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Fractional Action-Like Variational Problem and Its Noether Symmetries for a Nonholonomic System 被引量:3
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作者 张毅 龙梓轩 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2015年第4期380-389,共10页
For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are stu... For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are studied,based on the fractional action-like approach for dynamics modeling proposed by El-Nabulsi.Firstly,the fractional action-like variational problem is established,and the fractional action-like Lagrange equations of holonomic system and the fractional action-like differential equations of motion with multiplier for nonholonomic system are given;secondly,according to the invariance of fractional action-like Hamilton action under infinitesimal transformations of group,the definitions and criteria of fractional action-like Noether symmetric transformations and quasi-symmetric transformations are put forward;finally,the fractional action-like Noether theorems for both holonomic system and nonholonomic system are established,and the relationship between the fractional action-like Noether symmetry and the conserved quantity is given. 展开更多
关键词 nonholonomic system fractional action-like variational problem symmetric transformation Noether theorem conserved quantity
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4-Staining of “Staining Dilemma Configuration” in Four-Color Conjecture
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作者 Yudian Zhang Lichong Zhang 《Journal of Applied Mathematics and Physics》 2022年第3期915-929,共15页
This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral w... This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral with four-color vertices and its properties theorems, namely theorems 1 and 2. From this, the non-10-fold symmetry transformation rule of the geometric structure of Errera configuration is generated, and using this rule, according to whether the “staining dilemma configuration” is 10-fold symmetry, they are divided into two categories;2) Using this rule, combining the different research results of several mathematicians on Errera graphs, and using four different classifications of propositional truth and falsehood, a new Theorem 3 is established;3) Using Theorem 3, the theoretical proof that the non-10-fold symmetric “ staining dilemma configuration” can be 4-staining;4) Through 4-staining of the four configurations of Errera, Obtained the Z-staining program (also called Theorem 4), and using this program and mathematical induction, gave the 10-fold symmetric “staining dilemma configuration” 4-staining proof. Completed the complete and concise manual proof of the four-color conjecture. 展开更多
关键词 Four-Color Conjecture Kempe Proof Staining Dilemma Configuration Four-Color Vertex Quadrilateral Non-10 Fold symmetric transformation
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