This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation o...This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.展开更多
In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death(IBD) model and discuss the simulation of sample path and statistical inference with...In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death(IBD) model and discuss the simulation of sample path and statistical inference with complete observations of the IBD process by the exact transition density formula.展开更多
<img src="Edit_bdc7d851-e537-40df-990c-d678defa9648.png" alt="" />(M = Au, Ag, Cu;<span lang="EN-US" style="font-size:9pt;font-family:"color:black;"><i>n&...<img src="Edit_bdc7d851-e537-40df-990c-d678defa9648.png" alt="" />(M = Au, Ag, Cu;<span lang="EN-US" style="font-size:9pt;font-family:"color:black;"><i>n</i></span>= 1, 2, 3) clusters were used as a cluster model to study the activation of oxygen molecules on single-atom catalysts. Structures of <img src="Edit_bb84deb7-e24a-4777-a2f6-a1621ddd2afc.png" alt="" /> clusters were studied by density functional calculations with global optimization. For each <span style="font-family:"color:black;white-space:normal;"><i>n</i></span>, the most stable structures are quite similar for different metal types, and the oxygen molecule prefers to be adsorbed onto M atoms. It is found that the activation degree of oxygen is higher on clusters with non-noble metal Cu than that of Ag or Au containing clusters, by comparing the changes of O-O bond length and vibrational frequency, natural charge population analysis, Fuzzy bond order analysis, and energy barriers of O<sub>2</sub> dissociation. CO oxidation was used as a probe reaction to study the reactivity of Cu-containing clusters, and it is found that the reactivity decreases with the increase of the size of silicon-oxygen clusters. Our results give a new aspect to understand the reaction mechanism of non-precious metal single-atom catalyst for oxygen activation with high efficiency.展开更多
基金Supported by the National Natural Science Foundation of China (10371092)
文摘This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.
基金Supported by the Fundamental Research Funds for the Central Universities(JBK120405)
文摘In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death(IBD) model and discuss the simulation of sample path and statistical inference with complete observations of the IBD process by the exact transition density formula.
文摘<img src="Edit_bdc7d851-e537-40df-990c-d678defa9648.png" alt="" />(M = Au, Ag, Cu;<span lang="EN-US" style="font-size:9pt;font-family:"color:black;"><i>n</i></span>= 1, 2, 3) clusters were used as a cluster model to study the activation of oxygen molecules on single-atom catalysts. Structures of <img src="Edit_bb84deb7-e24a-4777-a2f6-a1621ddd2afc.png" alt="" /> clusters were studied by density functional calculations with global optimization. For each <span style="font-family:"color:black;white-space:normal;"><i>n</i></span>, the most stable structures are quite similar for different metal types, and the oxygen molecule prefers to be adsorbed onto M atoms. It is found that the activation degree of oxygen is higher on clusters with non-noble metal Cu than that of Ag or Au containing clusters, by comparing the changes of O-O bond length and vibrational frequency, natural charge population analysis, Fuzzy bond order analysis, and energy barriers of O<sub>2</sub> dissociation. CO oxidation was used as a probe reaction to study the reactivity of Cu-containing clusters, and it is found that the reactivity decreases with the increase of the size of silicon-oxygen clusters. Our results give a new aspect to understand the reaction mechanism of non-precious metal single-atom catalyst for oxygen activation with high efficiency.
