解析变换

As well as in previous work, we reduce this problem with the Schr\oder transformation to finding analytic solutions of a functional equation without iteration of the unknown function $f$.

通过Schr\{o}der变换把方程转化为不含未知函数迭代的函数方程，进而求出方程的解析解。

In the paper, the logarithmic transformation for the analytic solution on the space-time change of the tracer concentration during the instantaneous injection and the process of the one dimensional steady flow field and two-dimensional unsteady hydrodynamic dispersion is performed, and the linear equations have been obtained.

该文将描述瞬时投放示踪剂、一维稳定流场二维非稳定水动力弥散过程中的示踪剂浓度在时空上变化的解析解进行了对数变换，得到一直线方程。

To avoid the "crowding phenomenon" in conformal mapping,approximate analytical expressions of characteristic parameter for CPW′s on a thin substrate have been derived.

本文推导出了薄衬底共面波导特性参数计算的近似解析表达式，避免了薄衬底保角变换中的"拥挤现象"。

In chapter three, the dynamics of a driven spin-boson model is studied by means of the perturbation approach based on an unitary transformation. Analytical expressions for the population difference and the coherence of the two state system are obtained.

在第三章中，采用基于幺正变换的微扰方法，我们研究了驱动spin-boson模型的动力学，得到了在微波驱动下二能级系统的粒子数反转和相干性的解析表达式。

Based on integral transformation, analytical solution for the wave transmission equations in 1-D inhomogeneous media is derived. By dividing the media into layers and considering the continuous conditions between the interfaces, the transfer matrix of amplitude of waves is obtained.

利用积分变换，用解析方法求解了一维非均匀区域的不同性质对弹性波传播时波幅变化的影响；将非均匀区域离散成均匀的薄层，结合相邻层的连续条件，建立了数值解法的波幅传递矩阵。

A new non-conforming finite element FE eigenanalysis method is developed to determine the order and angular variation of singular stress states at material and geometric discontinuities in anisotropic materials subject to antiplane shear loading.

提出采用一种非协调元有限元特征法来计算各向异性材料在反平面剪切载荷作用下的奇性应力指数和奇性场角分布。该方法没有采用奇异变换技术。与以前的几种解析法比较，结果表明这种方法的收敛性好，精度高，可以求解关于复杂几何体问题

Moreover, the quasi-analytical expressions of the relative concentrations at the mobile region and the immobile region are deduced respectively by using Bessel equation, Bessel function and the method of Laplace transform under the initial concentration zero and the first or second boundary condition of a semi-infinite one-dimensional space.

并分别在初始浓度为零，半无限一维空间内第一类边界条件和第二类边界条件下，利用Bessel方程、Bessel函数和Laplace变换法推导出了可动区和不动区溶质相对浓度的准解析表达式。

Based on the process models and the desired closed-loop system responses, the analytical expressions of the tuning parameters of the primary and secondary controllers were proposed by means of first order Páde approximation, and then the digital PID controllers were obtained by using bilinear transformation method.

基于过程模型和期望闭环系统响应整定PID参数，采用一阶Páde近似纯迟延环节，以解析的形式推导出了主控制器和副控制器整定参数的表达式，并采用双线性变换法得到离散时间PID控制器。

Furthermore, it can be changed into singular integral equations with Cauchy kernel by introducing Sherman transformation. Then , the numerical example of the elastic welding problem with symmetric cracks is given, and the stress intensity factors can be obtained.

通过应用平面弹性复变方法，把满足已知边界条件的弹性平衡问题转化为解析函数的边值问题，再通过引入Sherman变换，把边值问题化为Cauchy核的奇异积分方程组。

An analytical model describing the dispersion with an exponential dispersion function is built, which be transformed into CDE problem with variable coefficient, using hypergeometric function and inversion technique, an analytical solution for two type boundary conditions is obtained.

文章对于具有指数弥散函数的弥散过程建立了对流-弥散微分方程模型，应用积分变换将问题转化为具有变系数的常微分方程问题；对于两种类型的边界条件，应用超几何函数和反演技术得到了问题的解析解，并分析了指数弥散过程和常数弥散过程的不同性质。

We will see more and more activist government policies that distinguish economic activities according to the nationality of the actors.

我们将看到越来越多激进的政府政策，这些政策根据企业的国籍来区分经济活动。

If we can prove the independence of an axiomatic system, then we can guarantee the conciseness of this system, ie.

如果能够证明某个一阶谓词系统的独立性，那么就能够保证该系统的建立是精炼的，即没有任何一条公理或推理规则是多余的。