This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability o...This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21].展开更多
A rectangular bimorph will vibrate in bending mode under alternating current （AC） electric field. If two opposite tips along longitudinal direction are both clamped, the maximum magnitude of bending displacement occ...A rectangular bimorph will vibrate in bending mode under alternating current （AC） electric field. If two opposite tips along longitudinal direction are both clamped, the maximum magnitude of bending displacement occurs on the short center line. Using bimorpb type vibrators forementioned as actuators, an invention of simple traveling machine based on stick-slip principle is presented. The machine can not only move along both x and y direction within horizontal working plane, furthermore, excellent bearing ability and agile response as well as stable step are also proved. In addition, the machine can work on stepping mode and scanning mode at the same time, hence the contradiction between long stroke and high precise positioning is solved. Therefore, it meets the needs of micro/nanometer precise positioning under long stroke and is desired to be used as carrying stage for micro-assembling system and locomotive mechanism for miniature robot system.展开更多
Combining the principle of homogeneous balance method, the exp function expansion method and traveling wave transformation method are applied to the Equalwidth equation to obtain the exact solution of the Equalwidth e...Combining the principle of homogeneous balance method, the exp function expansion method and traveling wave transformation method are applied to the Equalwidth equation to obtain the exact solution of the Equalwidth equation. The obtained solutions include trigonometric functions, hyperbolic functions and rational functions. The method can solve the exact traveling wave solutions of other nonlinear evolution equations.展开更多
The travelling wave group is a stable wave packet. Many surprising results are derived from it. The group is easily quantized for photons and applied, as a solution to the relativistic Klein-Gordon equation, to free p...The travelling wave group is a stable wave packet. Many surprising results are derived from it. The group is easily quantized for photons and applied, as a solution to the relativistic Klein-Gordon equation, to free particles. Further solutions to the resulting algebraic equation provide a stable wave function for free antiparticles. Consistency with the superstructure of quantum electrodynamics is obtained by an assignment to the electron antiparticle of negative mass and negative charge. Then in 5-dimensional space-time-mass, CPT invariance transforms to M’PT conservation in either charged or neutral particles, while many other consequences are also evident.展开更多
基金supported by NSF of China(11401478)Gansu Provincial Natural Science Foundation(145RJZA220)
文摘This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21].
基金This project is supported by National Hi-tech Research and Development Program of China (863 Program, No. 2002AA423150)National Natural Science Foundation of China (No. 50475010).
文摘A rectangular bimorph will vibrate in bending mode under alternating current （AC） electric field. If two opposite tips along longitudinal direction are both clamped, the maximum magnitude of bending displacement occurs on the short center line. Using bimorpb type vibrators forementioned as actuators, an invention of simple traveling machine based on stick-slip principle is presented. The machine can not only move along both x and y direction within horizontal working plane, furthermore, excellent bearing ability and agile response as well as stable step are also proved. In addition, the machine can work on stepping mode and scanning mode at the same time, hence the contradiction between long stroke and high precise positioning is solved. Therefore, it meets the needs of micro/nanometer precise positioning under long stroke and is desired to be used as carrying stage for micro-assembling system and locomotive mechanism for miniature robot system.
文摘Combining the principle of homogeneous balance method, the exp function expansion method and traveling wave transformation method are applied to the Equalwidth equation to obtain the exact solution of the Equalwidth equation. The obtained solutions include trigonometric functions, hyperbolic functions and rational functions. The method can solve the exact traveling wave solutions of other nonlinear evolution equations.
文摘The travelling wave group is a stable wave packet. Many surprising results are derived from it. The group is easily quantized for photons and applied, as a solution to the relativistic Klein-Gordon equation, to free particles. Further solutions to the resulting algebraic equation provide a stable wave function for free antiparticles. Consistency with the superstructure of quantum electrodynamics is obtained by an assignment to the electron antiparticle of negative mass and negative charge. Then in 5-dimensional space-time-mass, CPT invariance transforms to M’PT conservation in either charged or neutral particles, while many other consequences are also evident.
