映射

We establish an asymptotic Lipschitz homotopy invariance theorem for these K-homology groups and K-theory groups. We show that the asymptotic index maps are isomorphisms for the asymptotically scaleable spaces, which include Euclidean cones, simply connected complete Riemannian manifolds with nonpositive curvature.

我们证明了这些K-同调群和K-理论群具有渐近Lipschitz同伦不变性；对于渐近可标度的几何空间（包括欧氏锥、单连通非正曲率完备黎曼流形等），证明了渐近指标映射为同构。

The horseshoe is determined by an exact and explicit map.

该马蹄是由完整的、显式的映射所确定。

Only 45% of the surface was mapped (and, unfortunately, it is too close to the Sun to be safely imaged by HST).

只有45 ％的表面是映射（和，不幸的是，太靠近太阳是安全的哈勃空间望远镜拍摄）。

By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map, it is shown whether the system has transversaUy homoclinicpoints and chaos in the sense of Smale horseshoes.

Melnikov方法是用来判定一个系统是否存在Smale马蹄意义下的混沌的一种有效的数学方法，它通过测量Poincare映射的双曲不动点的稳定流形与不稳定流形之间的距离来判定系统横截同宿点的存在性及Smale马蹄意义下的混沌的存在性。

Transfer operator; Young's nonuniformly hyperbolic system; rational map; central limit theorem; large deviation

转移算子； Young非一致双曲系统；有理映射；中心极限定理；大偏差定理

A fuzzy membership model based on support vector data description is proposed to fuzzify all the training data. Then the model is introduced into least square support vector machines. Data samples in input space are mapped into a high dimensional feature space, and then the smallest enclosing hypersphere is found.

将模糊隶属度概念引入最小二乘支持向量机，提出一种基于支持向量数据域描述的模糊隶属度函数模型，将输入空间中的样本映射到一个高维的特征空间；然后根据其偏离数据域的程度赋予不同的隶属度。

Firstly, sample data stream by two neighbor windows of given length. Then the sampling data is projected to normalized high dimension feature space and the two minus hypersphere models of two window sampling data sets are constructed respectively. Finally, detect change by computing cosine of inclination angle of two centrals of hypersphere.

该算法首先以给定长度的两相邻时间窗口对数据流取样，然后以支持向量数据描述方法将这两相邻时间窗口取样的数据流子集映射到规范化的高维特征空间，并分别建立描述这两相邻时间窗口取样数据流子集映像的最小超球模型，最后通过计算两超球之间的球心矢量的夹角的余弦，度量该两相邻时间窗口取样数据流子集的相似性检测模式变化。

On the product of unit spheres,we give a kind of natural embeddings from the product unit spheres to the unit sphere in which the product of unit spheres can be viewed as a hypersurface.

第一个是在乘积单位球面上，我们给出自然的由乘积单位球面到高一维球面的嵌入映射，然后考虑了在乘积单位球面上预给定Gauss-Kronecker曲率后，我们所考虑的嵌入的存在性。

This will leave you with just a hyphen as a prompt .

这是因为所选择的设备的游戏动作映射可能对于要求快速动作的游戏并不适用。

This paper introduces the research achievement of nonlinear systems with hysteresis, which is a non-smooth and multi-valued-mapping nonlinearity.

介绍了对不平滑、多映射迟滞非线性系统的研究成果，重点阐述了迟滞建模与控制器设计的研究现状。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。