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Date: 2017
Language: eng
Resource Type: report
Identifier: http://hdl.handle.net/1959.13/1330341
Description: We provide supplementary material and additional detailed discussion pertaining to the paper “Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres”. [Final citation details to be advised... More
Date: 2017
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1353064
Description: Mathematical research is undergoing a transformation from a mostly theoretical enterprise to one that involves a significant amount of experimentation. Indeed, computational and experimental mathem... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1323186
Description: We derive an explicit piecewise-polynomial closed form for the probability density function of the distance travelled by a uniform random walk in an odd-dimensional space.
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1338235
Description: The story I tell is of research undertaken, with students and colleagues, in the last six or so years on short random walks. As the research progressed, my criteria for `beauty' changed. Things seemin... More
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Reviewed: Reviewed
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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1338274
Description: We discuss Lagrange multiplier rules from a variational perspective. This allows us to highlight many of the issues involved and also to illustrate how broadly an abstract version can be applied.
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1321817
Description: We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the cas... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1320081
Description: In recent times the Douglas-Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1319909
Description: Given a closed set C in a Banach space (X, || · ||), a point x ∈ X is said to have a nearest point in C if there exists z ∈ C such that dC(x) = ||x - z||, where dC... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1324961
Description: We discuss some key results from convex analysis in the setting of topological groups and monoids. These include separation theorems, Krein-Milman type theorems, and minimax theorems.
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.13/1317076
Description: Robust, concrete and abstract, mathematical computation and inference on the scale now becoming possible should change the discourse about many matters mathematical. These include: what mathematics is... More
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1315924
Description: In celebration of both a special “big” π Day (3/14/15) and the 2015 centennial of the Mathematical Association of America, we review the illustrious history of the constant π in the pages of the Ameri... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1331984
Description: We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1314534
Description: Stimulated by earlier work by Moll and his coworkers (Amdeberhan et al., Proc. Am. Math. Soc., 139(2):535-545, 2010), we evaluate various basic log Gamma integrals in terms of partial derivatives of T... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.13/1329905
Description: In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1314541
Description: Polylogarithms appear in many diverse fields of mathematics. Herein, we investigate relations amongst the restricted class of Nielsen-type (essentially, height one) polylogarithms, both generic and at... More
Reviewed: Reviewed