Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ...Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.展开更多
Using the closed orbit theory, we study the classical motion and calculatethe photoabsorption spectra of Rydberg hydrogen atom between two parallel metallic surfaces. The results show that the metallic surfaces have a...Using the closed orbit theory, we study the classical motion and calculatethe photoabsorption spectra of Rydberg hydrogen atom between two parallel metallic surfaces. The results show that the metallic surfaces have a significant effect on the photoabsorption process. When the distances between the hydrogen atom and the two metallic surfaces are close to a critical value dc, the number of the closed orbits is the greatest. When the distance larger or smaller than dc, the number of the closed orbits decreases and the absorption spectra are shown to exhibit a damping oscillation. This work is an interesting new application of closed-orbit theory and is of potential experimental interest.展开更多
Electron orbits under the external vertical field （Bv） and the self poloidal field of the toroidal plasma current in a toroidal geometry are investigated by using analytic model fields in order to search for the con...Electron orbits under the external vertical field （Bv） and the self poloidal field of the toroidal plasma current in a toroidal geometry are investigated by using analytic model fields in order to search for the conditions of occurence of appropriate confinement asymmetry of fast electrons along the field lines. This asymmetry efficiently and quickly generates a toroidal current, which may close the field lines in ECH-started plasmas. It is analytically shown that the characteristics of confinement asymmetry depend on the product of the major radius and the strength of the external vertical field. The results suggest that in large devices By should be lowered and also some artificial means to speed up the pitch angle scattering for the fast electrons at a higher energy range are beneficial to generate the toroidal current in order to close the filed展开更多
A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only ...A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only the Kannan type but also covers Reich, and Hardy and Roger's type contractive conditions. An example is given in its support.展开更多
Various times of light minima of the contact binary CK Boo are compiled and the correspnoding O C curve is analyzed with Kalimeris at al.’s method (1994). It is shown that the orbital period varies in a quasi sinusoi...Various times of light minima of the contact binary CK Boo are compiled and the correspnoding O C curve is analyzed with Kalimeris at al.’s method (1994). It is shown that the orbital period varies in a quasi sinusoidal form with a period of about 14 years and an amplitude of 0.26 × 10 -5 days while it undergoes a secular period increase dP/dE =+4 97 × 10 -7 days/year. The mechanisms that could explain the changes in the orbital period are also discussed.展开更多
文摘Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.
基金Project supported by the National Natural Science Foundation of China （Grant No 10604045） and the Doctorate Research Foundation of Ludong University, China （Grant No 202-23000301）.
文摘Using the closed orbit theory, we study the classical motion and calculatethe photoabsorption spectra of Rydberg hydrogen atom between two parallel metallic surfaces. The results show that the metallic surfaces have a significant effect on the photoabsorption process. When the distances between the hydrogen atom and the two metallic surfaces are close to a critical value dc, the number of the closed orbits is the greatest. When the distance larger or smaller than dc, the number of the closed orbits decreases and the absorption spectra are shown to exhibit a damping oscillation. This work is an interesting new application of closed-orbit theory and is of potential experimental interest.
文摘Electron orbits under the external vertical field （Bv） and the self poloidal field of the toroidal plasma current in a toroidal geometry are investigated by using analytic model fields in order to search for the conditions of occurence of appropriate confinement asymmetry of fast electrons along the field lines. This asymmetry efficiently and quickly generates a toroidal current, which may close the field lines in ECH-started plasmas. It is analytically shown that the characteristics of confinement asymmetry depend on the product of the major radius and the strength of the external vertical field. The results suggest that in large devices By should be lowered and also some artificial means to speed up the pitch angle scattering for the fast electrons at a higher energy range are beneficial to generate the toroidal current in order to close the filed
文摘A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only the Kannan type but also covers Reich, and Hardy and Roger's type contractive conditions. An example is given in its support.
文摘Various times of light minima of the contact binary CK Boo are compiled and the correspnoding O C curve is analyzed with Kalimeris at al.’s method (1994). It is shown that the orbital period varies in a quasi sinusoidal form with a period of about 14 years and an amplitude of 0.26 × 10 -5 days while it undergoes a secular period increase dP/dE =+4 97 × 10 -7 days/year. The mechanisms that could explain the changes in the orbital period are also discussed.
