型混合核函数中高斯核与多项式核的权重分配提供理论指导,从而分别为各组建立不同的支持向量数据描述检测模型,完成最大信息系数与支持向量数据描述的紧密结合,最终实现分布式故障检测。通过仿真对比,验证了该模型的可行性与有效性。

粤港澳大湾区休闲农业空间布局及影响因素

【目的】揭示休闲农业的空间分布特征,并剖析其影响因素,探索适宜建设都市农业休闲核心区路径,进一步优化粤港澳大湾区内地九市休闲农业的发展格局。【方法】以大湾区内地九市160个休闲农业与乡村旅游示范点为研究样本,结合区域休闲农业年营业收入、接待人次,采用最邻近点指数、核密度估计和GIS分组分析的方法对休闲农业空间分布特征进行定性和定量分析,并通过缓冲区分析和相关分析等方法探究影响其空间布局的主要因素。【结果】肇庆、中山、东莞等市休闲农业和乡村旅游示范点数量较多,但营业收入和接待人次较少;休闲农业与乡村旅游示范点的平均实际最邻近距离为7.90 km,理论预期最邻近距离为9.27 km,最邻近指数R=0.85<1;核密度分析呈现1个“Y”状高密度区和2个点状次高密度区;根据伪F统计量,大湾区内地九市各县(市、区)可分为3个组别;城市总体规划缓冲区20 km范围内休闲农业与乡村旅游示范点数量最多,休闲农业与经济状况、旅游资源之间存在显著的正相关关系。【结论】休闲农业与乡村旅游示范点在空间分布上呈现凝聚分布态势;休闲农业与乡村旅游示范点的的高密度区和次高密度区,适宜建设乡镇振兴示范带、乡村精品旅游线路、乡村休闲旅游示范单位等。内地九市中,形成两个休闲农业发展较好的组别,包含广州市从化区、增城区,惠州博罗县,东莞市,中山市,佛山市顺德区,珠海市斗门区和江门市新会区,适宜建设都市农业休闲核心区。休闲农业旅游的布局主要受到区位条件、经济发展水平、旅游资源禀赋和区域特色农业的影响。