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Structure-Based Approximation Learning Theory: Under the description of manifold and topological architecture of neural field, we have proposed a learning frameworks of neural networks based on global architecture approximation theory borrowed from the concept of topology and manifold to solve the optimal problems of learning in non-nonlinear and non-Euclidean space, and discussed a few basic components of the learning theory, learning mechanism and learning algorithm in the term of structure-based approximation and global structure analysis.

基于结构的逼近学习理论：通过人工神经网络模型神经场的流形结构和拓扑结构描述，我们提出了在非线性和非欧氏空间中基于整体结构逼近的神经场学习理论框架；用对偶流形理论和拓扑概念作为工具，讨论了神经网络的学习理论、学习机理、学习算法和算法的具体实现。

Toynbee not only studies thorough China's Yin-Yang theory, but also uses this theory to explain his own theory about civilization.

汤因比不仅仔细研究了中国的太极阴阳之说，并且用这一学说来解说自己的文明理论。

The paper combines investigative mode of theory analysis and numerical simulation analysis, based on elastic and plastic theory, explaining the relation of stress fields and stress- transmogrification. Then citing key stratum theory, the paper analyzing the moving rule of the stratum above the laneway along the gob, gaining some disciplinary cognition.

论文采用理论分析与数值计算模拟分析相结合的研究方式，根据弹塑性理论求解了巷道围岩的应力场及应力变形关系；进而引用关键层理论，对深井综放开采沿空巷道的上覆岩层运动规律进行分析，获得了一些规律性认识。

The main content of this dissertation can be described as follows: Firstly, the precision measuring theory of spindle rotatory error by the single, double, trinary sensor respectively is researched more thoroughly along with the elimination principle of measurement deviation. According to the characteristic of boring, a new measuring theory and its evaluation criteria of two radiating sensors is proposed based on the theory of relative axis trace movement.

全文围绕实现主轴回转误差的测量与补偿理论机器在镗削加工中的应用研究展开，具体内容概括如下：首先，在分析主轴回转误差的精密测试理论之后、对单传感器、双传感器、三传感器方法的测试理论，测量偏差的消偏原理等理论进行深入地研究。

The unaccomplished formation of joint crime is a cross theory concerned with both the theory of joint crime and the theory of criminal formation.

共同犯罪的未完成状态是涵盖刑法共同犯罪理论及犯罪形态理论两大部分的一个交点性理论问题。

From the defects in the basic theory of present classical infinite theory, the essential relationship between Russell's Paradox and Cantor's proof on the uncountability of real number set and the proof on the Cantor's Theorem of is analyzed and a mysterious error is found:The core of Cantor's above two important proofs in set theory are actually another versions of Russell's paradox and the very same paradoxical idea was applied in both Russell and Cantor's work, and Cantor made wrong use of this paradox idea with two logical mistakes.

从经典无穷理论体系中的缺陷入手，深入分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系，发现康托在这两个证明里的核心部分实际上是罗素悖论的翻版，它们与罗素悖论有完全相同的思路，并且康托犯了两个逻辑性错误而误用了这个悖论思路。

"Unified field theory," which would unite general relativity—his own theory of spacetime and gravitation—with Maxwell's theory of electromagnetism.

"统一场论"：爱因斯坦最后三十年试图实现的工作，将他的重力时空观和麦克斯韦的统一场论结合起来的理论。

The traditional circle theory about history was changed into a new unilinear development theory. In 1898, Yan Fu introduced the theory of evolution and the thought of struggle for life to China.

传统的历史循环进化观演变为新的单线前进的"三世进化说"。1898年，严复将西方的进化思想介绍到中国。

Kinetics theories: Know the theoretical model, solution, main conclusion, virtue and disadvantage of simple collision theory, transition state theory and unimolecular reaction theory.

了解简单碰撞理论、过渡态理论、单分子反应的理论模型、处理方法、主要结论和优缺点。

We introduce the basic theory of quasiconformal mappings of the development and the research situation of the theory of quasiconformal mappings, the theory of Schwarz derivatives and the inner radius of univalence.

在这一章中，我们简单介绍了拟共形映照的基本理论，回顾了拟共形映照及Schwarz导数理论的发展及区域单叶性内径的研究现状，并简要的介绍了作者的主要工作。

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。