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Based on the autoregression equation for the standard variation of the residual errors obtained by ordinary regression analysis, the least square estimates and the maximum likelihood estimates for the regression, the autoregression and the moving average coefficients are derived.

提出一种异方差回归－时序模型，通过建立回归分析残差的标准差自回归方程，给出回归系数、自回归系数和滑动平均系数的最小二乘估计和极大似然估计。

The AR spectrum is not restricted by length of data, and AR spectrum parameters are sensitive for law of condition change. Autoregressive transformation is made to vibration signals, and then AR spectrum coefficients are got which can be utilized as feature vectors. Fault diagnosis method for centrifugal pump Based on AR and 2D-HMM is produced in this paper. The topology of this model and its parameters were introduced too.

利用AR谱不受数据长度的限制，AR模型参数对状态变化规律反映敏感的特点，以振动信号做自回归变换后的AR谱系数作为特征向量，将基于AR的2D-HMM引入到离心泵故障诊断中，提出了一种基于AR的2D-HMM故障诊断方法，并论述了该模型的拓扑结构和主要参数以及相应的训练和识别算法。

By utilizing the auxiliary ordinary differential equation and its solutions, the first kind and second kind of KdV equation with variable coefficients were investigated by means of the extended tanh-function method, and abundant new exact solitary wave solutions were obtained under certain conditions.

利用该方程及其解，采用改进的tanh函数展开法研究了第1类和第2类变系数KdV方程，获得了在一定条件下的若干新精确孤波解。

Moreover, existence of analytic solutions for a linear iterative equation with variable coefficients is given by reducing to an auxiliary equation and using Schauder's fixed point theorem.

此外，本章还使用Schauder不动点定理，通过建立辅助方程，研究了变系数的线性型迭代方程解析解的存在性。

Moreover, existence of analytic solutions for a linear iterative equation with variable coefficients is given by reducing to an auxiliary equation and using Schauders fixed point theorem.

此外，、本章还使用Sehauder不动点定理，通过建立辅助方程，研究了变系数的线性型迭代方程解析解的存在性。

If available, may be used to obtain a better average value for the various coefficients.

尽可能地使用不同的条件下各种温度的平均值。

The theory of AVO is based on the Zoeppritz equations, which are complicated for reflection and transmission coefficients.

精确的Zoeppritz方程描述了反射振幅信息量与弹性参数之间的关系，其近似公式是进行AVO反演、AVO交汇图分析、岩性预测和烃类检测的基础。

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。

An RANS solver is used to predict roll hydrodynamic coefficients(added inertia moment and damping)of a two-dimensional section with/without bilge keel s on the free surface.

文章用RANSE求解器计算在自由面上带舭龙骨二维柱体的横摇水动力系数。

Accordingly, on the hypothetical condition that the material coefficients are the linear functions of tem perature and according to the theory of functional analysis, the authors use the method of combing the inner product form with convolution bilinear form, which leads to the functional of the quasistatic coupled thermo—viscoelasticity including the boundary and initial c...

因此，著者在物性系数是温度的线性函数的假设条件下，根据泛函分析理论，采用内积式与卷积双线性式相结合的方法，导出了包含所有边界条件，初始条件及热传导方程的拟静态耦合热粘弹性问题的泛函，并证明了与之相应的变分原理。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。