查询词典 decomposition

Based on the explicit formulation of matrices on the given linear manifold, the general expression of the solutions to this least squares problem is obtained by using the method of the singular value decomposition and the unitarily invariant of the Frobenius norm.

在推导出所给线性流形中任意矩阵的显式表达的基础上，利用奇异值分解和Frobenius范数的酉不变性得到了该最小二乘问题通解的一般表达式。

In addition, by applying the quotient singular value decomposition of a matrix pair, we obtained a general expression of the least-squares solutions of the matrix equation A~TXA — B on the linear manifold.

在第四章，我们研究了线性流形S={X∈CSR~|‖XY-Z‖=min，Y，Z∈R~}上矩阵方程A~TXA=B的中心对称解。

In Chapter 2, the D-symmetric solutions of matrix equation A~TXA = B on the linear manifold S ={X ∈ D~(-2)SR~|XZ = Y, Y = Y{D~2Z+D~2Z, Z~TD~2Y = Y~TD~2Z, Y,Z∈ R~}, by applying the generalized singular value decomposition of a matrix pair, the necessary and sufficient conditions for the existence and the expressions for the D-symmetric solutions of matrix equation A~TXA — B on the linear manifold are established.

运用矩阵对的广义奇异值分解，给出了这类线性流形上矩阵方程A~TXA=B存在D对称解的充要条件及其通解的表达式。另外给出了它的D对称最小二乘解的表达式。

In Chapter 4, the centro-symmetric solutions of matrix equation A~TXA = B on the linear manifold S ={X ∈ CSR~|||XY - Z||= min, Y,Z ∈ R~|}, using the quotient singular value decomposition of matrix pairs, the necessary and sufficient conditions for the existence and the expressions for the centro-symmetric solutions of matrix equation A~TXA = B on the linear manifold are established.

利用矩阵对的商奇异值分解，给出了这类线性流形上矩阵方程A~TXA=B存在中心对称解的充要条件及其通解表达式。

This paper discusses some generalized forms of the primary decomposition of vector space with regard to linear transformation.

本文讨论了向量空间关于线性变换σ的准素分解的一些推广形式。

Despite the many advantages over asbestos-based friction material, thermal decomposition or liquescence of phenolic resin due to frictional heating can cause semi-metallic friction material to fade away (a phenomenon of friction decline with operation time).

中文摘要半属基摩擦材主要是使用一种或多种耐热的树脂(以酚醛树脂最为广泛使用)为基材，添加各属粉末或纤维以强化基材，并添加润剂、摩擦调整剂等增加材的磨耗性能，其成份中通常含有超过50 wt%的属成份。

This 13C-depleted C is incorporated into the meteoric water pore fluids through decomposition of the constantly renewing biomass and becomes incorporated into limestone/dolostone during lithification.

这种相对缺乏13C的碳通过不断更新的生物体的分解混入了大气水孔隙的流体，最终在成岩过程中形成了灰岩或者白云岩。

The Hausdorff measure for the level sets of multi-parameter symmetric stable processes has been obtained and the inner connection of the measures and local times for it has been demonstrated, which describes the fractal nature for the level sets of this kind of processes. As we know, it is always one of the focuses in the field of random fractal. The reasult of the existence and continuity of the local time for multi-parameter stochastic processes with stable components has been got in the project. Then we gained the measure for the random fractal sets such as the range and graph of this kind of processes. Furthermore, a progress besides the mentioned above in the project is that we have resolved the multifractal analysis of the sample paths for Brownian sheet, that is the multifractal decomposition of white noise in high dimension.

解决了多指标对称稳定过程水平集的Hausdorff测度问题，同时给出N指标d维稳定过程水平集的Hausdorff测度下界的最佳估计，它们揭示了其水平集的测度与局部时之间的内在关系，刻划了多指标对称稳定过程水平集的分形特征，表明了研究此类问题的积极意义，该问题是随机分形研究领域的国内外学者所关注的热点问题之一；解决了多指标稳定分量过程的局部时存在性与连续性问题，进而解决了由多指标稳定分量过程产生的随机分形集--象集、图集的测度问题；此外，本研究项目还解决了布朗单样本轨道的重分形分析，即高维白噪音的重分形分析问题。

Based on a localization principle and subband decomposition, monoscale ridgelet and curvelet were proposed, both of which were derived from ridgelet transform and can efficiently deal with smooth images with smooth edges including straight and curve singularity. They, hence, are of better application potention. sparse representation;optimal basis;ridgelet;curvelet;image denoising;non-parametric estimation

单尺度脊波和Curvelet变换由脊波变换发展而来，分别利用了函数局部化和频带剖分的思想，将脊波理论发展到了一个更高的阶段，这两种变换都能"近似最优"的表示直线和曲线奇异，因而具有更好的应用前景。

Louis Pasteur, trained as a chemist, made some of his major contributions in microbiology as a result of his interest in the decomposition of natural products in the absence of air, the process of fermentation.

Louis Pasteur，一个训练有素的化学家，由于对在缺少空气情况下天然物质的腐烂现象和发酵过程很感兴趣，在微生物领域中作出了重要的贡献。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！