The quantum anomalous Hall(QAH)effect,characterized by dissipationless chiral edge states without requiring an external magnetic field,represents a cornerstone of topological physics.The first experimental observation...The quantum anomalous Hall(QAH)effect,characterized by dissipationless chiral edge states without requiring an external magnetic field,represents a cornerstone of topological physics.The first experimental observation of the QAH effect was achieved in chromium-doped(Bi,Sb)2Te 3 topological insulator(TI)thin films[1].展开更多
The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensiona...The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.展开更多
As we have known,the 20th century represents an era of quantum physics.Based on the quantum physics,the physics and technology of semiconductors andmicroelec-tronics,lasers and masers,superconductors and devices,etc.,...As we have known,the 20th century represents an era of quantum physics.Based on the quantum physics,the physics and technology of semiconductors andmicroelec-tronics,lasers and masers,superconductors and devices,etc.,have been developed rapidly and widely.These build the hardware for the information science and technology,which have become the main driving force behind the re-garded“third industrial revolution”.展开更多
文摘The quantum anomalous Hall(QAH)effect,characterized by dissipationless chiral edge states without requiring an external magnetic field,represents a cornerstone of topological physics.The first experimental observation of the QAH effect was achieved in chromium-doped(Bi,Sb)2Te 3 topological insulator(TI)thin films[1].
基金supported by the National Natural Science Foundation of China(Grant No.62303289)Tianyuan Fund for Mathematics of the National Natural Science Foundation of China(Grant No.12426105)+3 种基金the Scientific and Technological Innovation Programs(STIP)of Higher Education Institutions in Shanxi(Grant No.2024L022)Fundamental Research Program of Shanxi Province(Grant Nos.202403021222001 and 202203021222003)the“Wen Ying Young Scholars”Talent Project of Shanxi University(Grant Nos.138541088,138541090,and 138541127)Funded by Open Foundation of Hubei Key Laboratory of Applied Mathematics(Hubei University)(Grant No.HBAM202401).
文摘The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.
文摘As we have known,the 20th century represents an era of quantum physics.Based on the quantum physics,the physics and technology of semiconductors andmicroelec-tronics,lasers and masers,superconductors and devices,etc.,have been developed rapidly and widely.These build the hardware for the information science and technology,which have become the main driving force behind the re-garded“third industrial revolution”.
