查询词典 birational invariant

In this paper we study mainly the topological structures of some invariant sets and entropy of continuous self-maps on Warsaw circle and unstable mainifolds and entropy of continuous self-maps on a tree.

中文摘要：本文主要研究了华沙圈上连续自映射的一些不变集的拓扑结构、拓扑熵和树上连续自映射的非稳定流形和拓扑熵等某些动力性质。

Secondly,we derive the complete decomposition of U(1) and SO(2) gaugepotential using the unit vector of the wave function,through which we show thatthere exists a topological invariant number in quantum mechanics,which iscorresponding to the winding number.

其次，我们用波函数的单位矢量导出了U(1)和SO(2)规范势的完整分解式，表明在量子力学中存在着一个对应于环绕数的拓扑不变量。

It is pointed out for the first time, that if in the Chern-Simons field theory the vortex lines are knots, the Chern-Simons action itself is a topological invariant; a step further, this action is just the total sum of all the self-linking and linking numbers of knot family.

文中首次指出，当陈-Simons场论中的涡旋线是纽结时，陈-Simons作用量本身是一个拓扑不变量，并进而指出这一作用量恰是纽结族的所有Self-Linking数和Linking数之和。

In terms of the topological invariant in Riemann-Cartan spacetime proposed by Prof. Duan and the φ-mapping topological current theory, we gave the cosmic strings with the complex scalar field and showed that the strings appear in the zeroes of the scalar field. Meanwhile one can find that the length of cosmic strings is quantized in the topological level and the quantum number is determined by Hopf indices and Brouwer degrees.

以段一士教授提出的Riemann-Cartan流形中的新拓扑不变量为基础研究了宇宙弦的拓扑结构，指出宇宙弦只能存在于复标量场的零点处，而且在拓扑层面上是量子化的，而该量子数决定于Hopf指数和Brouwer度。

It investigates mainly infinite matrix conver-gence、infinite matrix transformations、the automatic continuity and boundedness of infinitematrix operators、infinite matrix topological algebras、invariant theory、infinite matrix meth-ods、compact operators series and Eberlein-Smulian theorem,etc.

主要研究了无穷矩阵收敛、无穷矩阵变换、无穷矩阵算子的自连续性和自有界性、无穷矩阵拓扑代数、不变性理论、无穷矩阵方法、紧算子级数与Eberlein-Smulian定理等。

Tracing an invariant optimization point can often alert us to a clean pocket of predictability.

而对一个不变量的优化点的追踪，则通常都会提醒我们注意一个规则的可预测性的口袋。

The CNEAR parameters are invariant to translation, rotation around the origin, scale and choice of the starting point in tracing a boundary.

CNEAR模型参数具有平移、旋转和比例不变性并与计算起始点的选择无关。

The CNE-AR model coefficients are invariant to translation, rotation, scale and choice of the starting point in tracing a boundary, in which both linear and nonlinear features of the shape boundary are taken into account, and the intrinsic characteristics of the shape boundary are further depicted.

CNE-AR模型系数具有平移、旋转、比例和轮廓跟踪起始点选择不变性，兼顾了图形轮廓中的线性与非线性特征，深刻反映了图形轮廓的本质特性。

With their invariant function of geometric transformation,they have been widely used in the field of image analysis.

不变矩是表达图像几何形状信息的参数，具有几何变换的稳定性，在图像识别领域已经得到广泛应用。

By using ways such as Darboux transformation, invariant group and Painleve analysis, we can find exact solutions of nonlinear evolution equations.

特别，在本课题中，我们发展了一套求解高维非线性方程和方程族的方法。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。