查询词典 Jacobi

It briefly includes several following aspects: First, Jacobi elliptic function were introduced and some of its main characters were discussed simply.

本文首先简要介绍了Jacobi椭圆函数及其性质，然后介绍了非线性发展方程的Jacobi椭圆函数展开法和目前的一些演化和扩展情况，最后着重介绍本人对Jacobi椭圆函数在求解非线性发展方程中的应用方面所作的研究。

Fourth, at basic of the improvement of Jacobi elliptic function expanded method, the extended Jacobi elliptic function expanded methods was proposed.

四、对Jacobi椭圆函数展开法进行改进和扩展，提出新的扩展的Jacobi椭圆展开法来求解非线性发展方程并得到许多新的周期波解。

Second, Jacobi elliptic function expanded methods proposed by Liu et al and its evolution and extendedness currently including double Jacobi elliptic function expanded method and F expanded method of solving nonlinear equations were introduced.

二、介绍刘等人提出的Jacobi椭圆函数展开法及当前一些主要的扩展——双Jacobi椭圆函数展开法和F展开法。

In the second part, we gave several basic and essential knowledge of inverse eigenvalue problems for Jacobi matrices: such as the properties of tridiagonal matrices, Jacobi matrices, orthogonal polynomials, Gauss quadrature formula and inverse eigenvalue problem for Jacobi matrices.

第二部分介绍了求解Jacobi矩阵反问题的基础：三对角矩阵和Jacobi矩阵，正交多项式，高斯积分方法的性质和Jacobi矩阵特征值反问题。

First, we consider an iterative algorithm of Jacobi type and the corresponding domain decomposition algorithm for a approximate quasivariational inequality system of the Hamilton- Jacobi- Bellman equation and the corresponding convergence problem.

本文研究了逼近Hamilton-Jacobi-Bellman方程的拟变分不等式组的离散问题的Jacobi型迭代算法和Jacobi型区域分解法及其收敛性问题。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

Using the dual characteristic pairs, we give the if and only if conditions for which a maximally isotropic subbundle of the double of a Jacobi bialgebroid is a Jacobi-Dirac structure.

在此基础上，建立Jacobi流形的两类对应约化定理，并且给出了约化Jacobi流形上的约化Jacobi结构的具体形式以及其与原流形上的Jacobi结构之间的对应关系。

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

Firstly, an inverse eigenvalue problem for Jacobi matrices is presented: we could construct the Jacobi matrix T if we know the spectral data: the eigenvalues of T and the eigenvalues of T_1 and of T_2, where T_1 is different to the k × k leading principal submatrix of T only at the position, while T_2 is different to the × remain submatrix only at the (1, 1) position.

首先给出的是一类Jacobi阵的逆特征值问题，即给定三组实数：一组是Jacobi阵的n个特征值，一组是只修改了最后一个对角元的它的前k阶顺序主子阵的特征值，最后一组是修改了第一个对角元的后n—k阶余子阵的特征值，用这些给定的特征值来确定相应的Jacobi矩阵。

When the coefficient matrice is index p cycle matrice (p = 3,4,5),we educe the relation between preconditionging Jacobi 、 GS iterative matrices" and classical Jacobi iterative matrices" eigenvalue; As an application, make some preconditioning iterative factors, when classical Jacobi iterative converge, the preconditioning iterative methods may converge faster.

2系数矩阵是指数p=3，4，5循环矩阵时，分别给出了预条件Jacobi、Gauss-Seidel迭代矩阵与传统块Jacobi迭代矩阵二者特征值之间的关系，作为一个应用，通过预条件因子的特殊取值，使传统Jacobi迭代收敛时，预条件块迭代法的收敛速度成倍提高。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。