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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。

This paper introduces basic concepts, representation methods and practiCal applications of computer internal division graph and external divistion graph, and presents a linear mapping method of representing internal divisio.

计算机内插图形和外插图形是计算机图形学中由图形生成图形的两种基本方法，用该方法可以生成许多有趣的图形、图案，在计算机动画模拟图案设计中有着广泛的应用。

This research adopted focus group interviews and mind-mapping to externalize expert's tacit knowledge related to core tools of QS-9000 requirements.

本研究系透过焦点团体法及心智图模式，外化专家的内隐知识，提供不同之学习媒介，进而帮助学习。

In the second and third part, some general methods and processes of "organizing" and "connecting" are detailed, including familiarization, coding, indexing, and mapping, etc., and some of these methods are compared.

文章第一部分简要介绍访谈资料整理和分析的特点，第二、三部分分别论述了"组织"和"连结"的具体方法，并对不同方法进行比较。

The role of the environment is very important.

的作用，环境是非常重要的。

At that time, the High Court of England and Wales Court of Queen's Bench president of William Murray, Lord Mansfield in June 22, 1772 ruling:"No matter then there is the inconvenience, but there must be a decision, I can not say that this case under the law in England are permitted or authorized; are so black should be released."

当时的英格兰及威尔士高等法院王座法庭院长William Murray， Lord Mansfield于1772年6月22日宣判：「无论有那麽不便，但总要有个决定，我不能说这件案在英格兰法律之下是准许或认可；所以黑人是应该被释放。