该文考虑了Kac-van de Leur版本下超KP可积系列的一类推广系统,即s-次推广的超KP可积系列.首先,利用克利福德超代数与A型无穷维李超代数给出该系统在超费米Fock空间中的定义,其表现形式是一个用τ函数表达的恒等式.其次,利用A型超玻色-...该文考虑了Kac-van de Leur版本下超KP可积系列的一类推广系统,即s-次推广的超KP可积系列.首先,利用克利福德超代数与A型无穷维李超代数给出该系统在超费米Fock空间中的定义,其表现形式是一个用τ函数表达的恒等式.其次,利用A型超玻色-费米对应给出s-次推广的超KP可积系列在超玻色Fock空间中的像,即一个含有超变量的偏微分方程系统.在此基础上,给出该系统的超Hirota双线性形式,并从中导出KP方程和超KP方程.最后,该系统被推广到多分量情形.展开更多
The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal ...The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical frameworks.This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents.This conversion occurs after the nonlinear system is transformed into its linear equivalent.Numerical analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous system.One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern.Interestingly,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal systems.This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.展开更多
With the development of educational digitalization,how to effectively apply digital animation technology to traditional classroom teaching has become an urgent problem to be solved.This study explores the application ...With the development of educational digitalization,how to effectively apply digital animation technology to traditional classroom teaching has become an urgent problem to be solved.This study explores the application of Manim in the course of Mathematical Methods for Physics.Taking the visualization of Fourier series,complex numbers,and other content as examples,it improves students’understanding of complex and abstract mathematical physics concepts through dynamic and visual teaching methods.The teaching effect shows that Manim helps to enhance students’learning experience,improve teaching efficiency and effectiveness,and has a positive impact on students’active learning ability.The research in this paper can provide references and inspiration for the educational digitalization of higher education.展开更多
文摘该文考虑了Kac-van de Leur版本下超KP可积系列的一类推广系统,即s-次推广的超KP可积系列.首先,利用克利福德超代数与A型无穷维李超代数给出该系统在超费米Fock空间中的定义,其表现形式是一个用τ函数表达的恒等式.其次,利用A型超玻色-费米对应给出s-次推广的超KP可积系列在超玻色Fock空间中的像,即一个含有超变量的偏微分方程系统.在此基础上,给出该系统的超Hirota双线性形式,并从中导出KP方程和超KP方程.最后,该系统被推广到多分量情形.
文摘The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical frameworks.This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents.This conversion occurs after the nonlinear system is transformed into its linear equivalent.Numerical analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous system.One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern.Interestingly,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal systems.This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.
基金supported by the Teaching Reform Research Project of Shaanxi University of Science&Technology(23Y083)the Project of National University Association for Mathematical Methods in Physics(JZW-23-SL-02)+3 种基金the Graduate Course Construction Project of Shaanxi University of Science&Technology(KC2024Y03)the 2024 National Higher Education University Physics Reform Research Project(2024PR064)the Teaching Reform Research Project of the International Office of Shaanxi University of Science&Technology(YB202410)Graduate Education and Teaching Reform Research Project of Shaanxi University of Science&Technology(JG2025Y18).
文摘With the development of educational digitalization,how to effectively apply digital animation technology to traditional classroom teaching has become an urgent problem to be solved.This study explores the application of Manim in the course of Mathematical Methods for Physics.Taking the visualization of Fourier series,complex numbers,and other content as examples,it improves students’understanding of complex and abstract mathematical physics concepts through dynamic and visual teaching methods.The teaching effect shows that Manim helps to enhance students’learning experience,improve teaching efficiency and effectiveness,and has a positive impact on students’active learning ability.The research in this paper can provide references and inspiration for the educational digitalization of higher education.
