On change of effective date of promotion in a university faculty system: a stochastic root-finding problem

This study considers the problem of changing the effective date of promotion in a university faculty (system) as an embedding problem. The problem is whether the observed discrete-time transition matrix of the system can be expressed as a fractional matrix root in the stochastic sense. Conditions for embeddable stochastic matrices in the literature are adapted for the study. By the method based on the Cauchy’s integral formula with the integrand defined on the Runnenburg’s heart-shaped region, it is found that the transition matrix describing the system is not embeddable. The implications of changing the effective date of promotion in the system vis-à-vis the evolution of the expected personnel structure are highlighted.

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