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Rice (Oryza sativa L.) sucrose transporter 4 (OsSUT4) is a rice sucrose transporter family gene. During the early seed germination stage, OsSUT4 was substantially expressed in seed aleurone layer, scutellum, and embryonic vascular bundle. The OsSUT4 mRNA level in the embryos of seeds that were germinated at 30 °C was higher than that of seeds germinated at(More)
We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by projecting to the x-line or Kummer surface, where we can exploit faster and more uniform pseudomultiplication, before recovering the proper " signed " output back on the curve or(More)
I n 2001 Thomas Hales ([H]; see [M1, Chap. 15]) proved the Honeycomb Conjecture, which says that regular hexagons provide a least-perimeter tiling of the plane by unit-area regions. In this paper we seek perimeter-minimizing tilings of the plane by unit-area pentagons. The regular pentagon has the least perimeter, but it does not tile the plane. There are(More)
We give one-and two-dimensional scalar multiplication algorithms for Jacobians of genus 2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudo-multiplication, before recovering the proper " signed " output back on the Jacobian. This extends the work of López and Dahab, Okeya and Saku-rai, and Brier and(More)
The prime number theorem is one of the most fundamental theorems of analytic number theory, stating that the prime counting function, π(x), is asymptotic to x/ log x. However, it says little about the parity of π(n) as an arithmetic function. Using Selberg's sieve, we prove a positive lower bound for the proportion of positive integers n such that π(n) is r(More)
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