一阶

Combining the definition of CWT and the derivative property of convolution, we constructed a general method to calculate the approximate derivative of signal through CWT by using the first and second derivative of Gaussian function, Haar, and the first derivative of three-order-Spline function as wavelets. As compared with the other approaches of calculating derivative, which include the numerical differentiation, polynomial filters, Fourier transform, and the recently proposed DWT method, fast calculation and simple mathematical operation were remarkable advantages of CWT method. For the signal corrupted by severe noise (Signal-toNoise Ratio=5), the satisfactory results could also obtained via CWT method through appropriately adiusting the dilations.

在此基础上，(1)结合连续小波变换的特点和卷积的微分性质，提出了使用Gaussian函数的一阶和二阶导数，Haar和三次样条函数的一阶导数作为小波函数的连续小波变换计算信号近似导数的一般性方法，与其他导数计算方法(包括数字微分法，多项式滤波法，Fourier变换法和离散小波变换法)相比，本法简单便捷，计算速度快，对于噪声含量较高的信号(S/N为5)，只要适当调节尺度即可获得比较满意的结果。

One bases on function value and another bases on arithmetic average difference quotient. In this paper, the author mainly studies the approximation properties of both the function value and the derivative of two kinds of splines interpolation mentioned before, and the optimal error constants are obtained finally.

文中分别就这两类插值样条的函数值及一阶导数的逼近性质展开讨论，相应得出这两种插值函数在被插函数分别为一阶连续可导和二阶连续可导情况下的最佳误差常数。

Assignment of infinite many poles for the first order generalized distributed parameter control system, coupled with the first order generalized lumped parameter control system, is discussed in Hilbert space with functional analysis and operator theory. The solutions with the constructive expression are given by the generalized inverse one of bounded linear operator.

应用泛函分析算子理论的方法，讨论了Hilbert空间中一阶广义分布参数控制系统与一阶广义集中参数控制系统所构成的一阶耦合广义控制系统的无限多极点配置问题，利用有界线性算子的广义逆给出了问题的解及解的构造性表达式。

Second order incident boundary condition on fixed incident boundary is derived for numerical simulations, based on the cnoidal or sinusoidal motions of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. 2 The analytical solution for higher-order Boussinesq equations is derived and its applicable range is discussed. 3 A 2-D fully non-linear numerical model using boundary element method is developed to obtain wave forces acting on rectangular obstacle. 4 The three-dimensional fully non-linear waves are studied in a numerical wave tank using finite element method.The studies on the coupled numerical model combined Boussinesq equations with Laplace equation are following.

非耦合非线性波浪计算模型：1 根据造波板做椭圆余弦运动或正弦运动速度，推导出数值模拟波浪水槽时固定入射边界上的二阶波浪入射边界条件，数值计算结果和实验结果的对比表明采用二阶入射边界条件对波面升高的预报比采用一阶入射边界条件对波面升高的预报更为精确；2 推导了波浪水槽造波板做正弦运动所产生波浪的高阶Boussinesq方程摄动展开解析解，讨论了该解析解的适用范围；3 对整个波浪水槽应用边界元方法数值模拟了波浪对物体的非线性作用；4 用有限元法求解三维Laplace方程模拟了三维完全非线性波浪水槽。

The main contents of this course include: the elementary solution of first order differential equations, the theory of existence, uniqueness and continuity dependency of initial value problem of first order differential equations, the structure theory of higher order linear differential equation and the solution of constant coefficient equations, the structure theory of system of linear equations, basic solution matrix and the solution of system of constant coefficient equations.

本课程内容有：一阶微分方程初等解法，一阶微分方程初值问题的存在性、唯一性、连续依赖性理论，高阶线性微分方程解的结构理论和常系数方程解法，线性方程组的结构理论、基解矩阵和常系数方程组的解法。

In addition, for a class of first-order predicate expression namely first-order predicate expression without free variable and with one quantifier, a necessary and sufficient condition for such first-order predicate expressions to be equivalent and a corresponding judging algorithm are come up with.

另外，对于一阶谓词公式的一个常见子类——无自由变元单量词的一阶谓词公式，提出了一个判定这种一阶谓词公式等价性的充分必要条件和判定算法。

The results are generalized to first-order neutral functional differential equation.

第四章讨论了一阶泛函微分方程解的零点分布，改进了一阶滞后型泛函微分方程在解的零点间距离的上界估计的结果，并将此结果推广到一阶中立型泛函微分方程。

Firstly, by adopting the thought of Adomian's decomposition method, the generic dynamic model in mechanical systems are transformed into a standard first-orderdifferential-equations, and then the inverse operator method for the approximate analytic solution of nonlinear mechanical system is developed based on the exact solution in form.

主要研 究工作如下：利用Adomian的分解方法的思想，把机械系统中最一般的动力学模型转化为一阶标准型微分方程组，以形式上的精确解的表达式为基础构造了求解机械系统非线性模型近似解析解的逆算符方法；针对机械系统非线性模型的特点，提出了直接处理高阶方程的不降阶逆算符方法；证明了该方法的收敛性。

The above problems are studied in this thesis. First, the implicit NND scheme with mix flux splitting method proposed by Zhang Hanxin that is first order accurate in time and second order in space is modified. The modified scheme keeps the characteristics of fast convergence and is second order accurate both in time and space. It can be capable of simulating the unsteacly flow. Second, the topological method founded by Zhang Hanxin is improved to study the characteristics of vortex near the singular point on its axis and the cross streamlines on the longitudinal section passing the vortex axis. On the basis of topological results, a program which visualises numerical results is made out. It can help us analyse the characteristics of vortex motion.

本文对上述问题做了研究：第一，在数值模拟方面，借助于张涵信提出的NND算法和混合通量法，我们将他建立的时间为一阶、空间为二阶精度的快速隐式算法推广为时间和空间均为二阶精度的算法，这样做保留了原格式收敛快的特点，而且能适用于真实的非定常流态的计算；第二，将张涵信的拓扑分析方法加以推广，研究了涡轴附近及破裂点邻域内流场的空间特征，并以这些拓扑分析结果为指导，研制了一套显示计算结果的软件，这一软件能很好地帮助我们分析流场的计算结果和旋涡演变的特征。

The vertical axis of the switch has a surface of positive first differential, comprised of splines drawn between points if varying distance from a datum plane, and has along the horizontal axis a surface of a positive first differential and negative second differential, comprised of a combination of splines drawn between points of varying distance from the datum plane.

开关的竖直轴线的表面具有正的一阶微分，其由多个在离基准平面不同距离的点之间绘制的样条构成，并且沿水平轴线具有一个表面，该表面具有正的一阶微分和负的二阶微分，其由一组在离基准平面不同距离的点之间绘制的样条构成。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。