# How to Tangle with a Nested Radical

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There has been frequent controversy over the years regarding the use of numerical rootfinding for the solution of queueing problems. It has been said that such problems quite often present computational difficulties. However, it turns out that rootfinding in queueing is so well structured that...

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Let $C$ be a curve in a closed orientable surface $F$ of genus $g\geq 2$ that separates $F$ into subsurfaces $\widetilde {{F}_{i} } $ of genera ${g}_{i} $, for $i= 1, 2$. We study the set of roots in $\mathrm{Mod} (F)$ of the Dehn twist ${t}_{C} $ about $C$. All roots arise from pairs of...

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This note presents an upper estimate of the least prime primitive roots g*(p) modulo p, a large prime. The current literature has several estimates of the least prime primitive root g*(p) modulo a prime p â‰¥ 2 such as g*(p) â‰ª pc, c > 2.8. The estimate provided within seems to sharpen...

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A stable set (or an independent set) in a graph G is a set of pairwise non-adjacent vertices, and the independence number Î± (G) is the cardinality of a maximum stable set in G. The independence polynomial of G is I(G; x) = s0 + s1x + s2x2 + â€¦ + sÎ±xÎ±, Î± = Î±(G), where sk is...