《数学原理》(Principia Mathematica)是罗素和怀特海的著作,也是早期分析哲学的基石,它的公理系统与《数学原则》(Principles of Mathematics)的公理系统不同。通过研究罗素如何在《数学原理》中找到证明方法的过程,可以发现经典命题...《数学原理》(Principia Mathematica)是罗素和怀特海的著作,也是早期分析哲学的基石,它的公理系统与《数学原则》(Principles of Mathematics)的公理系统不同。通过研究罗素如何在《数学原理》中找到证明方法的过程,可以发现经典命题逻辑公理形式化证明的一般方法。《数学原理》改变了《数学原则》中的初始命题,带来了新的证明,一些定理和引理随着论题的发展而被删除了,但《数学原则》中尽量多的结果还是被保留下来。《数学原理》中的命题逻辑系统是一个逐步演化的结果。展开更多
This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the ...This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.展开更多
Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method fo...Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method for flood classification, which is based on the mathematical theorem of dialectics basic laws. This newly proposed method explores a novel way to analyze and solve engineering problems by utilizing a dialectical thinking. In this paper, the Tuwei River basin, located in the Yellow River tributary, is taken as an example for flood classification. The results obtained in this study reveal the problems in a previous method—Set Pair Analysis classification method. The variable sets method is proven to be theoretically rigorous, computationally simple. The classification results are objective, accurate and consistent with the actual situations. This study demonstrates the significant importance of using a scientifically sound method in solving engineering problems.展开更多
文摘《数学原理》(Principia Mathematica)是罗素和怀特海的著作,也是早期分析哲学的基石,它的公理系统与《数学原则》(Principles of Mathematics)的公理系统不同。通过研究罗素如何在《数学原理》中找到证明方法的过程,可以发现经典命题逻辑公理形式化证明的一般方法。《数学原理》改变了《数学原则》中的初始命题,带来了新的证明,一些定理和引理随着论题的发展而被删除了,但《数学原则》中尽量多的结果还是被保留下来。《数学原理》中的命题逻辑系统是一个逐步演化的结果。
文摘This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51209032, 50779005)
文摘Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method for flood classification, which is based on the mathematical theorem of dialectics basic laws. This newly proposed method explores a novel way to analyze and solve engineering problems by utilizing a dialectical thinking. In this paper, the Tuwei River basin, located in the Yellow River tributary, is taken as an example for flood classification. The results obtained in this study reveal the problems in a previous method—Set Pair Analysis classification method. The variable sets method is proven to be theoretically rigorous, computationally simple. The classification results are objective, accurate and consistent with the actual situations. This study demonstrates the significant importance of using a scientifically sound method in solving engineering problems.
