从数学的角度来看，这属于反问题的一种。
From the viewpoint of mathematics, this is a kind of inverse problem.
我们完全无法从数学的角度理解PSO，这便是智能。
We are unable to comprehend PSO mathematically, and thus things for intelligence.
考虑到现有星球数量，从数学的角度来说，其他行星上面肯定存在生命。
Given the sheer number of stars that exist it's a mathematical certainty that there is life on other planets.
从数学的角度看，根据定义，投资者在这些衍生品上的总损失应该等于总利润。
From a mathematical viewpoint, the combined profits and losses on these derivatives will, by definition, cancel out, so they should not add anything to the total underlying loss.
根据挖掘机的工作原理，从数学的角度阐述了挖掘过程的轨迹方程应是对数螺线。
According to the working principle of a excavator, this paper describes mathematically that the trace equation of digging processes is of logarithmic helix.
从数学的角度给出并证明了在数理经济学中非常重要的利润函数与供给映射的几个性质。
The article deals with a few important properties of profit function and supply mapping in the mathematical economics from the view of mathematics.
从数学的角度，这充分说明某一研究领域的文献量内部变化趋势未必相近，有时甚至会相反。
From his standpoint, this fully demonstrates that a research field of literature among the trends are not similar, sometimes even be on the contrary.
从数学的角度论证了与效用最大化相对应的消费方案的存在唯一性以及求解方法，并通过图形对其进行了解释。
This paper discusses the existence and uniqueness of consumption plan to attain the utility maximization and solution of them by mathematic viewpoint.
民间遗产可以从不同的角度来作出定义：从哲学的角度、从知识的角度、从语义的角度、从程序的角度、从数学的角度、甚至从行政的角度。
Folk heritage can be defined from various angles: philosophically, from a knowledge point of view, semantically, from a procedural, mathematical or even administrative Angle.
从数学的角度，运用较新的群体多目标规划理论详细地推导了建立结构维修策略模型的全过程，并在此基础上，解释了如何定量考虑结构的最优可靠度。
The process of making the model is discussed in detail based on the latest group decision making theory. Meantime, it explained how to choose the structural optimal reliability quantitatively.
当然，那是从数学角度来说的。
没有一个人可以理解量子理论——不论从什么角度来说，他都是人类历史上最成功的物理理论——除非他们能够掌握最为深奥的数学。
No-one can understand quantum theory — by any account, the most successful physical theory there has ever been — unless they grasp the underlying mathematics.
他仅关心一个想法的数学结果，从各种对称的角度考虑看看能得出什么结果。
He was just concerned with the mathematical consequences of an idea, working out what can be deduced from the various symmetries.
这个谜团即将揭晓。这多亏了一项新的数学模式，从叶脉角度出发探讨这个问题。
The mystery of why leaves take such different shapes is closer to being solved thanks to a new mathematical model that looks at the problem from the perspective of leaf veins.
从数学角度来说，这四种关联的东西可以用6种方式连接。
Four interconnected things, mathematics says, can be related in six ways.
毫无疑问，返回的比赛是 Race_01，从数学和字母角度来说都是正确的，26.2大于 13.1。
Sure enough, the race that comes back is Race_01, which is correct: 26.2 is greater than 13.1, both mathematically and lexicographically.
并在此基础上，从宏观和微观两个角度，剖析了数学言语的特性，阐述了数学言语的教育功能。
Base on these, the characteristics and educational function of mathematical speech are analyzed from the two points of view of macrocosm and microcosm.
从现代数学的角度看来，它们都是符号。
From a modern mathematical point of view, they were all alike symbols.
本文仅就声波探查砼裂缝深度的可行性从数学角度进行了分析与论证，并给出了工程实例。
This paper, from the Angle or mathematics, makes analysis and discussion on the feasibility of acoustic wave detection of crack depth in concrete, and provides practical engineering examples.
因此，如何从数学教育的角度考虑数学实验，是在数学教育实践中必须深入研究探讨的问题。
Therefore, how to think of mathematics experiment from the view of mathematics education is the problem we must further investigate and probed into in the educational practice in mathematics.
从物理和数学的角度，对单相电路、三相电路瞬时有功功率和瞬时无功功率的概念进行了剖析。
From physical and mathematical points of view, this paper analyses the nature of instantaneous active and reactive power.
本文针对目前这种状况从安全评价的角度，应用可拓物元和模糊数学评价的方法对狭水道操纵安全进行评价。
Regarding this situation, the author here is trying to apply matter-element assessment method and fuzzy mathematical comprehensive assessment method to assess narrow channel manoeuver safety.
从数学教育史的角度看，我国古代教师是一种原始状态下的课程设计者、实践者、研究者；
From the history of mathematics education, teachers in the ancient time were the primeval designers, practitioners and researchers of the curriculum.
论文从能量平衡的角度探讨了射流切割的过程，建立了水射流切割深度数学模型。
It discusses the water-jet cutting process by the balance of energy, and builds a mathematic model of cutting depth.
结果爱因斯坦首次从理论和定量的角度对布朗运动进行了研究，这成为布朗运动理论数学化的起点。
Results Einstein first studied Brownian motion from the theoretical and quantitative point, and his work is the beginning of mathematical theory of Brownian motion.
因此，本文从积分的角度对TCIA与传统的分区旅行费用法(ZTCM)的数学本质进行了详细的对比分析。
Therefore, the paper makes a detailed comparing analysis of TCIA and the mathematical nature of traditional zonal travel cost method (ZTCM) from integral viewpoint.
最后从工程角度提出了有现实意义的软件测试框架，并从数学上证明了该框架的有效性。
Finally the article puts forward software test frame with practical significance from engineering point of view, and gives a mathematical proof for.
从数学角度对铅球出手前的运动过程进行生物力学分析，并对一般抛射运动规律进行数学逻辑分析。
From the Angle of mathematics the paper analyzes the moving process of shot according to the principles of biological mechanics.
从数学方法的角度，通过若干实例的分析，阐明了“数学构造性方法”的具体应用。
From the Angle of mathematical methodology, by analyzing some typical examples, the forth application are set on constructivity method of mathematics.
从数学方法的角度，通过若干实例的分析，阐明了“数学构造性方法”的具体应用。
From the Angle of mathematical methodology, by analyzing some typical examples, the forth application are set on constructivity method of mathematics.
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