极小

The associated Euler-Lagrange equation leads to a nonlinear partial differential equation of second order in the wavelet domain.

通过求解该模型的极小化，推导出其相应的Euler-Lagrange方程为小波域中的二阶非线性偏微分方程。

When the tadpole hatches, it is carried on one of the parents' back to a bromeliad where the parents feed it small insects, ants, spiders, crustaceans, and tiny water animals.

当蝌蚪孵的时候，它向后地被继续父母的中一个到父母喂它小的昆虫，蚂蚁，蜘蛛，甲壳类和极小的水动物的 bromeliad 。

Then, through tiny incisions, the fat is sucked up through a very small surgical tool, called a cannula.

然后，通过这极小的切口，油脂通过一个被称作插管的非常小的外科工具被吸走。

Given a finite training sample set, according to the proposal of establishing a Local Most Entropy probability density function to estimate the number of cluster a method for estimating 〓 is proposed, where a complicated method based on Maximum Likelihood Cross-Validation is replaced by Chebyshev inequality.

为改善BP算法的收敛速度慢、易陷入局部最小的问题，提出了带一类非线性特性动量项的变步长BP算法，构造了一个能自适应升降温的动量项非线性强度函数，在编程中又采用了有条件引入非线性特性动量项的措施，大大提高了搜索过程跳出局部极小、快速稳定收敛的能力。

Then,a new fast algorithm of the minimal norm least squares solution for linear system whose coefficients is an m×n symmetric Loewner matrix with full column rank is given by forming a special block matrix and researching the triangular factorization of its inverse.

对于工程计算中常常遇到的一类线性方程组的求解，通过构造特殊分块矩阵并研究其逆矩阵的三角分解，给出了求秩为n的m×n阶对称Loewner矩阵为系数阵的线性方程组，及极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

In this paper, for m× n Loewner-type matrix or symmetric Loewner-type matrix with full column rank, we form special block matrix firstly and research their triangular factorization or of its inverse, and then get the fast algorithm of the minimal norm least squaresolution .

本文对于秩为n的m×n阶Loewner型或对称Loewner型矩阵L，通过构造特殊分块矩阵并研究其逆的三角分解或自身三角分解，进而得到了线性方程组Lx=b的极小范数最小二乘解快速算法，计算复杂度为O+O(n~2)，而一般方法的计算复杂度为O(mn~2)+O(n~3)。

A new fast algorithm of the minimal norm least squares solution for the linear system whose coefficient matrix is an m×n Loewner-type matrix with full column rank is given by forming a special block matrix and researching its triangular factorization.

通过构造特殊分块矩阵及其三角分解给出了求秩为n的m×n阶Loewner型矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

In Chapter three, by constructing a special partitioned matrix and studying the fast triangular factorization of its inverse matrix, we respectively give fast algorithms for the minimal norm least squares solutions of linear equations which coefficient matrices are n×m Toeplitz type matrices and Vandermonde-Loewner type matrices with full column rank.

第三章通过构造特殊分块矩阵并研究其逆矩阵的快速三角分解，分别给出了求以秩为m的n×m阶Toeplitz型矩阵和Vandermonde-Loewner型矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法，并通过算例将新算法与已有的法方程组的方法和正交化方法作了比较。

Fast algorithm of minimal norm least square solution for Cauchy linear system;2. For the m×n Cauchy-type matrix with full column rank,the fast algorithm of the minimal norm least square solution to the linear system Cx=b was obtained by construction of a special block matrix and study of the triangular decomposition.

对于秩为n的m×n阶Cauchy型矩阵C，通过构造特殊分块矩阵并研究其三角分解，进而得到了线性方程组C x=b的极小范数最小二乘解的快速算法，所需运算量为O+O(n2)，而通常构造法方程组的方法所需运算量为O(m n2)+O(n3)，用正交化法虽然避免了构造法方程组，但所需的运算量更大些。

In order to solve the theoretical backlash problem of the teeth, which is crucial to the number of actual contact pairs of teeth in the research on multi teeth contact of crown gear coupling , the theoretical backlash of teeth flank with the concept of backlash angle is first time defined and described in the paper, and the minimization model of its variables is set up.

为解决鼓形齿联轴器多齿接触研究课题中的实际接触齿对数的关键技术轮齿理论间隙的问题，首次用间隙角的概念对轮齿理论间隙作了定义和描述；建立了该变量的极小化模型；对一鼓形齿联轴器作了实际优化计算，得出了鼓形齿联轴器多齿接触研究中计算实际接触齿对数所需的不同啮合状态下的最小间隙角

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。