展开系数

This paper is composed of the algorithm design of dual-tree binary coefficients complex wavelets,MGM algorithm for linear systems that can be diagonalized by generalized discrete Fourier transform and type-II discrete sine transform matrices, wavelet and MGM algorithms for Toeplitz systems and their applications in signal and image processing.

本文以多进制小波与对偶树二进制系数复数小波算法设计、三角变换对角化系统MGM算法、Topelitz系统的小波与MGM结合算法作为理论主线，以对偶树复数小波与扩散方程方法结合的图像去噪，信号与恢复作为应用背景展开讨论。

The propagation equations for oblique and off-axial Gaussian beams passing through cat-eye optical lens are deduced by using the theory of matrix optics and expanding the aperture function into a finite sum of complex Gaussian functions.

运用矩阵光学理论以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，进一步推导了倾斜离轴高斯光束通过猫眼光学镜头的解析传输公式，通过数值计算分析得到了倾斜系数和离轴量对猫眼效应反射光光强分布的影响规律。

The velocity potential is expanded about the still water level with the coefficients being the functions of horizontal coordinates.

将速度势沿静水面位置展开，其系数是水平位置的函数。

Recurrent formulas for calculating the coefficients of the Legendre polynomial and the expressions for calculating the sedimentation coefficient are deduced analytically.

为了研究多分散低Péclet数沉降问题，我们先以Legendre多项式展开法得到了计算对分布函数的普遍递推式，以及由Legendre多项式的系数表示的沉降积分。

This method is based on the weight allocation method. Through the introduction of the unascertained information into the matrix of weight coefficients, the unascertained model for the reliability allocation of spaceborne antenna deployment mechanism is built.

在综合评分为权的系统可靠性加权分配法的基础上，将未确知信息引入可靠性分配的权系数矩阵中，建立了星载天线展开机构系统可靠性分配的未确知模型。

During the T-matrix method of calculating light scattering by particle, incident and scattered fields are expand into spherical vector wave functions: which, via their relationship derived from the Maxwell equations, leads to the T-matrix, a transferring matrix between expansion coefficients of fields.

在粒子光散射计算的T矩阵方法中，将入射场和散射场用球矢量波函数展开，通过Maxwell方程推出二者之间的关系-零场方程，可获得散射场和入射场展开式系数之间的传输矩阵-T矩阵。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

Therefore, the matched filter bound for such channels can be expressed as the sum of the coefficients corresponding to the negative eigenvalues in the partial fraction expansion of the characteristic function.

因而该信道下的匹配滤波界可以简洁地表示为该特征函数部分分式展开中负特征值对应的系数之和。

Then, base on the equivalent circuit model for cascaded coupled resonator filter, the method for measuring or computing the phase of the reflection coefficient of short-circuit terminated networks and synthesizeing all the inter-resonator couplings and resonant frequencies of the filters to be tuned is studied intensively. The phase loading effect is removed and the tuning steps are analyzed. The method based on the partial fraction expansions of admittance matrix is used to synthesize coupling matrix of the filters under tuning.

然后，通过分析级联耦合滤波器的等效电路模型，着重研究了利用测量或计算终端短路网络的反射参数的相位来综合出待调级联耦合滤波器各个腔体的谐振频率和腔体间的耦合系数的方法，并且消除了端口相位加载的影响，给出了具体的调试步骤；接着利用导纳矩阵部分分式的展开来求得待调滤波器耦合矩阵，着重研究了消除端口相位加载的方法。

For polydisperse systems at large Péclet number, we establish the systems of differential equations describing the leading term and the second term of the pairdistribution function via regular perturbation method.

针对高Péclet数情形，通过正则扰动法我们建立了决定对分布函数的微扰展开的主导项和一阶项的联立方程组，并用由此算出的对分布函数的数值解计算了系统的沉降系数。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。