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Moreover, when X is a Hilbert space, Miaxoguchi and Takahashi provided the ergodic retraction theorem for general semigroups of asymptotically nonexpansive mapping by using the concept of invariant submean.

进一步，当X是Hilbert空间时，Miaxoguchi及Takahashi引入了不变子平均的概念，在一般拓扑半群上给出了渐近非扩张半群的遍历压缩定理。

In chapter 3, on the basis of measure, integration and ergodic theory, it is proved that the statistcal properties and the general complexity of the binary sequences (CG-sequences){b〓} b〓∈{1,-1} generated by a kind of chaos systems and mapping η〓 are as good as white noise sequences. These results lay the foundation of further development.

第三章运用测度、积分以及遍历理论中的一些基本原理，证明了由一类混沌差分系统和映射η〓所产生的二元序列{b〓}，b〓∈{-1，1}，具有与白噪声类似的统计特性和广义复杂度。

By making use of the ergodicity specific to the chaotic theory, one can improve the chaotic-searching optimization method based on Logistic mapping.

在优化设计领域中，混沌现象的遍历性特点可以作为搜索过程中避免陷入局部极小的一种优化机制。

Secondly, based on the decomposition of gauge potential and the φ-mapping theory,φ-topological field theory of vector and spinor field is established and the Euler class is quantized by nodal indices of vector field.

作为它在量子力学中的应用，分别给出了自旋为零和自旋为1／2粒子的整数及半整数量子化条件，发现它们仅取决于物理系统的内部对称性。

By the procedure, we first use the cosine values of the angle between view vector and normal vector on each vertex as the texture coordinates, through calculation of the dot product of the two vectors. The derivative of radial curvature on the model surface is used as the second pass texture mapping coordinates, by a calculation using Euler formula.

该方法首先通过模型顶点的视线向量和法线向量的点乘积计算其夹角的余弦值，作为第一步的纹理坐标进行映射；再通过欧拉公式计算径向曲率及其方向导数值，作为第二步映射的纹理坐标。

The execution model, task mapping strategy and performance evaluation functions of this algorithm is also illustrated.

该算法在不同的计算阶段之间进行数据重映射。

The new features include the distinguishable ground fault LED, true input to output mapping, a power supply expansion board, and a larger chassis on the PS-8. The units can be used in a split mode operation, allowing the independent operation of the two inputs to any of the outputs.

PS-6和PS-8具备了新的特征，包括可识别的接地故障LED、输入与输出图示、电源扩展板和PS-8大底盘等装置，各装置可在分割模式下运行，允许相互独立的两个输入和任何输出同时工作。

The experiment results of a real mobile robot indicate that the computational expensiveness of designed algorithms is less than other evolutionary algorithms of single-objection for simultaneous localization and mapping and accuracy of obtained maps are higher .

通过移动机器人物理实验证实了所构造算法的计算代价比其他基于进化算法的单目标优化方法少，获取的地图准确性更高。

In some real-world problems, the mapping of the variational inequalities does not have any explicit forms and only the function value can be evaluated or observed for given variables.

现实世界中，变分不等式问题中的映射没有具体表达式而只能在计算过程中对给定的自变量观测到相应的函数值。

Now turn on GI, I wouldn't describe settings now, because it will be in other section, but in shortcut i used QMC + LC, and HSV exponential as color mapping type.

现在打开gi，我现在还不想描述我的设置，因为我把它放在另一部分去讲解，但简粗略的说一下，我使用了qmc+lc，hsv曝光方式。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。