Representations for the extreme zeros of orthogonal polynomials

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed

Representations for the extreme zeros of orthogonal polynomials

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed

An intuitive approach to inventory control with optimal stopping

In this research note, we show that a simple application of Breiman's work on optimal stopping in 1964 leads to an elementary proof that (s,S) policies minimize the long-run average cost for periodic-review inventory control problems. The method of proof is appealing as it only depends on the fundamental concepts of renewal-reward processes, optimal stopping, dynamic programming, and root-finding. Moreover, it leads to an efficient algorithm to compute the optimal policy parameters. If Breiman's paper would have received the attention it deserved, computational methods dealing with (s,S)-policies would have been found about three decades earlier than the famous algorithm of Zheng and Federgruen (1991).</p