对角化

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

The diagonalization of the Cauchy kernel is one of the most important theorems in the theory of symmetric functions.

Cauchy核的对角化是对称函数理论中最重要的定理之一。

The latter one is our effort in attacking the diagonalization of the Cauchy kernel on Schubert polynomials (the noncommutative version conjectured by Alain Lascoux is still open).

后者是我们在关于Schubert多项式的Cauchy核对角化方面所做的努力（Alain Lascoux猜想在非交换的情况下也成立，但目前为止还没有被证明）。

The diagonal form of implicit approximate factorizated NND difference scheme is used to solve the three-dimensional compressible Navier-Stokes equations.

本文采用计算效率较高的标量对角化隐式NND格式，通过求解Navier-Stokes方程对影响再入体表面热流计算准确的诸因素进行了综合分析。

Two forms of implicit TVD schemes are proposed in this paper for the simulation of nonequilibrium flows past hypersonic re entry vehicle, which are derived from the diagonal form of an approximate factorization algorithm and lower upper scheme applied to the implicit part of Harten Yee's TVD scheme respectively.

针对高超音速化学非平衡流提出了两种隐式格式。一种是近似因子分解算法对角化形式在隐式TVD格式上的推广，另一种可视为隐式TVD格式的LU分解形式。

A sufficient condition is firstly established such that a nonsymmetric saddle point matrix is diagonalizable with real and positive eigenvalues.

首先给出使得非对称鞍点矩阵具有实正特征值且可对角化的充分条件，该条件比已有著名条件更弱。

A diagonalization algorithm was presented for the model.

给出了模型的对角化算法。

I n this note,a necessary and sufficient condition of diagonalization for square matrix is considering.

方阵是否可以对角化，是矩阵的一条很重要的性质。

By using conclusions of matrix rank,a necessary and sufficient condition of diagonalization for square matrix is given.

本文利用矩阵秩的相关结论，给出并证明了方阵可对角化的一个充要条件。

In this paper, a suboptimal user selection method is proposed based on Block Diagonalization.

摘要该文基于块对角化的思想提出了一种次最优用户选择方案。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。