We consider two variants of the secretary problem, the Best-or-Worst and the Postdoc problems, which are closely related. First, we prove that both variants, in their standard form with binary payoff 1 or 0, share the same optimal stopping rule. We also consider additional cost/perquisites depending on the number of interviewed candidates. In these situations the optimal strategies are very different. Finally, we also focus on the Best-or-Worst variant with different payments depending on whether the selected candidate is the best or the worst.
Adapting the Newton-Puiseux Polygon process to nonlinear q−difference equations of any order and degree, we compute their power series solutions, study the properties of the set of exponents of the solutions and give a bound for their q−Gevrey order in terms of the order of the original equation.
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