查询词典 eigenvalue

By using a gauge transformation between thetwo eigenvalue problems, we obtain a correspondence between the hie -rarchy of nonlinear evolution equations associated with the Kaup-Newelleigenvalue problem and the hie rarchy of nonlinear evolution equationsassociated with the AKNS eigenvalue problem.

利用规范变换，我们得到了与Kaup-Newell特征值问题相联系的一族非线性演化方程和与AKNS特征值问题相联系的一族非线性演化方程之间的一个对应关系，并给出了Kaup-Newell系统的Darboux变换及其证明。

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。

Constructing an entire function a;, the zeros of which are the eigenvalue of Dirac eigenvalue problem with general two points' linear algebra boundary conditions.

根据ω各项系数的不同情况，将一般两点边界条件分为八种基本类型，并得到相应的八个决定特征值的整函数ω和它们在相应围道上的渐近估计。

Thesolutions compose self-contained inner product space (weight function is constant 1),i.e., they are basic series of Hilbert space; hence any internal waves could beexpanded into generalized Fourier series. With difference method, Sturm-Liouvilleequation is transformed to matrix eigenvalue problem. Each eigenvalue is related to ahorizontal wave number, and relevant solution is a certain mode of internal wave.

其解系构成完备的加权(权函数为1)内积空间，即Hilbert空间，从而内波现象可以展成该解系的广义Fourier级数；采用差分方法，将 Sturm-Liouville 方程转化为矩阵特征值问题，每一个特征值对应一个内波波数，该特征值对应的解则是内波的某一模态。

A compound inverse eigenvalue problem of Jacobi matrix and some generalized inverse eigenvalue problems have been discussed in this paper.

本文研究了一类Jacobi矩阵混合逆特征值问题及几类矩阵广义逆特征值问题。

There are all kinds of inverse eigenvalue and generalized inverse eigenvalue problems in the fields of structural design, vibration system, automation control and matrix decision etc.

在结构设计、振动系统、自动控制、矩阵对策等领域中存在各种各样的矩阵逆特征值问题及广义逆特征值问题。

This paper surveys a new exact method which uses exact dynamic stiffnesses and therefore results in a nonlinear eigenvalue problem in contrast to the traditional finite element method which reduces the problem into a linear algebraic eigenvalue problem by using approximate shape functions.

与常规有限元方法采用近似形函数将原问题化为线性特征值问题不同，本文的精确方法从杆件精确的形函数出发获得精确的动力刚度，将原问题化为非线性特征值问题。

Firstly, we give a new upper bound of a mixed graph′s largest Laplacian eigenvalue, which is more precise. And also we give a lower bound of a mixed connected graph′s largest Laplacian eigenvalue.

首先给出了混合图的最大Laplace特征值的一个新的上界，并且用实例说明我们的结果与以往结果相比更精确，同时也给出了一个连通混合图的最大Laplace特征值的一个新的下界。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

With the aid of the adjoint relationship of symplectic ortho-normalization and integral transformation, solutions of duality equations were obtained, or Saint-Venant solutions and local solutions, reducing the original problem to finding zero eigenvalue solutions and non-zero eigenvalue solutions.

利用辛正交归一关系和积分变换得到了对偶方程的解，即圣维南解和局部解，从而将原问题转化为寻找零本征值本征解和非零本征值本征解问题。

Methods Clinical data of 3 cases of bile duct injury during laparoscopic cholecystectomy were analyzed retrospectively.

回顾总结3例LC术中胆管损伤的临床资料，分析3例胆管损伤的原因及对策。

These techniques are applied to the gobang.

本文将这些技术用于五子棋中。