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Monotonically increasing intervals
ProblemĀ A real sequence satisfies for all , where . Let be the length of the th interval. Show that there exists a unique such that for all . RemarkĀ This is a problem that arises from nonlinear quantization in … Continue reading
Posted in Analysis, mathematics, signal processing
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Dense Circle
Proposition 1. Let be an irrational number and denote the set of fractional parts of for all . Then is dense in . Proof. We shall first prove that is dense at , then proceed to the whole range of … Continue reading
Posted in Analysis, mathematics
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Originally posted on What's new:
I’ve just uploaded to the arXiv my paper “Every odd number greater than 1 is the sum of at most five primes“, submitted to Mathematics of Computation. The main result of the paper is…
Posted in mathematics
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