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Comment on “On the imaginary-real ratio rule of power spectra” [J. Math. Phys.50, 063301 (2009)]
3.M. -P. Qian and M. Qian, Sci. Sin. Special Issue 2, 69 (1979).
4.D. -Q. Jiang, M. Qian, and M. -P. Qian, Mathematical Theory of Nonequilibrium Steady States (Springer, Berlin, 2004).
5.S. Kalpazidou, Cycle Representations of Markov Processes, 2nd ed. (Springer, New York, 2006).
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For the three-state ergodic Markov process, the condition of all the fluctuation spectra (i.e., power spectra) with respect to real observables being monotonic over [Y. Chen, Fluct. Noise Lett.7, L181 (2007)(Theorem 2.6)] is deduced from Theorem 1 of Qian and Xie [J. Math. Phys.50, 063301 (2009)]. In addition, we present two examples using Theorem 3 of Qian and Xie [J. Math. Phys.50, 063301 (2009)].
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