By David H. Bailey, Heinz H. Bauschke, Peter Borwein, Frank Garvan, Michel Théra, Jon D. Vanderwerff, Henry Wolkowicz
The examine of Jonathan Borwein has had a profound impression on optimization, practical research, operations examine, mathematical programming, quantity thought, and experimental arithmetic. Having authored greater than a dozen books and greater than three hundred guides, Jonathan Borwein is among 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 massive effect: MathSciNet lists greater than 2500 citations by means of greater than 1250 authors, and Borwein is without doubt one of the 250 such a lot brought up 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 enhancing the CMS ebook series.
Jonathan Borwein’s imaginative and prescient and initiative were the most important in starting up and constructing a number of associations that offer help for researchers with a variety of medical pursuits. a couple of extraordinary examples contain the Centre for Experimental and confident arithmetic and the IRMACS Centre at Simon Fraser college, the Dalhousie allotted examine Institute at Dalhousie college, the Western Canada study Grid, and the Centre for laptop Assisted examine 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 quite a lot of mathematical fields. This current quantity is an outgrowth of the workshop on ‘Computational and Analytical arithmetic’ held in may well 2011 in social gathering of Dr. Borwein’s sixtieth Birthday. the gathering comprises numerous state of the art learn manuscripts and surveys providing contributions that experience risen from the convention, and is a wonderful chance to survey state of the art examine and speak about promising learn instructions and approaches.
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Extra resources for Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday
48, 2513–2515 (2009) 2. : Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011) 3. : The Douglas-Rachford algorithm in the absence of convexity. , Wolkowicz, H. ) Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer Optimization and Its Applications, vol. 49, pp. 93–109. Springer, New York (2011) 4. : Convex Functions. Cambridge University Press, Cambridge (2010) 5. : Op´erateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert.
For the leader we denote by Jl the scalar objective, by ul the control function and by Ul the set of admissible controls. For the followers we denote by Jf = (J1 , . . , J p ) the vector objective (p-scalar objectives) and by uf = (u1 , . . , u p ) the control function whose values belong to the set Uf = U1 × · · · × U p ⊆ Rm f = Rm1 × · · · × Rm p . Uf is assumed to be nonempty, closed and convex, and 0 ∈ Uf . Real numbers t0 , T are fixed (t0 < T ) and represent respectively the initial time and an upper bound of the final time.
In fact, for all m ≥ 1, m m (3/4)3 (3/4)3 < Q < (1 + 2 · 10−6). 23) Let Zm = log6 1/Qm be the number of zeroes in the base-6 expansion of α that immediately follow position 3m . 23) can be rewritten 3m log6 4 + (m + 1) log6 3 − 2 3 < Zm < 3m log6 4 + (m + 1) log6 3. , up to the end of the block of zeroes that immediately follows position 3m ). 25) 1 Normal Numbers and Pseudorandom Generators 15 since the numerator only counts zeroes in the long stretches. The summation in the numerator satisfies, for all sufficiently large m, m 3 ∑ Zk > 2 3m − k=1 1 log6 3 3 m · 3 log6 2 > 4 m(m + 3) log6 3 − 2m + 3 2 4 1 − log6 3 2 4 − 2m.
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