直接分解

Due to the effect of curvature of shell, the equation of motion of elastic waves in shell is much more complex than that in plate. The method of operator factorization can't be directly used to solve the equation of motion of elastic waves in shell by reducing it to the second order partial differential equations.

由于壳体曲率的影响，使得壳体的弹性波动方程比平板的运动方程复杂得多，难以直接采用算子因式分解方法，将其化成二阶偏微分方程求解。

Boley and Golub used Gauss quadrature formula to solve the inverse problem, but I used other different methods and thoughts. I obtained a new decomposition form of orthogonal matrix consisted by the unit eigenvectors of Jacobi matrix and found the direct relations between the first row and the orther rows of this orthogonal matrix.

Boley和Golub的算法是用高斯求积公式，而本人另辟蹊径，推出了关于Jacobi矩阵单位特征向量组成的正交阵的一种分解形式，并找到此正交阵第一行和其它行的直接联系，由此避免了通过求特征多项式计算尾主子阵的特征值，得到了新的稳定解法。

Some formulas of the weighted Moore-Penrose generalized inverse of the sum of two matrices are given under two different kinds of conditions, related existing results are extend and modified with a sample and direct proof method.

在两种情形下，利用矩阵的加权Moore-Penrose逆导出了两矩阵和的加权Moore-Penrose逆的公式，其推导证明简洁而直接，文中还给出两矩阵可以同时加权奇异值分解的充要条件，指出了J.K。

In Chapter 5, a new method with direct partitioned column updates of cholesky factorization for solving large scale sparse unconstrained optimization problems is proposed, which depends on a consistent partition of the columns and cholesky factorization of the Hessian matrix.

第5章基于稀疏Hesse阵的列的相容分划，并在其Cholesky分解的基础上建立了求解大型稀疏无约束优化问题的直接校正Cholesky因子算法。

If an improper basis function is adopted for decomposing signals, the fault feature information can be weakened.

小波基函数的选择直接影响故障特征的提取效果，如果在信号分解时采用了不合适的基函数，会冲淡故障特征信息。

Firstly, by adopting the thought of Adomian's decomposition method, the generic dynamic model in mechanical systems are transformed into a standard first-orderdifferential-equations, and then the inverse operator method for the approximate analytic solution of nonlinear mechanical system is developed based on the exact solution in form.

主要研 究工作如下：利用Adomian的分解方法的思想，把机械系统中最一般的动力学模型转化为一阶标准型微分方程组，以形式上的精确解的表达式为基础构造了求解机械系统非线性模型近似解析解的逆算符方法；针对机械系统非线性模型的特点，提出了直接处理高阶方程的不降阶逆算符方法；证明了该方法的收敛性。

Different from the traditional approach of solving GDA by singular value decomposition,the new algorithm utilizes kernel modified Gram-Schmidt orthogonalization algorithm to extract the optimal transformation matrix directly,which can not only effectively hold the most discriminant information in the null space of within-class scatter matrix,but also make the solution more stable in numeric.

与传统用奇异值分解获取目标特征子空间的方式不同，新算法运用核修正格兰-施密特正交化过程直接提取最优投影变换矩阵，不仅有效地地保留了类内散度矩阵最具辨别力的零空间信息，同时使所求解在数值上更稳定。

In order to get more statistic features involved, the wavelet parameters of infrared cloudy sky images are directly put on the table after that. A set of self-contained features is extracted and simulation experiments are done by feature matching.

为研究图像的更多统计特性，我们还通过直接对目标图像小波分解系数进行研究，从中提取出了一组较为完备的统计量作为特征，同时利用特征匹配的方法进行了仿真实验。

Third,a heterogeneous domain decomposition method is devised to solve aclass of special piecewise smooth systems.

第三，对一类特殊的分片光滑抛物系统提出一种非均匀区域分解直接算法。

We prepared the pyrethric acid II through four reactions: esterification, oxidation, decomposition, diesterification. And the original synthesis route of the pyrethric acidII was improved: the yield of oxidation of allyl rise through increasing the activity of Selenium dioxide; in the document, tert-butyl-trans -2, 2-dimethy1-3-(2"-methoxycarbony1-1"-propenyl)cyclopropanecarboxy late was synthesized from tert-butyl-trans-2,2-dimethyl-3-(2 -formyl-r -propenyl) cyclopropanecarboxylate with two steps, with low yield.

我们经过酯化，氧化，成双酯，热分解四步反应，成功地得到了第二菊酸，并改进了原第二菊酸的合成路线：通过改变二氧化硒的活性提高了烯丙甲基的氧化产率；将原路线中醛氧化成羧酸、羧酸酯化的两步反应改为醛和甲醇、二氧化锰等作用一步直接酯化的方法，减少了反应步骤，提高了总收率。

He and Nina moved to California and lived at 2005 Ivar Street, Apt.

他和Nina搬到加州，并在2005年伊瓦尔街，公寓生活。

Droperidol （ potently inhibits transfected HERGchannels and this is the probable mechanism for QT prolongation.

氟哌利多有效地抑制了转染的 HERG 钾通道，可能是 QT 间期延长的机制。