K－框架的冗余和扰动

主要讨论Hilbert空间K-框架的冗余性和扰动稳定性,给出Hilbert空间K-框架的基础上去掉一些元素后剩余的元素还构成K-框架的两个充分条件和一个不构成K-框架的充分条件,同时给出Hilbert空间K-框架的一个比较一般的3系数扰动结论.     

Hilbert空间连续K-框架的若干研究

在Hilbert空间引入连续K-框架的概念,给出连续K-框架的多种等价刻画,同时给出连续K-框架的交错对偶对所涉及的两个序列可互换的一个充分条件及一种具体的构造连续K-框架交错对偶对的方法.最后给出两种不同的方法去构造新的连续K-框架.     

K-fusion框架的刻画

引入Hilbert空间中K-fusion框架的概念,利用合成算子的性质进行刻画,并讨论其与K-框架的关系.     

Hilbert空间的算子刻画与广义框架

给出了Hilbert空间的算子刻画,并利用Hilbert空间的算子刻画建立了Hilbert空间中的框架与广义框架之间的联系.     

K-g-框架与斜对偶

在Hilbert空间中定义了K-g-框架,探讨K-g-框架与g-框架的一些本质差别,并对K-g-框架加以刻画.此外,将斜对偶原则应用到K-g-框架上,研究斜对偶K-g-框架分解中涉及的两个框架可交换的充分条件以及斜对偶K-g-框架分解的等价刻画.     

Hilbert空间上的连续算子值框架若干性质

目的 引入了Hilbert 空间连续算子值框架的概念,并研究Hilbert 空间上连续算子值框架的若干性质.方法 用算子理论的方法进行研究.结果 对(等范数)连续算子值框架做怎样的变换仍是连续算子值框架.结论 知道连续算子值框架的证明与离散算子值框架证明方法的差异且丰富了算子值框架的理论知识.     

K-fusion框架的若干研究

刻画了与K-fusion框架有关的算子K的值域的包含与K-fusion框架包含的相互关系,同时给出了K-fusion框架的一个等价刻画.通过一个例子讨论说明在K-fusion框架的基础上删除一些元素后可能不再是K-fusion框架,同时给出了从K-fusion框架中删除一些元素后还构成K-fusion框架的两个充分条件.     

Fredholm框架及其扰动

引入了Hilbert空间H的Fredholm框架概念,它是一种介于普通框架与Riesz基之间的一类特殊框架.应用算子论方法,给出了Fredholm框架的重要性质及其等价刻画,证明了H上全体Fredholm框架构成了由H中全体Bessel列组成的Banach空间中的开集.研究了Fredholm框架在小扰动下和算子扰动下的稳定性,证明了框架与Riesz基的膨胀不变性.     

Hilbert K-模上广义框架的不相交性

引入了紧算子代数模(简称Hilbert K-模)上广义框架,广义框架变换,广义框架算子,(强)不相交等概念,给出并证明了Hilbert K-模上广义框架(强)不相交的充要条件。     

有界线性算子L的应用

在复的Hilbert空间中,通过举例说明有界线性算子L满足满的等不同条件时,可以用来刻画不同的推广框架:g-框架、g-Bessel序列和g-Besselian框架.     

Parseval K-框架的一些等式与不等式

利用一个关于K-框架的等式与不等式的结论,给出Parseval K-框架的等式与不等式,然后引入Parseval K-框架的上指标与下指标的概念,并对Parseval K-框架的上指标与下指标的一些性质进行讨论. 所得结果推广了已有的相关结论.     

完全图Kn的{P5,C5}分解

图分解问题已在很多邻域中得到了广泛的应用。用P₅表示5个顶点的路，C₅表示5个顶点的圈，本研究讨论了完全图K_n分解成5个顶点的路P₅和圈C₅的存在性，给出完全图K_n存在{P₅,C₅}-强制分解的充分必要条件是n≥7(n≠8)，以及完全图K_n存在{P₅,C₅}-分解的充分必要条件是n≥5(n≠6)。     

Stable initialization scheme for K -means clustering

Though K-means is very popular for general clustering, its performance which generally converges to numerous local minima depends highly on initial cluster centers. In this paper a novel initialization scheme to select initial cluster centers for K-means clustering is proposed. This algorithm is based on reverse nearest neighbor (RNN) search which retrieves all points in a given data set whose nearest neighbor is a given query point. The initial cluster centers computed using this methodology are found to be very close to the desired cluster centers for iterative clustering algorithms. This procedure is applicable to clustering algorithms for continuous data. The application of proposed algorithm to K-means clustering algorithm is demonstrated. Experiment is carried out on several popular datasets and the results show the advantages of the proposed method. Foundation item: Supported by the National Natural Science Foundation of China (60503020, 60503033, 60703086), the Natural Science Foundation of Jiangsu Province (BK2006094), the Opening Foundation of Jiangsu Key Laboratory of Computer Information Processing Technology in Soochow University (KJS0714) and the Research Foundation of Nanjing University of Posts and Telecommunications (NY207052, NY207082)     

Nitric oxide suppresses stomatal opening by inhibiting inward-rectifying K<Stack><Subscript>in</Subscript><Superscript>+</Superscript></Stack> channels in <Emphasis Type="Italic">Arabidopsis</Emphasis> guard cells

We explore nitric oxide （NO） effect on K^＋in, channels in Arabidopsis guard cells. We observed NO inhibited K^＋in, currents when Ca^2＋ chelator EGTA （Ethylene glycol-bis（2-aminoethylether）-N,N,N′,N;tetraacetic acid） was not added in the pipette solution; K^＋in currents were not sensitive to NO when cytosolic Ca^2＋ was chelated by EGTA. NO inhibited the Arabidopsis stomatal opening, but when EGTA was added in the bath solution, inhibition effect of NO on stomatal opening vanished. Thus, it implies that NO elevates cytosolic Ca^2＋ by activating plasma membrane Ca^2＋ channels firstly, then inactivates K^＋in, chartnels, resulting in stomatal opening suppressed subsequently.     

基于多重分形降趋算法与改进的K均值聚类滚动轴承故障诊断

针对滚动轴承振动信号非线性、非平稳的特点,提出采用多重分形降趋算法计算多重分形谱参数作为特征参数,对比分析了多重分形降趋波动分析法及多重分形降趋移动平均法提取轴承故障特征的优劣性.并提出改进的K均值聚类分析对多重分形降趋算法提取的特征参数进行分类,从而实现轴承故障诊断的目的.运用滚动轴承公开数据对方法进行验证,提取时域特征与多重分形谱参数进行对比分析,并对两种多重分形降趋算法的效果进行对比分析,验证了多重分形降趋波动分析法与改进K均值聚类相结合对轴承故障诊断的有效性,为轴承故障诊断方法提供了一种新的尝试.      

The fourier transformations of positive distributions on lorentz groupSO (3, 1)

With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed intoμ=μ ₁+μ ₂, whereμ ₁ is a bounded measure on 0<=s<=2 andμ ₂ is slowly increasing measure on (sχC|Re(s)=1)} Foundation item: Supported by the National Natural Science Foundation of China (19871065) and Hua Cheng Mathematics Science Foundation. Biography: Zhu Li (1976-), male, Graduate student, research interest: partial differential equation     

K-uniformly rotund spaces andk-uni formly smooth spaces

The conception ofk-uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that thek-uniform smoothness and Sullivan’sK-uniform rotundity (KUR) are the daul notions. X* is a KUR space if and only if X is a KUS space, X* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K + 1) US space. It is also proved that the KUS space includes the Nan’sk-strongly smooth space.     

Molecular characterization of a K+ channel blocker in the scorpionButhus martensii Karsch

K⁺ channel blockers of scorpion venoms are of important value in studying pharmacology and physiology of specific K⁺ channel of cells. Based on the amino acid sequences of BmP01 previously characterized as a small-conductance Ca²⁺-activated K⁺ channel blocker, two “back to back” degenarate primers have been designed and synthesized for inverse PCR strategy, its full-length cDNA has been cloned from the venom gland of the Chinese scorpionButhus martensii. The cDNA is composed of 3 parts: 5′ UTR, ORF and 3′ UTR. The flanking sequence of translation initiation codon ATG is AAAATGA, which is highly conserved in scorpion Na⁺ channel toxin and protozoan genes, suggesting that these genes may have followed a common mechanism for translation initiation. The 3′ UTR contains poly(A) signal AATAAA. The open reading frame encodes a precursor of 57 residues with a signal peptide of 28 residues and a mature peptide of 29 residues. The signal peptide is rich in hydrophobic amino acid residues and its length is significantly different from that of the determined scorpion Na⁺ channel toxin. The deduced amino acid sequence of mature peptide is completely consistent with BmP01 previously determined by primary structure analysis.     

块结构r-循环矩阵的性质及其算法研究

提出了一种新的块循环矩阵,称之为块首尾差r-循环矩阵(简记为bFLDCM_r)。首先,验证了其线性运算结果和矩阵乘积仍是bFLDCM_r;其次,给出了bFLDCM_r的判别法和非奇异性判定的充要条件,并讨论了bFLDCM_r的对角化;最后,利用Sherman-Morrison-Woodbury公式,给出了三对角块r-循环线性系统求解的直接算法。     

砂土介质中多类型土压力盒标定试验

针对厂家给出的土压力盒标定系数K值与实际岩土工程中土压力盒K值之间存在误差的问题,进行了多类型土压力盒标定试验,并结合各类型土压力盒工作原理分析其在相同埋设环境下的差异及其产生原因。选取3类具有代表性的土压力盒(振弦式单膜土压力盒、振弦式双膜土压力盒、电阻应变式土压力盒),采用砂标法对其进行标定试验,将试验所得K值和厂家给定的K值做对比分析,并依据试验结果提出线性拟合公式,给出砂土介质中各类土压力盒的标定系数。结果表明:振弦式土压力盒砂标K值小于厂家提供K值,差值在50%左右;电阻应变式土压力盒砂标K值大于厂家提供K值,差值在3倍左右。