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Category Archives: Analysis
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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