查询词典 orientation preserving parameter transformation

Then we in-vest gate Seiberg-Witten map, which defines the equivalence relation of the gauge symmetries in different spaces. We also analyse the U gauge electromagnetic field in noncommutative space. Finally we discuss the ambiguities of Seiberg-Witten map, and find although that some part of the ambiguities can be absorbed by gauge transformation and hence negligible, the existence of the matter field makes some other parts difficult to be absorbed by gauge transformation or field redefinition.

然后利用Seiberg-Witten映射，我们研究了不同空间的规范对称性的等价问题，并对非对易空间的电磁场进行了微扰分析，最后我们对Seiberg-Witten映射的松动进行了讨论，研究发现这些松动中的一部分可以由规范变换吸收因而是可以忽略的，由于物质场的存在，另外一部分很难用规范变换和场的重定义吸收。

For the timelike surfaces with constant positive Gaussian curvature (K=1) in R〓, we construct the correspondence between R〓 and sl (2, R), and deduce the fundamental equations for a special choice of the velocity of motion of time-like surfaces in asymptotic coordinates under suitable conditions, meanwhile, we give the B〓cklund transformation and one soliton solution of the evolution equations, then in terms of a gauge transformation we obtain the explict expression of the motion of surfaces.

对于三维Minkowski空间R〓中具有正常高斯曲率（K=1）的类时曲面，取定特定速度，在以渐近线作为坐标曲线的情况下，曲面运动满足两个基本方程，即sinh-Gordon方程和θ随时间演化的方程（其中θ表示两条渐近线之间的夹角），同时给出两个基本方程的B〓cklund变换和单孤子解，并通过规范变换给出相应的正常高斯曲率曲面的显式表达式。

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。

In this paper, a new technology of laser transformation hardening which could replace the present method of gear case hardening is introduced. Its significant and economic value are analyzed. The key techniques of laser transformation hardening gear , such as surface pretreatment coating and its methods, laser scanning pattern, are discussed in detail.

通过分析可替代常规齿轮渗碳淬火的激光齿面淬火新技术研究的意义及经济价值，着重讨论了齿面激光淬火的关键技术--表面预处理涂层与方法、激光扫描方式。

In two-dimensional space, derived from the geometric transformation matrix from the transformation matrix to understand its geometric meaning.

详细说明：在二维空间内，从几何变换推导变换矩阵，从变换矩阵理解其几何意义。

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。

A transformation that is most useful in the application of the hodograph method is the inversion transformation.

在速端曲线法的应用中，一种最有用的变换是反演变换。

In this paper,we firstly utilize homogeneous linear coordinate transformation to express the object image conjugate theory of Gauss optic system;then compare it with the acting matrix in Theory of Motion Optics,expatiate on the relations between the coordinate transformation method and Theory of Motion Optics.

利用齐次线性坐标变换，将光学系统的高斯物像共轭理论用齐次坐标变换的方法来描述，并与动态光学理论中的作用矩阵相比较，阐述坐标变换方法与动态光学理论的关系。

The innovation of our thesis lies in:1 We do not require quadratic space to have hyperbolic basis. Moreover, we only require M to be projection module instead of free module;2 Eichler transformation is used instead of the traditional matrix transformation in our proof;3 Not only do we extend the relative results obtained by Bak and Vavilov and the results obtained by Vaserstein and You hong , we also simplify the proof significantly.

我们的创新之处在于： 1 不要求二次型空间具有双曲基，甚至不要求M是自由模，而仅要求M是投射模； 2 我们在论证中使用的是Eichler变换而不是传统的矩阵； 3 我们的结果不仅推广了Bak与Vavilov以及Vaserstein与游宏的相应结果，而且论证也极大地简化了。

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。