• Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
  • Title: Expectation integrals on fractal sets
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: UNewcastle [ENQUIRIES]
  • Time and Date: 3:00 pm, Mon, 13th Aug 2012
  • (Joint talk with Michael Rose.)
  • Abstract:

    (Joint speakers, Jon Borwein and Michael Rose)

    p>Using fractal self-similarity and functional-expectation relations, the classical theory of box integrals is extended to encompass a new class of fractal “string-generated Cantor sets” (SCSs) embedded in unit hypercubes of arbitrary dimension. Motivated by laboratory studies on the distribution of brain synapses, these SCSs were designed for dimensional freedom: a suitable choice of generating string allows for fine-tuning the fractal dimension of the corresponding set. We also establish closed forms for certain statistical moments on SCSs and report various numerical results. The associated paper is at http://www.carma.newcastle.edu.au/jon/papers.html#PAPERS.

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