By David H. Bailey, Heinz H. Bauschke, Peter Borwein, Frank Garvan, Michel Théra, Jon D. Vanderwerff, Henry Wolkowicz

ISBN-10: 1461476208

ISBN-13: 9781461476207

ISBN-10: 1461476216

ISBN-13: 9781461476214

The study of Jonathan Borwein has had a profound effect on optimization, sensible research, operations learn, mathematical programming, quantity concept, and experimental arithmetic. Having authored greater than a dozen books and greater than three hundred courses, Jonathan Borwein is without doubt one of the best Canadian mathematicians ever. His examine spans natural, utilized, and computational arithmetic in addition to excessive functionality computing, and keeps to have a massive impression: MathSciNet lists greater than 2500 citations through greater than 1250 authors, and Borwein is without doubt one of the 250 so much stated mathematicians of the interval 1980-1999. He has served the Canadian arithmetic group via his presidency (2000–02) in addition to his 15 years of modifying the CMS booklet series.

Jonathan Borwein’s imaginative and prescient and initiative were an important in starting up and constructing a number of associations that offer help for researchers with quite a lot of medical pursuits. a number of striking examples comprise the Centre for Experimental and optimistic arithmetic and the IRMACS Centre at Simon Fraser collage, the Dalhousie allotted study Institute at Dalhousie collage, the Western Canada examine Grid, and the Centre for laptop Assisted learn arithmetic and its purposes, college of Newcastle.

The workshops that have been held through the years in Dr. Borwein’s honor attracted high-caliber scientists from a variety of mathematical fields. This current quantity is an outgrowth of the workshop on ‘Computational and Analytical arithmetic’ held in may perhaps 2011 in party of Dr. Borwein’s sixtieth Birthday. the gathering comprises numerous state of the art learn manuscripts and surveys featuring contributions that experience risen from the convention, and is a wonderful chance to survey cutting-edge examine and talk about promising learn instructions and approaches.

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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

### Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday by David H. Bailey, Heinz H. Bauschke, Peter Borwein, Frank Garvan, Michel Théra, Jon D. Vanderwerff, Henry Wolkowicz

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