The computations that are suggested by String Theory in the B model requires the existence of degenerations of CY manifolds with maximum unipotent monodromy. In String Theory such a point in the moduli space is called a large radius limit (or large complex structure limit). In this paper we are going to construct one parameter families of n dimensional Calabi-Yau manifolds, which are complete intersections in toric varieties and which have a monodromy operator $T$ such that $(T^N − id)^{n+1} =0 $ but $(T^N −id)^n \ne 0$, i.e the monodromy operator is maximal unipotent.

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In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semialgebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the basic semialgebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the basic semialgebraic convex sets.