加权条件数在矩阵扰动问题中的极小性质

设A∈C_r~(m×n),r≤min(m,n)。对于加权条件数K_(MN)(A)=‖A‖MN‖A_(MN)~+‖NM,本文指出在一定条件假设下,K_(MN)(A)在矩阵扰动问题中的极小性质。主要结果如下:1.设A∈C_r~(m×n),E是A的任意小扰动矩阵。R(E)(?)r(A),R(E~*)(?)R(A~*)且‖A_(MN)~+‖NM‖E‖MN<1,有(?)成立,则有K_(MN)(A)≤(?)MN(A)。2.设A∈C_r~(m×n),E为A的任意小扰动矩阵。r(A+E)=r(A),且‖A_(MN)~+‖NM‖E‖MN<1,有(?)成立,则K_(MN)(A)≤(?)MN(A)。其中(?)当r相似文献   

Kinetic evaluation of the size-dependent decomposition performance of solvent-free microcellular polylactic acid foams

A thermal gravimetric method is described for evaluating the kinetics of cell size-dependent decomposition and lifetime estima- tion for microcellular tissue engineering scaffolds made of biodegradable polylactic acid(PLA)foams.PLA foam cell sizes from 550 to 20?m were fabricated experimentally using a solvent-free solid-state foaming technique under saturation pressures from 1 to 5 MPa.The thermal properties of the PLA foams with respect to the cell sizes were measured using thermal gravimetric analy- sis in a nitrogen atmosphere and the activation energy and pre-exponential factor were derived to evaluate the decomposition ki- netics and estimate lifetime.It was found that small cell sizes can be achieved under high saturation pressures and that the thermal stability of PLA decreases after the fabrication process.The cell size-dependent thermal stability and degradation rate indicate that a PLA foam of larger cell sizes has a shorter degradation time,a few tenths that of the PLA raw material,at a temperature of 37°C. The results suggest that it is feasible to optimize fabrication parameters to obtain appropriate cell sizes and lifetimes that satisfy the application requirements for various organs.This study provides the basis for precise scaffold design and quantitative analysis of PLA foams in tissue engineering applications.     

基于改进小波神经网络的大气质量评价模型

为了缩短人工神经网络的训练时间、减少迭代次数和提高输出结果的准确率,将小波基函数应用于人工神经网络,并用专家评分后归一化处理的方法对输入层的权值初始值进行优化,建立了优化的小波神经网络模型。将该模型对井冈山区域2012年大气监测数据进行评价,实验结果表明:经过优化的小波神经网络模型的评价精度较高。最后与将该模型与其它评价方法相比,该模型还具有计算快速、评价客观、可靠性强、效率更高的特点。     

Wavelet fractal character of overlapping signal

A new method based on the combining of the wavelet theory with the fractal theory and named wavelet fractal peak position method (WFPPM) is introduced to extract the number of the components and the relevant peak positions from overlapping signals in chemistry .The overlapping signal is first transformed into continuous wavelet transform value of time domain in certain dilation range via continuous wavelet transform (CWT),and then changed into capacity dimensions (Dc),The number of the components and the relevant positions of overlapping peaks can be identified easily according to the change of Dc.An investigation concerning the influence of different dilation ranges on the peak positions extracted by WFPPM is also provided .Studies show that the WFPPM is an efficient tool for extracting the peak positions and identifying the number of peaks from unresoloved signals,even when this kind of overlapping is significantly serious,Relative errors of lless than 1.0% in peak positions are found when WFPPM is used in the processing of the cadmium (Ⅱ)-indium(Ⅲ) mixture system .The analytical results demonstrate that the desired peak positions can be extracted conveniently ,accurately and rapidly from an unresoled signal via WFPPM,Tremendous developing and applications based on currently reported WFPPM in extracting overlapping signals would be expected in the near future.     

基于小波分解的设备状态预测方法

首次提出将小波分解应用于非平稳时间序列的预测中,通过小波分解将非平稳时间序列分解为多层近似意义上的平稳时间序列,并且用ＡＲ（ｎ）模型对分解后的时间序列进行预测,进而得到最终的预测结果．将该方法应用于压缩机轴承座磨损的趋势预测中,通过与基于ＢＰ网络的预测方法相比较表明：该方法预测精度高,而且预测速度快,可以有效地应用设备状态的预测和设备故障趋势的分析中．     

变换域时间序列相似性搜索

在时间序列的研究中，经常需要计算二个序列的相似程度。由于序列变化的多样性和，复杂性，结果通常不能很好地满足要求。采用变换法则对时间序列进行从时域到频域的转换，再将转换后的数据按照一定的规则变换成字符序列；利用求最长公共子序列的方法计算三个序列的匹配度，实现时间序列的相似性搜索。     

广义Calderón－Zygmund算子的H~p有界性

ＣｏｉｆｍａｎＲ等引入了广义Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子，并研究了这些算子的Ｌｐ有界性及弱（１，１）有界性，本文讨论这些算子的Ｈｐ有界性     

宇宙线较长周期变化研究

利用羊八井ASγ阵列实验数据分析宇宙线的较长周期变化.收集整理Tibet ASγ阵列1994～2003年间记录的宇宙线触发率数据和气象数据,发现这段时间的宇宙线触发率存在明显的年周期变化,气压、室内温度、室外温度与宇宙线触发率有着相似的年变化,存在较强关联;对宇宙线触发率进行多元气象参量修正,修正后的宇宙线触发率不再有明显的年变化;利用小波分析和数学统计方法分析气象修正后的宇宙线触发率,没有发现确定的几日周期.统计结果显示：宇宙线周期变化中4日周期和6日周期较多,其次是5日7、日和8日周期.     

CO2弧焊电源动特性的模糊逻辑推理评定

ＣＯ２弧焊电源动特性的评定方法一直是焊接界未能很好解决的问题,论文中研究了用子波统计分析方法由焊接过程电信号中提取与电源动特性相关的特征信息,并在大量的实验基础上,根据实际经验研究了动特性的模糊逻辑推理评定方法,建立了模糊逻辑推理评定系统,实验证明了该评定系统的有效性。     

非线性不规则波二阶分离模型

基于二阶波势流理论,建立了一个非线性不规则波浪二阶分离模型．通过求解频域内一、二阶成分之间的传递函数,建立起二阶项求解关系式,将二阶项变换到与一阶项同一个傅里叶频域空间,采用Newton-Raphson迭代方法分别求解出目标波浪中一阶、二阶和频与二阶差频．利用所建立模型分别对规则波和二阶非线性不规则波进行了数值验证,并对波浪非线性的影响进行了分析,典型数值计算结果表明模型是有效的．