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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。

The principle of defocus detection by critical angle method is introduced and the expression of defocus is deduced with Gauss optical formula based on Fresnel formula and a reasonable hypothesis.

介绍了临界角法离焦检测的基本原理，通过合理假设，利用菲涅尔公式和高斯光学公式得到了离焦误差信号的计算公式。

For calculation of the double integration on the boundary, the analytical formula of the first integral is deduced in detail with linear basic function, and a Gauss integration formula is used in the second integral.

以上算法利用Fortran 90 程序语言编制了计算程序。

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。

A simplified computed formula of a piezoelectric microgripper transmission organ′s transmission ratio and the angle of rotation is deduced according to the traditional method of the static equilibrium, geometric relation of mechanistic kinematics and flexible gemel.

以压电驱动式微夹钳为例进行微夹钳传动系分析，按传统的静力平衡和机构运动几何关系及柔性铰假设方法推导出其速比和转角简化计算公式。

Based on the theoretical analysis, the general buckling equation of semi-rigid frame column is deduced.

通过理论分析，推导了具有半刚性连接框架柱的一般屈曲方程。

It seems only to be of possible interest in that some computation formulae are deduced in terms of the geodesic and its azimuth.

可能关心的，看来只是某些公式是用大地线及其方位角来推导的。

In this study, a new classification method of tolerances according to semantics and mathematical representation of basic geometric elements based on DOF is given. The representation of tolerance semantics is systematically deduced based on its mathematical definition that can characterize the semantics exactly an...

给出了基于语义的几何公差分类方法及基于自由度变动的基本几何要素数学表示方法；基于公差的数学定义，系统地推导了各种类型公差的三维语义表示方法，准确完整地表示出了其语义；最后给出实例进行应用分析

Firstly, the formulation of geometrical non-linear finite element is deduced for analyzing cable-membrane structure in the paper. The judgments of cable slack and membrane fold, solution and convergence of non-linear equations are given.

本文首先推导了索膜结构几何非线性分析的有限元基本方程，并且给出了判断索单元松弛和膜单元褶皱的准则、非线性有限元方程组的解法及其收敛判定。

The preparation and essay of endogenousβ-glucosidase in white rose cut flowers during the culture process were examined, it was deduced that the amount of released geraniol concerned with the endogenousβ-glucosidase activity. That would be the flavor enhancing mechanism.

葡萄糖苷酶制备和检测最佳条件，得出了香叶醇的开释量与体内的β-葡萄糖苷酶活性变化具有相关性的结论，初步阐明了香叶醇-β-D-葡萄糖苷作为一种切花增香剂的机理。

The teacher likes the honeymouthed little girl very much.

老师很喜欢这个嘴甜的小姑娘。

Mr. Notker Bien's interests are traveling, spending quality time with the family and long-distance-running.

诺特卡·柏恩先生热爱旅游，长跑，以及和家人一起共度美好时光。