Assuming the Generalized Riemann Hypothesis (GRH), we show that the norm-Euclidean Galois cubic fields are exactly those with discriminant ∆ = 7, 9, 13, 19, 31, 37, 43, 61, 67, 103, 109, 127, 157 . A large part of the proof is in establishing the following more general result: Let K be a Galois number field of odd prime degree ` and conductor f . Assume the GRH for ζK(s). If 38(`− 1)(log f) log...

Under 5 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 9.9 5 to 9 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.8 10 to 14 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.5 15 to 19 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.9 20 to 24 years . . . . . . . . . . . . . . . . . . . . . . ...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

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We study the semi-classical limit of the nonlinear Schrödinger-Poisson (NLSP) equation for initial data of the WKB type. The semi-classical limit in this case is realized in terms of a density-velocity pair governed by the Euler-Poisson equations. Recently we have shown in [ELT, Indiana Univ. Math. J., 50 (2001), 109–157], that the isotropic Euler-Poisson equations admit a critical threshold ph...

BACKGROUND Kasabach-Merritt syndrome (KMS) is a rare but life-threatening illness. The purpose of this study is to report our single-center experience with KMS. METHODS We reviewed the medical records of 13 patients who were diagnosed with KMS between 1997 and 2012 at Samsung Medical Center. Treatment response was defined as follows: 1) hematologic complete response (HCR) - platelet count >13...

109 Bone grafting is an important aspect of foot and ankle surgery.1 Despite the long history and widespread use of bone grafts and substitutes,2 there have been few studies documenting patterns of utilization of bone grafting by podiatric surgeons. A survey on the use of bone grafts among orthopedists was reported in 1984 by Miller et al.3 The present study was undertaken in order to determine...