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Firstly, a quantitative relation about finite deformation and geometrical parameters which exhibit variation of laser spectral image was introduced. And then, particular emphasis was put on some important computer processing steps related to the analysis of spectral image, such as digitizing, segmentation, feature extraction and analytical algorithms. Lastly, some examples about an experiment of a ring subject to large diametral compression were given.

文中首先给出了有限应变和平均整旋角与反映频谱图像变化的几何参数之间的定量关系，然后着重介绍了与频谱图像分析有关的数字化、分割、特征提取和分析算法等重要的图像处理过程，最后给出圆环受径向荷载大变形实验的分析实例。

For Dryden power spectral density function, using the rational spectral theory to set up the linear state-space model.

针对Dryden频谱函数，通过有理谱成形理论，建立了阵风的线性化模型。

According to spectral characteristics of the HCVAW arc in a body, energy factor which value equals to the ratio of two spectral lines' intensity, was defined.When τ's value was less than 0.1, the HCVAW arc was exhibitive of diffusedshape with lower energy density instinct; and when τ's value was higher than 0.5,the arc was a fine-constricted arc with higher energy density.

从积聚态电弧的谱线空间分布来看，阳极材料为水冷铜板时，自空心阴极端面到阳极工件，氩原子谱线相对辐射强度具有比氩一次离子谱线相对辐射强度更快的减弱趋势，最大辐射强度均出现在距空心阴极端面2mm左右的位置。

A efficient LU decomposition method is spectral factorization. That is, after the minimum phase correlative function of each array of matrix had be given by a spectral factorization method, all of the functions are arranged in a position according to its former location to get a lower triangular matrix.

谱法LU分解的优点是在对大量具有相同非零结构的矩阵分解时，通过建立包含所有具有不同非零元素的列对应的自相关函数的分解表，使得随后的所有矩阵分解只需通过查表实现。

The intensity of grating diffraction spectrum is obtained by the Fourier series expansion of the transmissivity function. Finally, the design feasibility is analyzed by comparing the minimum signal spectral intensity with the maximal spectral intensity of the background light and the noise intensity.

通过对透射率函数的傅立叶级数展开，得到光栅衍射谱线的强度，对信号光谱线的最小强度、背景光谱线的最大强度和噪声强度的比较，得到设计的可行性。

One of the important tasks in my dissertation is to investigate Fraunhofer diffraction pattern of a polychromatic, spatially coherent wave diffracted by an annular aperture. The phenomena of spectral anomalies in the vicinity of the Airy rings in Fraunhofer diffraction pattern are investigated in detail. The effect of the parameters of the annular aperture on the spectral changes is studied particularly.

本学位论文的一部分内容进一步研究了在夫琅和费衍射模型下，多色空间相干光经过环形光阑衍射后的光谱变化情况，详细讨论了在该模型下振幅为零的点附近的光谱奇异现象，着重研究了改变环形光阑参数等对光谱变化的影响。

The stability and convergence for spectral methods and spectral element methods are presented, with the aid of the knowledge of functional analysis and calculus and with the help of the theorem of Lax-Milagram, the stability and convergence for steady problems, evolution equations and Navier-Stokes Equations are analyzed in detail.

利用泛函分析和微积分的基本知识，运用Lax-Milagram定理等，从理论上比较详细地分析了谱方法和谱元方法在定常问题、非定常问题以及求解Navier-Stokes方程方面的稳定性和收敛性问题，得出了Navier-Stokes方程谱近似的稳定性条件和收敛性准则。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

A geometric structure representation of images based on the angle between spectral coefficient vectors of Laplacian graph was proposed. Graph clustering of spectral features was also investigated.

提出一种用拉普拉斯图的谱系数夹角谱特征来描述图像几何结构的方法，同时研究了基于图的谱聚类系统。

The spectral element method, which combines the high-order precision of spectral methods and the geometrical flexibility of finite element methods, has achieved great success and is becoming a useful tool for investigation of such equations.

谱元法作为一种高阶的数值方法，结合了谱方法的高精度和有限元法灵活的网格剖分技术，在不可压流体的计算中已取得了很大的成功，并正成为计算随机微分方程的一个有力工具。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。