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

The study of Jonathan Borwein has had a profound influence on optimization, sensible research, operations study, mathematical programming, quantity thought, and experimental arithmetic. Having authored greater than a dozen books and greater than three hundred guides, Jonathan Borwein is likely one of the most efficient Canadian mathematicians ever. His examine spans natural, utilized, and computational arithmetic in addition to excessive functionality computing, and maintains to have a huge impression: MathSciNet lists greater than 2500 citations through greater than 1250 authors, and Borwein is likely one of the 250 so much brought up mathematicians of the interval 1980-1999. He has served the Canadian arithmetic neighborhood via his presidency (2000–02) in addition to his 15 years of modifying the CMS ebook series.

Jonathan Borwein’s imaginative and prescient and initiative were an important in beginning 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 college, the Dalhousie dispensed examine Institute at Dalhousie collage, the Western Canada examine Grid, and the Centre for machine Assisted learn arithmetic and its functions, collage 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 get together of Dr. Borwein’s sixtieth Birthday. the gathering comprises a number of state of the art examine manuscripts and surveys providing contributions that experience risen from the convention, and is a wonderful chance to survey cutting-edge study and speak about promising examine instructions and approaches.

**Read Online or Download Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday PDF**

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**Example text**

However, the question of its normality in any other base (not a power of r) is open. For example, it is not known whether the base-10 Champernowne number is normal in the base 2. In 1917, Sierpi´nski [15] gave a construction of an absolutely normal number (in fact, one such number for each ε with 0 < ε ≤ 1). A computable version of this construction was given by Becher and Figueira [2]. √ Most fundamental irrational constants, such as 2, log 2, π , and e, appear to be normal, and statistical tests done to date are consistent with the hypothesis that they are normal.

The graph of a maximally monotone operator A : X ⇒ X is denoted by graA, its resolvent (A + Id)−1 by JA , its set of zeros by zer A = A−1 (0), and we set RA = 2JA − Id, where Id is the identity operator. Weak convergence is indicated by . Let T : X → X. Recall that T is firmly nonexpansive if (∀x ∈ X)(∀y ∈ X) T x − Ty 2 + (Id−T )x − (Id−T )y 2 ≤ x − y 2. , (∀x ∈ X)(∀y ∈ X) Rx − Ry ≤ x − y . 3) Clearly, every firmly nonexpansive operator is nonexpansive. Building on work by Minty [19], Eckstein and Bertsekas [13] clearly linked firmly nonexpansive mappings to maximally monotone operators—the key result is the following: T is firmly nonexpansive if and only if T = JA for some maximally monotone operator A (namely, T −1 − Id).

Mori, Y. ) Handbook of Computational Statistics, Chap. 2. Springer, Berlin (2004) 12. : TestU01: A C Library for empirical testing of random number generators. ACM Trans. Math. Software 33, 15 (2007) 13. : The Hausdorff dimension of a set of normal numbers. Pacific J. Math. 95, 193–204 (1981) 14. : Old and new results on normality. Lecture Notes – Monograph Series, Dynamics and Stochastics, vol. 48, pp. 225–236. Institute of Mathematical Statistics, Beachwood (2006) 15. : On normal numbers. Pacific J.