Results 11 to 20 of about 167,140,582 (172)
Dimension and measure theory of self-similar structures with no separation condition [PDF]
, 2015 We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any separation condition.
Farkas, Ábel
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Directed graph iterated function systems [PDF]
, 2011 This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that ...
Boore, Graeme C.
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Codimension formulae for the intersection of fractal subsets of Cantor spaces [PDF]
, 2015 We examine the dimensions of the intersection of a subset E of an m-ary Cantor space Cm with the image of a subset F under a random isometry with respect to a natural metric.
Falconer, Kenneth John, Donoven, Casey
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The geometry of self-affine fractals [PDF]
, 2008 In this thesis we study the dimension theory of self-affine sets. We begin by introducing a number of notions from fractal geometry, in particular, dimensions, measure properties and iterated functions systems.
Miao, Jun Jie
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Dimension and measure for generic continuous images [PDF]
, 2013 This work is supported by EPSRC Doctoral Training GrantsWe consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, X, into R-n.
James T. Hyde +9 more
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Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure [PDF]
, 2012 "GCB was supported by an EPSRC Doctoral Training Grant whilst undertaking this work"For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of ...
Boore, Graeme, Falconer, Kenneth John
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On the Hausdorff Measure of Shrinking Target Sets on Self-Conformal Sets
, 2021 In this article, we study the Hausdorff measure of shrinking target sets on self-conformal sets. The Hausdorff dimension of the sets we are interested in here was established by Hill and Velani in 1995.
Allen, Demi +2 more
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Hölder differentiability of self-conformal devil's staircases [PDF]
, 2014 In this paper we consider the probability distribution function of a Gibbs measure supported on a self-conformal set given by an iterated function system (devil's staircase) applied to a compact subset of ℝ. We use thermodynamic multifractal formalism to
Troscheit, S., Sascha Troscheit
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Compactness in asymmetrically normed lattices. [PDF]
, 2012 Includes abstract.Includes bibliographical references.The aim of the thesis is to investigate aspects of the theory of such spaces, concentrating mainly, but not exclusively, on nite dimensional spaces.
Mabula, Mokhwetha Daniel
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Crystal Structure Prediction of Inorganic Materials: A Benchmark and Modern Evaluation
Advanced Intelligent Discovery, EarlyView.Predicting a crystal’s structure from composition alone is a long‐standing challenge in materials discovery. The CSP180 benchmark of 180 inorganic crystals evaluates thirteen crystal structure prediction algorithms requiring no density functional theory (DFT) against DFT‐based baselines across twelve metrics.
Lai Wei +9 more
wiley +1 more source