By L.J. Jr. Ratliff

ISBN-10: 3540087583

ISBN-13: 9783540087588

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H. M. Borwein References 1. : Random generators and normal numbers. Exp. Math. 11(4), 527–546 (2002) 2. : A strong hot spot theorem. Proc. Am. Math. Soc. 134(9), 2495–2501 (2006) 3. : On the rapid computation of various polylogarithmic constants. Math. Comput. 66(218), 903–913 (1997) 4. : On the binary expansions of algebraic numbers. J. Number Theor. Bordeaux 16, 487–518 (2004) 5. : Mathematics by Experiment: Plausible Reasoning in the 21st Century. AK Peters, Natick (2008) 6. : On a problem of Steinhaus about normal numbers.

Academic Press, New York (1971) Chapter 3 Champernowne’s Number, Strong Normality, and the X Chromosome Adrian Belshaw and Peter Borwein This paper is dedicated to Jon Borwein in celebration of his 60th birthday Abstract Champernowne’s number is the best-known example of a normal number, but its digits are far from random. The sequence of nucleotides in the human X chromosome appears nonrandom in a similar way. ” We show that almost all numbers are strongly normal and that strong normality implies normality.

We claim that every element of Eε is absolutely strongly normal. For each base r and 1-string k ∈ {0, 1, . . , r − 1}, we have specified a set of integers M1 < M2 < M3 < · · · , depending on r and k. By our construction, if α ∈ Eε , then, recalling that f depends on α , we have sup f (n) − 1 < δi inf f (n) + 1 < δi Mi ≤n

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Chain conjectures in ring theory by L.J. Jr. Ratliff


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