| EPSRC Reference: |
GR/J64429/01 |
| Title: |
THE GEOMETRY OF MULTIFRACTAL MEASURES |
| Principal Investigator: |
Falconer, Professor K |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Computer Science |
| Organisation: |
University of St Andrews |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 1994 |
Ends: |
30 September 1997 |
Value (£): |
95,068
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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Summary on Grant Application Form |
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The multi-fractal spectrum (or `mass distribution') provides a description of the spatial distribution of singularities of the measure. For measures of interest there is a range of over which the points where the singularities have `intensity' and form a fractal set, and the spectrum reflects the dimensions of these sets. This project aims to study the geometry of multifractal spectra, for example by relating the spectrum of a general measure to those of its projections, sections, and intersections with certain sets. Such properties may be thought of as measure analogues of the geometrical properties of fractal sets that have been established over the years. It is proposed to extend the methods that have been used to study fractals to the multifractal situation. Multifractal analysis is attracting considerable current interest not only theoretically but also as a practical tool for analysing physical phenomena, Both from the theoretical and practical viewpoints it is desirable that the geometry of multifractals be put onto a rigorous mathematical foundation.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.st-and.ac.uk |