We consider a branching random walk on N with a random environment in time （denoted by ξ）. Let Zn be the counting measure of particles of generation n, and let Zn（t） be its Laplace transform. We show the converge...We consider a branching random walk on N with a random environment in time （denoted by ξ）. Let Zn be the counting measure of particles of generation n, and let Zn（t） be its Laplace transform. We show the convergence of the free energy n-llog Zn（t）, large deviation principles, and central limit theorems for the sequence of measures {Zn}, and a necessary and sufficient condition for the existence of moments of the limit of the martingale Zn（t）/E[Zn（t）ξ].展开更多
We present the spatial resolution estimation methods for a photon counting system with a Vernier anode.A limiting resolution model is provided according to discussions of surface encoding structure and quantized noise...We present the spatial resolution estimation methods for a photon counting system with a Vernier anode.A limiting resolution model is provided according to discussions of surface encoding structure and quantized noise. The limiting resolution of a Vernier anode is revealed to be significantly higher than that of a microchannel plate. The relationship between the actual spatial resolution and equivalent noise charge of a detector is established by noise analysis and photon position reconstruction. The theoretical results are demonstrated to be in good agreement with the experimental results for a 1.2 mm pitch Vernier anode.展开更多
基金Acknowledgements The authors would like to thank the anonymous referees for valuable comments and remarks. This work was partially supported by the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology （HIT. NSRIF. 2015102）, the National Natural Science Foundation of China （Grant Nos. 11171044, 11101039）, and by the Natural Science Foundation of Hunan Province （Grant No. 11JJ2001）.
文摘We consider a branching random walk on N with a random environment in time （denoted by ξ）. Let Zn be the counting measure of particles of generation n, and let Zn（t） be its Laplace transform. We show the convergence of the free energy n-llog Zn（t）, large deviation principles, and central limit theorems for the sequence of measures {Zn}, and a necessary and sufficient condition for the existence of moments of the limit of the martingale Zn（t）/E[Zn（t）ξ].
基金supported by the National Natural Science Foundations of China under Grant Nos.10878005/A03 and 61007017
文摘We present the spatial resolution estimation methods for a photon counting system with a Vernier anode.A limiting resolution model is provided according to discussions of surface encoding structure and quantized noise. The limiting resolution of a Vernier anode is revealed to be significantly higher than that of a microchannel plate. The relationship between the actual spatial resolution and equivalent noise charge of a detector is established by noise analysis and photon position reconstruction. The theoretical results are demonstrated to be in good agreement with the experimental results for a 1.2 mm pitch Vernier anode.
