Spelling suggestions: "subject:"fractal""
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Spectral Analysis of Laplacians on Certain FractalsZhou, Denglin January 2007 (has links)
Surprisingly, Fourier series on certain fractals can have better
convergence properties than classical Fourier series. This is a
result of the existence of gaps in the spectrum of the Laplacian. In
this work we prove a general criterion for the existence of gaps.
Most of the known examples on which the Laplacians admit spectral
decimation satisfy the criterion. Then we analyze the infinite
family of Vicsek sets, finding an explicit formula for the spectral
decimation functions in terms of Chebyshev polynomials. The
Laplacians on this infinite family of fractals are also shown to
satisfy our criterion and thus have gaps in their spectrum.
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Spectral Analysis of Laplacians on Certain FractalsZhou, Denglin January 2007 (has links)
Surprisingly, Fourier series on certain fractals can have better
convergence properties than classical Fourier series. This is a
result of the existence of gaps in the spectrum of the Laplacian. In
this work we prove a general criterion for the existence of gaps.
Most of the known examples on which the Laplacians admit spectral
decimation satisfy the criterion. Then we analyze the infinite
family of Vicsek sets, finding an explicit formula for the spectral
decimation functions in terms of Chebyshev polynomials. The
Laplacians on this infinite family of fractals are also shown to
satisfy our criterion and thus have gaps in their spectrum.
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Standard and nonstandard roughness - consequences for the physics of self-affine surfacesGheorghiu Ștefan, January 2000 (has links)
Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 87-91). Also available on the Internet.
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Fractal geometry of iso-surfaces of a passive scalar in a turbulent boundary layerSchuerg, Frank, January 2003 (has links) (PDF)
Thesis (M.S. in E.S.M.)--School of Civil and Environmental Engineering, Georgia Institute of Technology, 2004. Directed by Donald R. Webster. / Includes bibliographical references (leaves 118-121).
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Visualization tools for information exploration /Hong, Kam-kee, Kay. January 2001 (has links)
Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 119-122).
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Visualization tools for information exploration康錦琦, Hong, Kam-kee, Kay. January 2001 (has links)
published_or_final_version / Computer Science and Information Systems / Master / Master of Philosophy
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Fraktalinis vaizdų suspaudimo metodo tyrimas / Fractal image compressionŽemlo, Gražina 11 June 2004 (has links)
One of the images compression methods – fractal image compression is analyzed in the work. After work carried out, it is possible to state, that selecting parameters of method of fractal compression depends on user’s demands.
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A fractal theory of iterated Markov operators with applications to digital image codingJacquin, Arnaud E. 08 1900 (has links)
No description available.
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On estimating fractal dimensionDubuc, Benoit January 1988 (has links)
No description available.
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POROSITY, PERCOLATION THRESHOLDS, AND WATER RETENTION BEHAVIOR OF RANDOM FRACTAL POROUS MEDIASukop, Michael C. 01 January 2001 (has links)
Fractals are a relatively recent development in mathematics that show promise as a foundation for models of complex systems like natural porous media. One important issue that has not been thoroughly explored is the affect of different algorithms commonly used to generate random fractal porous media on their properties and processes within them. The heterogeneous method can lead to large, uncontrolled variations in porosity. It is proposed that use of the homogeneous algorithm might lead to more reproducible applications. Computer codes that will make it easier for researchers to experiment with fractal models are provided. In Chapter 2, the application of percolation theory and fractal modeling to porous media are combined to investigate percolation in prefractal porous media. Percolation thresholds are estimated for the pore space of homogeneous random 2-dimensional prefractals as a function of the fractal scale invariance ratio b and iteration level i. Percolation in prefractals occurs through large pores connected by small pores. The thresholds increased beyond the 0.5927 porosity expected in Bernoulli (uncorrelated) networks. The thresholds increase with both b (a finite size effect) and i. The results allow the prediction of the onset of percolation in models of prefractal porous media. Only a limited range of parameters has been explored, but extrapolations allow the critical fractal dimension to be estimated for many b and i values. Extrapolation to infinite iterations suggests there may be a critical fractal dimension of the solid at which the pore space percolates. The extrapolated value is close to 1.89 -- the well-known fractal dimension of percolation clusters in 2-dimensional Bernoulli networks. The results of Chapters 1 and 2 are synthesized in an application to soil water retention in Chapter 3.
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