Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent wh...Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent when μ 〈 1; is null recurrent when μ= 1; and is transient when μ 〉 1. In this paper, the integrability of the first returning time and the last exit time are discussed. Keywords Geom/G/1 queuing model, first returning time, last exit time, Markov chain展开更多
In terms of single-atom induced dipole moment by Lewenstein model, we present the macroscopic high-order harmonic generation from mixed He and Ne gases with different mixture ratios by solving three-dimensional Maxwel...In terms of single-atom induced dipole moment by Lewenstein model, we present the macroscopic high-order harmonic generation from mixed He and Ne gases with different mixture ratios by solving three-dimensional Maxwell＇s equation of harmonic field. And then we show the validity of mixture formulation by Wagner et al. [Phys. Rev. A 76 （2007） 061403（R）] in macroscopic response level. Finally, using/east squares fitting we retrieve the electron return time of short trajectory by formulation in Kanai et al. [Phys. Rev. Lett. 98 （2007） 153904] when the gas jet is put after the laser focus.展开更多
Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrenc...Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.） for the processes are presented.展开更多
In this paper,it is shown that for a minimal system(X,G),if H is a normal subgroup of G with finite index n,then X can be decomposed into n components of closed sets such that each component is minimal under H-action....In this paper,it is shown that for a minimal system(X,G),if H is a normal subgroup of G with finite index n,then X can be decomposed into n components of closed sets such that each component is minimal under H-action.Meanwhile,we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms,the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension,extending a previous result by Glasscock,Koutsogiannis and Richter.展开更多
This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping...This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11001070,11101113)Zhejiang Provincial Natural Science Foundation(Grant No.R6090034)
文摘Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent when μ 〈 1; is null recurrent when μ= 1; and is transient when μ 〉 1. In this paper, the integrability of the first returning time and the last exit time are discussed. Keywords Geom/G/1 queuing model, first returning time, last exit time, Markov chain
基金Supported by the National Natural Science Foundation of China under Grant No. 10674112the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20096203110001+1 种基金the Foundation of Center of Theoretical Nuclear Physics of National Laboratory of Heavy Ion Accelerator of LanzhouFoundation of Northwest Normal University under Grant No. NWNUKJCXGC-03-62
文摘In terms of single-atom induced dipole moment by Lewenstein model, we present the macroscopic high-order harmonic generation from mixed He and Ne gases with different mixture ratios by solving three-dimensional Maxwell＇s equation of harmonic field. And then we show the validity of mixture formulation by Wagner et al. [Phys. Rev. A 76 （2007） 061403（R）] in macroscopic response level. Finally, using/east squares fitting we retrieve the electron return time of short trajectory by formulation in Kanai et al. [Phys. Rev. Lett. 98 （2007） 153904] when the gas jet is put after the laser focus.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11131003）, the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20100003110005）, the ＂985＂ project from the Ministry of Education in China, the Fundamental Research Funds for the Central Universities, and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.） for the processes are presented.
文摘In this paper,it is shown that for a minimal system(X,G),if H is a normal subgroup of G with finite index n,then X can be decomposed into n components of closed sets such that each component is minimal under H-action.Meanwhile,we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms,the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension,extending a previous result by Glasscock,Koutsogiannis and Richter.
文摘This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.
