变换

By using a gauge transformation between thetwo eigenvalue problems, we obtain a correspondence between the hie -rarchy of nonlinear evolution equations associated with the Kaup-Newelleigenvalue problem and the hie rarchy of nonlinear evolution equationsassociated with the AKNS eigenvalue problem.

利用规范变换，我们得到了与Kaup-Newell特征值问题相联系的一族非线性演化方程和与AKNS特征值问题相联系的一族非线性演化方程之间的一个对应关系，并给出了Kaup-Newell系统的Darboux变换及其证明。

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。

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

Using the relations between Hermite and Laguerre-Gaussian modes and expanding the window function of two-dimensional rectangular hard-edged apertures into a finite sum of complex Gaussian functions, the propagation of complex- argument Laguerre-Gaussian beams through a paraxial optical ABCD system with a rectangular hard-edged aperture is studied. An analytical propagation equation is derived and used to study the diffraction at the rectangular hard-edged aperture and the focusing properties of complex-argument LG beams.

利用拉盖尔－高斯模和厄米－高斯模的变换公式，并使用将二维矩孔光阑窗口函数展开为有限个复高斯函数之和的方法，得到了复宗量拉盖尔－高斯光束通过含矩形硬边光阑近轴ABCD光学系统的变换的解析传输公式，并对复宗量LG光束通过矩形硬边光阑的衍射和聚焦特性进行了研究。

Asynchronous loading of control parameters · Rapid (25ns per pixel) rotation, warping, panning, and scaling of images · Three-dimensional image addressing capability · General third-order polynomial transformations in two dimensions on-chip · Three-dimensional transformation of up to order 1.5 also supported · Flexible, user-congurable pixel datapath timing structure · Static convolutional ltering of up to 16 x 16 Pixel, 256 x 256 pixel or 256 x 256 x 256 pixel windows · User-selectable source image subpixel resolution of 2-8 to 2-16 · Pin-compatible upgrade to TMC2302 · 24-bit (optional 36-bit) positioning precision within the source image space, 48-bit internal precision · Low power CMOS process · Available in a 120-pin Plastic Pin Grid Array and 120-lead Metric Quad Flat Pack

1第1页，本页显示记录1-11，共11条记录分1页显示·异步控制参数加载·快速（25ns的每个像素）旋转，弯曲，平移，缩放和图像·三维图像处理能力·一般二维三阶多项式变换片·三高达1.5三维变换命令也支持·灵活，用户可配置的数据通道的静态时序结构·高达16 × 16像素滤波卷积像素，256 × 256像素或256 × 256 × 256像素（3通）窗口·用户可选的源图像亚像素分辨率的2-8 2-16·引脚兼容的升级TMC2302·24位（可选36位）的定位源图像的空间内，48位内部高精度·低功耗CMOS精密加工·提供120引脚塑料针栅阵列和120引脚公制四方扁平封装

We obtain the transient distribution of queue length and probability generating function of queue equilibrium distribution.

研究了服务前需要重新调整机器的单重休假M~x/G/1排队系统，在LS变换和L变换下得到了服务员忙期中队长的瞬态分布和队长稳态分布的概率母函数。

If average values before or after catastrophe point when the pressure at both ends reduces exceed the threshold value, judging that there is leak and positioning: calculating approximate wavelet transformation coefficient of pressure data at both ends, initializing searching interval, calculating a signal time delay value corresponding to approximate wavelet transformation coefficient in the searching interval from maximal scale N; converting the time delay value under scale N to that under N-1 by geometric proportion relation; updating the searching interval, repeating above processes until the scale is 0 and positioning based on the time delay value.

若两端压力下降突变点前后的均值变化均超过阈值，判定有泄漏并进行定位：计算两端压力数据的近似小波变换系数，初始化搜索区间，从最大尺度N开始在搜索区间内计算对应近似小波变换系数的信号时延值，利用等比关系将尺度N下的时延估计值转换为N-1下时延估计值，以该值更新搜索区间，重复以上过程至尺度为0，以此时延估计值进行定位。

Fourier transform is used to analyze the grazing incidence X-ray reflectivity curve of nanometer multilayer structures.

利用傅里叶变换分析了纳米多层膜的X射线掠入射反射率测试曲线，模拟了各种制备和测试条件对多层膜结构参数测试结果的影响，检验了傅里叶变换方法的适用性和精确度。

The Fourier transformations about the azimuthal angle and Hankel transformation about the radial direction have been used to convert the basic equations of elasticity into a non-homogenous first-order ordinary differential equation system in cylindrical coordinates.

在柱坐标系下，利用关于方位角的Fourier变换及关于径向的Hankel变换，将弹性力学基本方程组转化为非齐次的一阶常微分方程组的标准形式。

Chapter 3 describes somemeans to measure harmonic and compares two most popular of them. As the mainpart of this thesis, chapter 4 presents the whole process of building the simulationmodel of the water-heated system.

论文第三章列举了多种谐波检测的方法，比较了各种谐波检测方法的优缺点及目前的应用状况，并主要对其中的两种算法，即快速傅立叶变换法和小波变换法进行了对比和分析。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷