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Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1’s in the binary expansions of real algebraic numbers. A central result is that if a real has algebraic degree , then the number of 1-bits in the expansion of through bit position satisfies
for a positive number (depending on ) and sufficiently large . This in itself establishes the transcendency of a class of...
Recent positive experiences applying convex feasibility algorithms of Douglas–Rachford type to highly combinatorial and far from convex problems are described. 2010 Mathematics Subject Classification: 90C27, 90C59, 47N10.
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