The multi-radiation of X-rays was investigated with special attention to their energy spectrum in a Mather-type plasma focus device （operated with argon gas）. The analysis is based on the effect of anomalous resista...The multi-radiation of X-rays was investigated with special attention to their energy spectrum in a Mather-type plasma focus device （operated with argon gas）. The analysis is based on the effect of anomalous resistances. To study the energy spectrum, a four-channel diode X-ray spectrometer was used along with a special set of filters. The filters were suitable for detection of medium range X-rays as well as hard X-rays with energy exceeding 30 keV. The results indicate that the anomalous resistivity effect during the post pinch phase may cause multi-radiation of X-rays with a total duration of 300 ± 50 ns. The significant contribution of Cu-Kα was due to the medium range X-rays, nonetheless, hard X-rays with energies greater than 15 keV also participate in the process. The total emitted X-ray energy in the forms of Cu-K and Cu-K/3 was around 0.14 ± 0.02 （J/Sr） and 0.04 ±0.01 （J/Sr）, respectively. The total energy of the emitted hard X-ray （〉 15 keV） was around 0.12± 0.02 （J/Sr）.展开更多
Let(M,g)be a closed,connected and orientable Riemannian manifold with nonnegative Ricci curvature.Consider a Lagrangian L(x,v):TM→R defined by L(x,v):=1/2gx(v,v)-ω(v)+c,where c∈R andωis a closed 1-form.From the pe...Let(M,g)be a closed,connected and orientable Riemannian manifold with nonnegative Ricci curvature.Consider a Lagrangian L(x,v):TM→R defined by L(x,v):=1/2gx(v,v)-ω(v)+c,where c∈R andωis a closed 1-form.From the perspective of differential geometry,we estimate the Laplacian of the weak Kolmogorov-Arnold-Moser(KAM)solution u to the associated Hamilton-Jacobi equation H(x,du)=c[L]in the barrier sense.This analysis enables us to prove that each weak KAM solution u is a constant if and only ifωis a harmonic 1-form.Furthermore,we explore several applications to the Mather quotient and the Ma??éLagrangian.展开更多
In this paper, we apply Aubry-Mather theory developed in recent years about monotone twist mappings to the study of the superlinear Duffing equation+g(x)=p(t), (0)where p(t)∈C^0(R) is periodic with period 1 and g(x) ...In this paper, we apply Aubry-Mather theory developed in recent years about monotone twist mappings to the study of the superlinear Duffing equation+g(x)=p(t), (0)where p(t)∈C^0(R) is periodic with period 1 and g(x) satisfies the superlinearity condition Consequently, this gives descriptions of the global dynamical behavior, particularly periodic solutions and quasi-periodic solutions of a wide class of Eq. (0), not requiring high order smoothness assumption.展开更多
The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the applicat...The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the application of a generalized version of Aubry-Mather theoremon semi-cylinder with finite twist assumption.展开更多
文摘The multi-radiation of X-rays was investigated with special attention to their energy spectrum in a Mather-type plasma focus device （operated with argon gas）. The analysis is based on the effect of anomalous resistances. To study the energy spectrum, a four-channel diode X-ray spectrometer was used along with a special set of filters. The filters were suitable for detection of medium range X-rays as well as hard X-rays with energy exceeding 30 keV. The results indicate that the anomalous resistivity effect during the post pinch phase may cause multi-radiation of X-rays with a total duration of 300 ± 50 ns. The significant contribution of Cu-Kα was due to the medium range X-rays, nonetheless, hard X-rays with energies greater than 15 keV also participate in the process. The total emitted X-ray energy in the forms of Cu-K and Cu-K/3 was around 0.14 ± 0.02 （J/Sr） and 0.04 ±0.01 （J/Sr）, respectively. The total energy of the emitted hard X-ray （〉 15 keV） was around 0.12± 0.02 （J/Sr）.
基金supported by National Natural Science Foundation of China(Grant No.12231010)。
文摘Let(M,g)be a closed,connected and orientable Riemannian manifold with nonnegative Ricci curvature.Consider a Lagrangian L(x,v):TM→R defined by L(x,v):=1/2gx(v,v)-ω(v)+c,where c∈R andωis a closed 1-form.From the perspective of differential geometry,we estimate the Laplacian of the weak Kolmogorov-Arnold-Moser(KAM)solution u to the associated Hamilton-Jacobi equation H(x,du)=c[L]in the barrier sense.This analysis enables us to prove that each weak KAM solution u is a constant if and only ifωis a harmonic 1-form.Furthermore,we explore several applications to the Mather quotient and the Ma??éLagrangian.
文摘In this paper, we apply Aubry-Mather theory developed in recent years about monotone twist mappings to the study of the superlinear Duffing equation+g(x)=p(t), (0)where p(t)∈C^0(R) is periodic with period 1 and g(x) satisfies the superlinearity condition Consequently, this gives descriptions of the global dynamical behavior, particularly periodic solutions and quasi-periodic solutions of a wide class of Eq. (0), not requiring high order smoothness assumption.
文摘The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the application of a generalized version of Aubry-Mather theoremon semi-cylinder with finite twist assumption.
