Spectroscopy of ovarian masses can be recorded at 3.0 T with acceptable spectral quality and good signal-to-noise ratio. There are stringent technical considerations to be considered in obtaining good spectral quality. Further experience with a larger and more biologically variable range of tumors needs to be undertaken to determine the final clinical utility of this technique, but initial results from this small cohort are promising.

Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ for $ n $ large enough.

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We prove that a non-degenerate simple linear recurrence sequence (Gn(x)) ∞ n=0 of polynomials satisfying some further conditions cannot contain arbitrary large powers of polynomials if the order of the sequence is at least two. In other words we will show that for m large enough there is no polynomial h(x) of degree ≥ 2 such that (h(x)) m is an element of (Gn(x)) ∞ n=0 . The bound for m depends here only on the sequence (Gn(x)) ∞ n=0 . In the binary case we prove even more. We show that then there is a bound C on the index n of the sequence (Gn(x)) ∞ n=0 such that only elements with index n ≤ C can be a proper power.

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