It has been shown that non-rotating black holes Recently study showed that thermal fluctuations would give in three or four dimensions possess a canonical entropy. rise to logarithmic corrections to Bekenstein Hawking...It has been shown that non-rotating black holes Recently study showed that thermal fluctuations would give in three or four dimensions possess a canonical entropy. rise to logarithmic corrections to Bekenstein Hawking entropy in area with a model-dependent uncertain coefficient. In this paper, the thermal fluctuations on Bekenstein-Hawking entropy in three-dimensional AdS black holes, Schwarzschild-de Sitter space and Kerr-de Sitter （KdS） spacetime with J = 0 will be considered based on a uniformly spaced area spectrum approach. Our conclusion shows that there is the same correction form in all cases we considered.展开更多
The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data...The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data being required. After a homogenization technique, a sequence of spatial boundary functions at least the fourth-order polynomials are derived, which satisfy the homogeneous boundary conditions. The boundary functions and the zero element constitute a linear space, and then a new boundary functional is proved in the linear space, of which the energy is preserved for each dynamic energetic boundary function. The linear systems and iterative algorithms used to recover unknown wave speed and wave source functions with the dynamic energetic boundary functions as bases are developed, which converge fast at each time step. The input data are parsimonious, merely the measured boundary strains and the boundary values and slopes of unknown functions to be recovered. The accuracy and robustness of present methods are confirmed by comparing exact solutions with estimated results under large noises up to 20%.展开更多
This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations i...This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.展开更多
Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied i...Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied in the cases of critical and intermediate dimensions. The results show that the limit processes are time-independent measure-valued Wiener processes with simple spatial structure.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No. 10573004
文摘It has been shown that non-rotating black holes Recently study showed that thermal fluctuations would give in three or four dimensions possess a canonical entropy. rise to logarithmic corrections to Bekenstein Hawking entropy in area with a model-dependent uncertain coefficient. In this paper, the thermal fluctuations on Bekenstein-Hawking entropy in three-dimensional AdS black holes, Schwarzschild-de Sitter space and Kerr-de Sitter （KdS） spacetime with J = 0 will be considered based on a uniformly spaced area spectrum approach. Our conclusion shows that there is the same correction form in all cases we considered.
文摘The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data being required. After a homogenization technique, a sequence of spatial boundary functions at least the fourth-order polynomials are derived, which satisfy the homogeneous boundary conditions. The boundary functions and the zero element constitute a linear space, and then a new boundary functional is proved in the linear space, of which the energy is preserved for each dynamic energetic boundary function. The linear systems and iterative algorithms used to recover unknown wave speed and wave source functions with the dynamic energetic boundary functions as bases are developed, which converge fast at each time step. The input data are parsimonious, merely the measured boundary strains and the boundary values and slopes of unknown functions to be recovered. The accuracy and robustness of present methods are confirmed by comparing exact solutions with estimated results under large noises up to 20%.
基金supported by the National Natural Science Foundation of China under Grant Nos.11371084,11471070 and 11171060the Fundamental Research Funds for the Central Universities under Grant Nos.14ZZ2222 and 2412015BJ011+1 种基金the National Basic Research Program of China(973 Program)under Grant No.2011CB808002the Fok Ying Tong Education Foundation under Grant No.141001
文摘This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.
基金supported by National Natural Science Foundation of China (Grant No. 10901054)
文摘Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied in the cases of critical and intermediate dimensions. The results show that the limit processes are time-independent measure-valued Wiener processes with simple spatial structure.
