Type synthesis of lower-mobility parallel mechanisms is a hot and frontier topic in international academic and industrial field. Based on the Lie group theory, a displacement manifold synthesis method is proposed. For...Type synthesis of lower-mobility parallel mechanisms is a hot and frontier topic in international academic and industrial field. Based on the Lie group theory, a displacement manifold synthesis method is proposed. For all the nine kinds of lower-mobility parallel mechanisms, the mechanism displacement manifold, limb displacement manifold and the geometrical conditions which guarantee that the intersection of the limb displacement manifold is the desired mechanism displacement manifold are enumerated. Various limb kinematic chains can be obtained using the product closure of displacement subgroup. Parallel mechanisms can be constructed with these limbs while obeying the geometrical conditions. Hence, all the nine kinds of lower-mobility parallel mechanisms can be synthesized using this method. Since displacement manifold deals with finite motion, the result mechanism of synthesis have full-cycle mobility. Novel architectures of lower-mobility parallel mechanisms can be obtained using this method.展开更多
Lie group machine learning is recognized as the theoretical basis of brain intelligence,brain learning,higher machine learning,and higher artificial intelligence.Sample sets of Lie group matrices are widely available ...Lie group machine learning is recognized as the theoretical basis of brain intelligence,brain learning,higher machine learning,and higher artificial intelligence.Sample sets of Lie group matrices are widely available in practical applications.Lie group learning is a vibrant field of increasing importance and extraordinary potential and thus needs to be developed further.This study aims to provide a comprehensive survey on recent advances in Lie group machine learning.We introduce Lie group machine learning techniques in three major categories:supervised Lie group machine learning,semisupervised Lie group machine learning,and unsupervised Lie group machine learning.In addition,we introduce the special application of Lie group machine learning in image processing.This work covers the following techniques:Lie group machine learning model,Lie group subspace orbit generation learning,symplectic group learning,quantum group learning,Lie group fiber bundle learning,Lie group cover learning,Lie group deep structure learning,Lie group semisupervised learning,Lie group kernel learning,tensor learning,frame bundle connection learning,spectral estimation learning,Finsler geometric learning,homology boundary learning,category representation learning,and neuromorphic synergy learning.Overall,this survey aims to provide an insightful overview of state-of-the-art development in the field of Lie group machine learning.It will enable researchers to comprehensively understand the state of the field,identify the most appropriate tools for particular applications,and identify directions for future research.展开更多
近年来逐步发展的概率密度演化方法理论为随机动力系统的分析与控制研究提供了新的途径.过去若干年来,已经发展了一系列数值方法如有限差分法、无网格法用于求解广义概率密度演化方程.但是,针对典型随机系统,关于这一方程解析解尚比较缺...近年来逐步发展的概率密度演化方法理论为随机动力系统的分析与控制研究提供了新的途径.过去若干年来,已经发展了一系列数值方法如有限差分法、无网格法用于求解广义概率密度演化方程.但是,针对典型随机系统,关于这一方程解析解尚比较缺乏.本文以李群方法为工具,研究给出了Van der Pol振子、Riccati方程和Helmholtz振子3类典型随机非线性系统的广义概率密度演化方程解析解.这些结果,不仅可以作为检验求解广义概率密度演化方程的数值方法结果正确性的判别依据,也为概率密度演化理论的进一步深入研究提供了若干分析实例.展开更多
基金the National Natural Science Foundation of China (Grant No. 50075074).
文摘Type synthesis of lower-mobility parallel mechanisms is a hot and frontier topic in international academic and industrial field. Based on the Lie group theory, a displacement manifold synthesis method is proposed. For all the nine kinds of lower-mobility parallel mechanisms, the mechanism displacement manifold, limb displacement manifold and the geometrical conditions which guarantee that the intersection of the limb displacement manifold is the desired mechanism displacement manifold are enumerated. Various limb kinematic chains can be obtained using the product closure of displacement subgroup. Parallel mechanisms can be constructed with these limbs while obeying the geometrical conditions. Hence, all the nine kinds of lower-mobility parallel mechanisms can be synthesized using this method. Since displacement manifold deals with finite motion, the result mechanism of synthesis have full-cycle mobility. Novel architectures of lower-mobility parallel mechanisms can be obtained using this method.
基金supported by the National Key Research and Development Program(Nos.2018YFA0701700 and 2018YFA0701701)Scientific Research Foundation for Advanced Talents(No.jit-b-202045)
文摘Lie group machine learning is recognized as the theoretical basis of brain intelligence,brain learning,higher machine learning,and higher artificial intelligence.Sample sets of Lie group matrices are widely available in practical applications.Lie group learning is a vibrant field of increasing importance and extraordinary potential and thus needs to be developed further.This study aims to provide a comprehensive survey on recent advances in Lie group machine learning.We introduce Lie group machine learning techniques in three major categories:supervised Lie group machine learning,semisupervised Lie group machine learning,and unsupervised Lie group machine learning.In addition,we introduce the special application of Lie group machine learning in image processing.This work covers the following techniques:Lie group machine learning model,Lie group subspace orbit generation learning,symplectic group learning,quantum group learning,Lie group fiber bundle learning,Lie group cover learning,Lie group deep structure learning,Lie group semisupervised learning,Lie group kernel learning,tensor learning,frame bundle connection learning,spectral estimation learning,Finsler geometric learning,homology boundary learning,category representation learning,and neuromorphic synergy learning.Overall,this survey aims to provide an insightful overview of state-of-the-art development in the field of Lie group machine learning.It will enable researchers to comprehensively understand the state of the field,identify the most appropriate tools for particular applications,and identify directions for future research.
文摘近年来逐步发展的概率密度演化方法理论为随机动力系统的分析与控制研究提供了新的途径.过去若干年来,已经发展了一系列数值方法如有限差分法、无网格法用于求解广义概率密度演化方程.但是,针对典型随机系统,关于这一方程解析解尚比较缺乏.本文以李群方法为工具,研究给出了Van der Pol振子、Riccati方程和Helmholtz振子3类典型随机非线性系统的广义概率密度演化方程解析解.这些结果,不仅可以作为检验求解广义概率密度演化方程的数值方法结果正确性的判别依据,也为概率密度演化理论的进一步深入研究提供了若干分析实例.
