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The feasibility and validity of the method have been proved by the examples of statical analysis, stability problem, dynamical eigenvalue calculation, and dynamical response analysis.

文中将这一方法成功地应用于随机结构的静力学分析、稳定性问题、动力特征值求解和动力响应分析之中，对随机梁、板结构编制了静力分析计算通用程序，证明了此法的正确性、有效性。

The numerical calculation commonly used for the Delphi process more than 100, including solutions of linear algebraic equations, interpolation, numerical integration, special, function approximation, eigenvalue problems, data fitting equation Root and solve nonlinear equations, functions and the extreme optimization, statistical data description, Fourier transform spectra, solution of ordinary differential equations reconciliation partial differential equations.

本书共有数值计算中常用的Delphi子过程100多个，内容包括解线性代数方程组、插值、数值积分、特殊函数、函数逼近、特征值问题、数据拟合、方程求根和非线性方程组求解、函数的极值和最优化、数据的统计描述、傅里叶变换谱方法、解常微分方程组和解偏微分方程组。

Then, the convergence and convergence rate of three kinds of GA above are analyzed comprehensively from the point of view of stochastic matrix and matrix eigenvalue. The general convergence analysis methods of GA by Markov chains are presented and the convergence rates are discussed emphatically.

然后，利用有限Markov链从随机矩阵和矩阵特征值两个角度全面分析了上述三种类型GA的收敛性和收敛速度，给出了利用Markov链分析GA收敛性的通用方法，重点讨论了它们的收敛速度问题。

First of all, a system of linearized equations was set up with respect to an atmosphere at rest, and a couple eigenvalue-eigenfunction problem was formulated, which consists of horizontal and vertical structure equations with suitable boundary conditions.

首先，建立了静止大气状态下模式的线性化系统，并在适当的边界条件下将线性化系统分解成具有垂直与水平结构方程的本征值、本征函数耦合问题。

These results are applied to solve a class of inverse eigenvalue problems for real matrices with a submatrix constraint and the expression of general solution and best approximation are also given.

最后，将所得的结果应用于子阵约束下实矩阵特征值反问题的最小二乘问题，得到了该问题解的表达式与最佳逼近解。

And the sufficient and necessary conditions are obtained and the uniqueness of T is discussed and an algorithm for solving the inverse problem is provided. The other kind of structure inverse eigenvalue problem is for unitary Hessenberg matrices with positive subdiagonal elements. That is, a unitary Hessenberg matrices with positive sub-diagonal elements can be constructed when its eigenvalues and the eigenvalues of H_(11) and H_(22) are known. Here H_(11) and H_(22) are rank-one modifications of k × k leading principal submatrix of H and of its × remain submatrix respectively. In the end, the uniqueness of H and an algorithm is obtained.

文中首先讨论了这三组特征值之间的交错关系，接着确定了该逆问题有解的充要条件，并论证了其解的唯一性问题，最后给出了相应的数值算法；本文第二个问题解决的是一类不可约的酉Hessenberg阵的逆特征值问题：即一个不可约的酉Hessenberg阵可以由它的特征值、它的前k阶秩一修正的顺序主子阵的特征值以及它的后n—k阶余子阵的秩一修正阵的特征值来确定，文中最后讨论了唯一性和相应的算法。

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。

The effect of inter-block interaction can be taken into account by projecting the state of the superblock (with connecting sub-blocks, which are addressed"system"and"environment", respectively) into the system block to obtain the density matrix, the importance of each state derived by the density matrix is evaluated by the corresponding eigenvalue.

通过比较数值重整化群方法在Kondo模型中成功和在Heisenberg模型中失败的原因，得到能量最低的态不是强相关模型中的优选态的结论，从而引出密度矩阵重整化群方法。

By simply changing the sign of given symmetric matrix, an algorithm for computing the smallest eigenvalue is also obtained.

对该对称矩阵添加负号，得到了计算最小特征值的RNNs模型。

The use of the web to spread fears that flicking the switch on the LHC could create a Black Hole that could swallow up the Earth particularly concerned him, he said.

他说，使用互联网散布恐慌说启动LHC会生成一个可能吞噬地球的黑洞的做法让他感到忧虑。

Not a single word have I written down.

我一个字也没有写下来。