Liutex is a mathematical definition of vortex,which is called the third generation of vortex definition and identification.This paper introduces the mathematical foundation of the Liutex theoretical system including d...Liutex is a mathematical definition of vortex,which is called the third generation of vortex definition and identification.This paper introduces the mathematical foundation of the Liutex theoretical system including differences in definition and operations between tensor/vector and matrix.The right version of velocity gradient tensor matrix is given to correct the old version which has been widely distributed by many mathematics and fluid dynamics textbooks.A unique velocity gradient principal matrix is provided.The mathematical foundation for Liutex definition is given.The coordinate rotation(Q-and P-rotation)for principal coordinate system and principal matrix is derived,which is the key issue of the new fluid kinematics.The divergence of velocity gradient tensor is given in different forms which may be beneficial in developing new governing equations for fluid dynamics.展开更多
Mathematics foundations of information security is a core course in the subject of information security.In view of the current national ideological and political conference in universities,finding a way to integrate t...Mathematics foundations of information security is a core course in the subject of information security.In view of the current national ideological and political conference in universities,finding a way to integrate this course with ideological and political education attracts a lot of attention from the education community.This paper makes an assay of the significance of the combination of mathematics foundations of information security course and ideological and political education,and introduces the teaching practice of mathematics foundations of information security course combined with ideological and political education.Through the combination of ideological and political education and curriculum content,cultivating all-round development of talents who study information security.展开更多
The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of r...The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of reality;quantum mechanics believes the behavior of micro particles is random and jumping. The second is the loss of certainty;the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will influence the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell’s inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell’s inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not equal relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which provide intuitionistic teaching materials for the new interpretation of quantum theory.展开更多
In this paper,a new diagnostic method,the rotated complex empirical orthogonal function (RCEOF)analysis is developed.The general principle and the mathematical foundation of RCEOF are discussed.
基金The current development of Liutex theory and application is under support by US National Science Foundation(Grant No.2300052)the University of Texas at Arlington for providing financial support.
文摘Liutex is a mathematical definition of vortex,which is called the third generation of vortex definition and identification.This paper introduces the mathematical foundation of the Liutex theoretical system including differences in definition and operations between tensor/vector and matrix.The right version of velocity gradient tensor matrix is given to correct the old version which has been widely distributed by many mathematics and fluid dynamics textbooks.A unique velocity gradient principal matrix is provided.The mathematical foundation for Liutex definition is given.The coordinate rotation(Q-and P-rotation)for principal coordinate system and principal matrix is derived,which is the key issue of the new fluid kinematics.The divergence of velocity gradient tensor is given in different forms which may be beneficial in developing new governing equations for fluid dynamics.
文摘Mathematics foundations of information security is a core course in the subject of information security.In view of the current national ideological and political conference in universities,finding a way to integrate this course with ideological and political education attracts a lot of attention from the education community.This paper makes an assay of the significance of the combination of mathematics foundations of information security course and ideological and political education,and introduces the teaching practice of mathematics foundations of information security course combined with ideological and political education.Through the combination of ideological and political education and curriculum content,cultivating all-round development of talents who study information security.
文摘The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of reality;quantum mechanics believes the behavior of micro particles is random and jumping. The second is the loss of certainty;the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will influence the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell’s inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell’s inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not equal relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which provide intuitionistic teaching materials for the new interpretation of quantum theory.
基金National 9th Five-Year Project under Grant 95-11.
文摘In this paper,a new diagnostic method,the rotated complex empirical orthogonal function (RCEOF)analysis is developed.The general principle and the mathematical foundation of RCEOF are discussed.
