This paper studies phantom linear scalar field （LSF） and phantom non-linear Born-Infeld （NLBI） scalar field with square potential of the form V（Ф） =1/2m^2Ф^2. The equation of state parameter w（z）, and evolut...This paper studies phantom linear scalar field （LSF） and phantom non-linear Born-Infeld （NLBI） scalar field with square potential of the form V（Ф） =1/2m^2Ф^2. The equation of state parameter w（z）, and evolution of scale factor a（t） in both phantom LSF and phantom NLBI scalar model are explored. The age of universe Hot and the transition redshift Z are obtained. The Gold data set of 157-SN-Ia is used to constrain parameters of the two models by numerical calculation. The phantom LSF is slightly better than the phantom NLBI type scalar field model for a large m. Although a smaller m corresponding to a slower rolling of field Ф better fits the observation data, the difference between phantom NLBI scalar field and phantom LSF is not distinct in this case.展开更多
In this paper,we propose a kind of unified strict efficiency named E-strict efficiency via improvement sets for vector optimization.This kind of efficiency is shown to be an extension of the classical strict efficienc...In this paper,we propose a kind of unified strict efficiency named E-strict efficiency via improvement sets for vector optimization.This kind of efficiency is shown to be an extension of the classical strict efficiency andε-strict efficiency and has many desirable properties.We also discuss some relationships with other properly efficiency based on improvement sets and establish the corresponding scalarization theorems by a base-functional and a nonlinear functional.Moreover,some examples are given to illustrate the main conclusions.展开更多
This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral...This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative(PID for short) boundary control is addressed. In the proportional-integral(PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system sub ject to PID control is always unstable.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos.10573012, 10575068）, and the Shanghai Municipal Science and Technology Commission （Grant No.04dz05905）
文摘This paper studies phantom linear scalar field （LSF） and phantom non-linear Born-Infeld （NLBI） scalar field with square potential of the form V（Ф） =1/2m^2Ф^2. The equation of state parameter w（z）, and evolution of scale factor a（t） in both phantom LSF and phantom NLBI scalar model are explored. The age of universe Hot and the transition redshift Z are obtained. The Gold data set of 157-SN-Ia is used to constrain parameters of the two models by numerical calculation. The phantom LSF is slightly better than the phantom NLBI type scalar field model for a large m. Although a smaller m corresponding to a slower rolling of field Ф better fits the observation data, the difference between phantom NLBI scalar field and phantom LSF is not distinct in this case.
基金This research was supported by the National Natural Science Foundation of China(No.11671062)the Chongqing Municipal Education Commission(No.KJ1500310)the Doctor startup fund of Chongqing Normal University(No.16XLB010).
文摘In this paper,we propose a kind of unified strict efficiency named E-strict efficiency via improvement sets for vector optimization.This kind of efficiency is shown to be an extension of the classical strict efficiency andε-strict efficiency and has many desirable properties.We also discuss some relationships with other properly efficiency based on improvement sets and establish the corresponding scalarization theorems by a base-functional and a nonlinear functional.Moreover,some examples are given to illustrate the main conclusions.
基金supported by the ERC Advanced Grant 266907(CPDENL)of the 7th Research Framework Programme(FP7)FIRST,Initial Training Network of the European Commission(No.238702)PITNGA-2009-238702
文摘This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative(PID for short) boundary control is addressed. In the proportional-integral(PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system sub ject to PID control is always unstable.
