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Speed of stability for birth-death processes
Mu-Fa CHEN,
Front. Math. China. 2010, 5 (3): 379-515.
https://doi.org/10.1007/s11464-010-0068-7
This paper is a continuation of the study on the stability speed for Markov processes. It extends the previous study of the ergodic convergence speed to the non-ergodic one, in which the processes are even allowed to be explosive or to have general killings. At the beginning stage, this paper is concentrated on the birth-death processes. According to the classification of the boundaries, there are four cases plus one more having general killings. In each case, some dual variational formulas for the convergence rate are presented, from which, the criterion for the positivity of the rate and an approximating procedure of estimating the rate are deduced. As the first step of the approximation, the ratio of the resulting bounds is usually no more than 2. The criteria as well as basic estimates for more general types of stability are also presented. Even though the paper contributes mainly to the non-ergodic case, there are some improvements in the ergodic one. To illustrate the power of the results, a large number of examples are included.
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Recognizing alternating groups A p +3 for certain primes p by their orders and degree patterns
A. A. HOSEINI, A. R. MOGHADDAMFAR,
Front. Math. China. 2010, 5 (3): 541-553.
https://doi.org/10.1007/s11464-010-0011-y
The degree pattern of a finite group M has been introduced by A. R. Moghaddamfar et al. [Algebra Colloquium, 2005, 12(3): 431―442]. A group M is called k-fold OD-characterizable if there exist exactly k nonisomorphic finite groups having the same order and degree pattern as M. In particular, a 1-fold OD-characterizable group is simply called OD-characterizable. In this article, we will show that the alternating groups Ap+3 for p = 23, 31, 37, 43 and 47 are OD-characterizable. Moreover, we show that the automorphism groups of these groups are 3-fold OD-characterizable. It is worth mentioning that the prime graphs associated with all these groups are connected.
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8 articles
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