查询词典 Jacobi

In chapter one, firstly, we introduced several kinds of diagonally dominant matrices definition and their connection. Secondly, the relationship between those kinds of matrices and the convergence of some basic iteration methods (such as Jacobi, Seidel and SOR iteration methods) are also mentioned.

第一章，我们先简介了几类对角占优阵的定义及它们之间的关系，并介绍了一些基本迭代法(指Jacobi，Seidel及SOR迭代法等)的收敛性与这些矩阵类的关系。

Thirdly, we adopt the Jacobi approximation in the radial direction and thus overcome the difficulty of dealing with the singularity of equations at the center of ball. which is caused by the spherical coordinates. Furthermore.

第二，我们在球面上采用球面调和逼近，而在半径方向采用Jacobi逼近，从而既克服了奇异性的困难又将原问题转化为便于并行计算的简单问题。

In spherical polar coordinates, DRSC potential have supersymmetry and shape invariance for θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrodinger equation with double ring-shaped Coulomb potential are presented. The normalized angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

本文研究了双环形Coulomb势Schrdinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schrdinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示。

In this paper, by using the notable Mountain Pass Lemma of critical point theory, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to a class of second order nonlinear functional difference equations with Jacobi operators are obtained.

论文研究了一类具有Jacobi算子类型的二阶非线性泛函差分方程(1)的周期解和次调和解的存在性与多重性。首先将方程（1）的解的存在性问题转化为某个泛函临界点的存在性问题，然后验证此泛函满足著名的山路引理的条件，从而得到论文的主要结论。

From special to normal, the problem of constructing a Jacobi matrix with a prescribed principle submatrix and two ordered defective eigen-pairs has been solved gradually in this paper.

遵循从特殊到一般的原则，本文逐步解决了由给定一个顺序主子阵和两个有序缺损特征对构造Jacobi矩阵的问题。

These three algorithms can avoid to recompute the nth order head submatrix of the Jacobi matrix. Moreover, the last two algorithms are more stable, their precision can match well with the algorithm of Boley and Golub.

这三种算法都可以避免重构Jacobi矩阵的n阶首主子阵，并且后两种算法更稳定，数值精度可以与Boley和Golub的算法媲美。

In this paper, Jacobi iteration methods for system of linear equations are derived from mulitparameter projection methods.

从线性方程组的多参数投影法推出Jacobi迭代法。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

Symmetric tridiagonal matrix; Jacobi matrix; Eigenvalue problem; Inverse eigenvalue problem; Spring-Mass system; inverse problem in vibration; double dimension; Laplace equation

基础科学，数学，代数、数论、组合理论对称三对角矩阵； Jacobi矩阵；特征值问题；特征值反问题；弹簧-质点系统；振动反问题；双倍维； Laplace方程

Multivariate hypergeometric functions, multivariate Jacobi polynomials and h-harmonic polynomials connected with root systems and Coxeter groups are introduced.

多元超几何函数，多元Jacobi多项式和h与根系考克斯特集团有关的调和多项式介绍。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。