矩阵函数

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。

For the beam buckling problem, this paper presents the Barycentric Lagrange interpolation collocation method to get the differentiation Matrix of unknown function.

采用重心Lagrange插值多项式建立未知函数的微分矩阵，采用配点法将梁的控制方程表示为代数方程组。

Differential matrices are obtained on the element in accordance with continuous intervals of discontinuous boundary value problem to divide the computing elements and approximating unknown function on the element in term of barycentric Lagrange interpolation.

按照间断边值问题的连续区间划分计算单元，在每一个单元上采用重心Lagrange插值近似未知函数，得到每一个单元上的微分矩阵。

In this thesis,using the Bernstein polynomial approximation,Stieltjes transform method and the central limit theorem of martingale,under suitable moment conditions,we prove the CLT of LSS G_n with a generalized regular class C4 of the kernel functions for large dimensional sample covariance matrices.

在适当的矩条件下，当核函数f属于C4时，我们证明了大维随机协方差矩阵的线性谱统计量的中心极限定理。

Applying the theory of Bessel function, the exact transfer matrix formulae of the asymmetric free vibration of the circular and annular plate elements with uniform thickness can be obtained.

应用贝塞尔函数理论，求得等厚度圆板和环板单元非对称自由振动传递矩阵的正确公式。

Functions, relations and graphs; inverse functions; inequalities; theory of equations; introduction to matrices; determinants; binomial theorem; sequences and series.

函数， 图表，曲线。反函数，不等公式，等式，矩阵的介绍，定列式，序列和系列等。

By means of Boolean matrix operation method, a study is made of defining the prime implicant of multi output function and the operation routine of the method is illustrated with some examples.

运用布尔矩阵运算的方法对确定多输出函数的质蕴涵进行了研究，并通过示例说明了这种方法的运算程序。

From [1], Every transition function is a positive strongly continuous semigroup of contractions on l\, but it isnt a strongly continuous semigroup on l_∞- In fact, the sufficient and necessary condition for a transition function to be a strongly continuous semigroup on l_∞ is that the q—matrix Q is an uniformly bounded q—matrix on l_∞- This is the trivial case.

由Anderson[1]知道转移函数P是l_1空间上正的强连续压缩半群，但P一般来说不是l_∞空间上的强连续半群，而P是l_∞上强连续半群的充要条件是q—矩阵Q是l_∞。

Standard neural network model is the interconnection of a linear dynamic system and a bounded static nonlinear operator, which is depicted as a linear differential inclusion to be analyzed easily with linear matrix inequalities technique.

标准神经网络模型(SNNM-Standard Neural Network Model)由一个线性动力学系统和有界激励函数构成的静态非线性算子连接而成，被表示为线性微分包含的形式，便于利用线性矩阵不等式技术进行分析。

A new non-linear quadratic programming Bayesian prestack three-terms inversion method is developed; Firstly, this method is based on Bayesian parameter estimation theory, Gaussian distribution is used for likelihood function and modified Cauchy distribution is used for prior distribution; Secondly, covariance matrix is used to describe the degree of correlation between the parameters; rock physics relations are used to constrain the inversion results; at last, this method is transformed into non-linear quadratic programming problem, and inversion results are acquired under several constraints.

本文提出了一种基于非线性二次规划的叠前三参数反演方法。首先基于贝叶斯参数估计理论，假设似然函数服从高斯分布，并使待反演的参数服从于改进的Cauchy分布，从而提高了反演结果的分辨率；其次用协方差矩阵来描述参数间的相关程度，进一步提高了反演结果的稳定性；最后将问题转化为一个非线性二次规划的求解问题，并在多种约束下得到问题的解。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。