In nature, quadrupeds as horses or cats change their gait to be suited to their motion speed. This fact is very important to realize smooth motion with different gaits. In this article a method of the gait transition ...In nature, quadrupeds as horses or cats change their gait to be suited to their motion speed. This fact is very important to realize smooth motion with different gaits. In this article a method of the gait transition for the quadruped walking machine is proposed. With analyzing the accustomed gaits of quadruped, some standard gaits and the relationships between duty factor and the phasic differences of the legs corresponding to the first leg could be concluded. With this, the gaits transferring could be continuous. Besides, celerity and on line method for generation and modifying gaits is studied, which can make the robot have a smooth motion to adapt the uncharted rough terrain.展开更多
In this paper,travelling wave solutions for the generalized time-delayed Burgers-Fisher equation arestudied.By using the first-integral method,which is based on the ring theory of commutative algebra,we obtain aclass ...In this paper,travelling wave solutions for the generalized time-delayed Burgers-Fisher equation arestudied.By using the first-integral method,which is based on the ring theory of commutative algebra,we obtain aclass of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation.A minor error in theprevious article is clarified.展开更多
By employing Hirota bilinear method and Riemann theta functions of genus one,explicit triply periodic wave solutions for the(2+1)-dimensional Boussinesq equation are constructed under the Backlund transformation u =(1...By employing Hirota bilinear method and Riemann theta functions of genus one,explicit triply periodic wave solutions for the(2+1)-dimensional Boussinesq equation are constructed under the Backlund transformation u =(1 /6)(u0 1) + 2[ln f(x,y,t)] xx,four kinds of triply periodic wave solutions are derived,and their long wave limit are discussed.The properties of one of the solutions are shown in Fig.1.展开更多
This paper reviews a less known rational structure on the Siegel modular variety X（N） = F（N）／Hg over Q for integers g, N ≥ 1. The author then describes explicitly how Galois groups act on CM points on this varie...This paper reviews a less known rational structure on the Siegel modular variety X（N） = F（N）／Hg over Q for integers g, N ≥ 1. The author then describes explicitly how Galois groups act on CM points on this variety. Finally, another proof of the Shimura reciprocity law by using the result and the q-expansion principle is given.展开更多
基金Supported by the china postdoctoral Science Foundation （No. 20080430362）.
文摘In nature, quadrupeds as horses or cats change their gait to be suited to their motion speed. This fact is very important to realize smooth motion with different gaits. In this article a method of the gait transition for the quadruped walking machine is proposed. With analyzing the accustomed gaits of quadruped, some standard gaits and the relationships between duty factor and the phasic differences of the legs corresponding to the first leg could be concluded. With this, the gaits transferring could be continuous. Besides, celerity and on line method for generation and modifying gaits is studied, which can make the robot have a smooth motion to adapt the uncharted rough terrain.
基金Supported by the Research Foundation of Education Bureau of Hubei Province under Grant No.Z200612001the Natural Science Foundation of Yangtze University under Grant No.20061222
文摘In this paper,travelling wave solutions for the generalized time-delayed Burgers-Fisher equation arestudied.By using the first-integral method,which is based on the ring theory of commutative algebra,we obtain aclass of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation.A minor error in theprevious article is clarified.
基金Supported by the National Natural Science Foundation of China under Grant No. 11101382the Natural Science Foundation of Henan Province under Grant No. 2010A110001the Basic and Advanced Technology Project of Henan Province under Grant No. 112300410199
文摘By employing Hirota bilinear method and Riemann theta functions of genus one,explicit triply periodic wave solutions for the(2+1)-dimensional Boussinesq equation are constructed under the Backlund transformation u =(1 /6)(u0 1) + 2[ln f(x,y,t)] xx,four kinds of triply periodic wave solutions are derived,and their long wave limit are discussed.The properties of one of the solutions are shown in Fig.1.
基金supported by the National Science Foundation Grants(No.DMS-1200380,DMS-1500743)the Chinese Qian Ren Plan of Tsinghua(No.543100001)
文摘This paper reviews a less known rational structure on the Siegel modular variety X（N） = F（N）／Hg over Q for integers g, N ≥ 1. The author then describes explicitly how Galois groups act on CM points on this variety. Finally, another proof of the Shimura reciprocity law by using the result and the q-expansion principle is given.
