Two-photon laser-induced fluorescence spectrum (TP-LIF) of NO is obtained with a Nd:YAG pumped optical parametric generator and amplifier as radiation source. Spectral intensity distribution shows that the electronic ...Two-photon laser-induced fluorescence spectrum (TP-LIF) of NO is obtained with a Nd:YAG pumped optical parametric generator and amplifier as radiation source. Spectral intensity distribution shows that the electronic transition moment for NO (A2 X2II) transition varies significantly with inter-nuclear distance. The variation relationship of the electronic transition moment versus inter-nuclear distance is deduced with polyminal fit procedure. The spontaneous radiative coefficients for NO (A2X2II) transition from v' = 0,1 are obtained by combing this transition moment variation with the measurements of spontaneous radiative lifetime.展开更多
We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial ...We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW. The error estimate obtained herein improves the corresponding result in previous literatures.展开更多
In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropr...In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein's method and coupling.展开更多
基金This work was supported by the Natural Science Foun-dation of Hebei Province,China (Grant No,102090)
文摘Two-photon laser-induced fluorescence spectrum (TP-LIF) of NO is obtained with a Nd:YAG pumped optical parametric generator and amplifier as radiation source. Spectral intensity distribution shows that the electronic transition moment for NO (A2 X2II) transition varies significantly with inter-nuclear distance. The variation relationship of the electronic transition moment versus inter-nuclear distance is deduced with polyminal fit procedure. The spontaneous radiative coefficients for NO (A2X2II) transition from v' = 0,1 are obtained by combing this transition moment variation with the measurements of spontaneous radiative lifetime.
基金Supported by National Natural Science Foundation of China(Grant No.11071021)
文摘We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW. The error estimate obtained herein improves the corresponding result in previous literatures.
基金supported by National Natural Science Foundation of China (Grant No. 11071021)
文摘In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein's method and coupling.
