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Constructing families of moderate-rank elliptic curves over number fields
We generalize a construction of families of moderate rank elliptic curves
over to number fields . The construction, originally
due to Steven J. Miller, \'Alvaro Lozano-Robledo and Scott Arms, invokes a
theorem of Rosen and Silverman to show that computing the rank of these curves
can be done by controlling the average of the traces of Frobenius, the
construction for number fields proceeds in essentially the same way. One
novelty of this method is that we can construct families of moderate rank
without having to explicitly determine points and calculating determinants of
height matrices.Comment: Version 1.0, 4 pages, sequel to arXiv:math/040657
Management of Mechanical Ventilation During Extracorporeal Membrane Oxygenation
This chapter explores the best practices of mechanical ventilation during extracorporeal membrane oxygenation (ECMO) through a detailed discussion of the physiologic theory and clinical evidence. Future areas of study and unanswered questions about mechanical ventilation during ECMO are also delineated
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