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  • Author or Editor: T. A. Sos x
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Abstract

ASTRAL and STAR, two recent prospective randomized trials to compare renal artery stenting with optimal medical management versus optimal medical management alone for patients with renal insufficiency and renal artery stenosis, have concluded that there was no additional benefit to stenting. Patient selection and methodological issues in these studies cast doubt on the validity of their results and conclusions for patients with renal insufficiency and physiologically (hemodynamically) significant renal artery stenosis, i.e. true ischemic nephropathy.

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Let be a real irrational number and A =(xn) be a sequence of positive integers. We call A a characterizing sequence of or of the group Z mod 1 if lim n 2A n !1 k k =0 if and only if 2 Z mod 1. In the present paper we prove the existence of such characterizing sequences, also for more general subgroups of R = Z . Inthespecialcase Z mod 1 we give explicit construction of a characterizing sequence in terms of the continued fraction expansion of. Further, we also prove some results concerning the growth and gap properties of such sequences. Finally, we formulate some open problems.

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