A Characterization on the Spectra of Self-Affine Measures
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-018-9621-7
Abstract: A discrete set $$\Lambda \subseteq {\mathbb {R}}^d$$Λ⊆Rd is called a spectrum for the probability measure $$\mu $$μ if the family of functions $$\{e^{2 \pi i \langle \lambda ,\, x\rangle }: \lambda \in \Lambda \}$${e2πi⟨λ,x⟩:λ∈Λ} forms… read more here.
Keywords: lambda; characterization spectra; spectra self; affine measures ... See more keywords
Tree structure of spectra of spectral self-affine measures
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2019.04.006
Abstract: Abstract For an integral self-affine spectral measure, if the zeros of its Fourier transform are all integral vectors, it is proven that any its spectrum has a tree structure. For any subset with such tree… read more here.
Keywords: self affine; structure; spectra spectral; tree structure ... See more keywords
Non-spectrality of self-affine measures
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DOI: 10.1016/j.jfa.2019.05.015
Abstract: Abstract Under some supportive evidences of known results about non-spectral self-affine measures, Li proposed a conjecture in [18] (J. Funct. Anal. 255, 2008), which is so-called “non-spectral conjecture”. In this paper, we prove that Li's… read more here.
Keywords: self affine; non spectrality; affine measures; non spectral ... See more keywords
Topological structure of a class of planar self-affine sets
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2016.09.016
Abstract: Abstract Let T = T ( A , D ⁎ ) be a disk-like Z 2 -tile generated by an expanding 2 × 2 matrix A and a digit set D ⁎ ⊂ Z 2… read more here.
Keywords: structure class; planar self; affine sets; topological structure ... See more keywords
Plastic contact of self-affine surfaces: Persson’s theory versus discrete dislocation plasticity
Sign Up to like & getrecommendations! Published in 2019 at "Journal of the Mechanics and Physics of Solids"
DOI: 10.1016/j.jmps.2019.07.019
Abstract: Abstract Persson’s theory allows for a fast and effective estimate of contact area and contact stress distributions when a flat and a self-affine rough surface are pressed into contact. For elastic bodies, the results of… read more here.
Keywords: contact; dislocation plasticity; self affine; discrete dislocation ... See more keywords
Spectrality of a class of self-affine measures on R2
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DOI: 10.1088/1361-6544/ac2493
Abstract: In this work, we study the spectral property of a class of self-affine measures μ M,D on R2 generated by an expanding real matrix M=diagρ1−1,ρ2−1 and a non-collinear integer digit set D={(0,0)t,(α1,α2)t,(β1,β2)t} with αi−2βi∉3Z ,… read more here.
Keywords: affine measures; class self; self affine;
DOUBLING PROPERTIES OF SELF-AFFINE MEASURES SUPPORTED ON GATZOURAS–LALLEY FRACTALS
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DOI: 10.1142/s0218348x19501275
Abstract: In this paper, we study the doubling properties of self-affine measures supported on a class of self-affine sets named Gatzouras–Lalley sets. First, we show that every self-affine measure is doubli... read more here.
Keywords: properties self; measures supported; affine measures; doubling properties ... See more keywords
Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture
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DOI: 10.1155/2018/9095143
Abstract: This pore-scale modeling study in single self-affine fractures showed that the heterogeneous flow field had a significant influence on the mixing-induced reaction transport. We generated the single self-affine fracture by the successive random additions (SRA)… read more here.
Keywords: single self; transport; reaction; mixing ... See more keywords
On the structure of self-affine Jordan arcs in ℝ2
Sign Up to like & getrecommendations! Published in 2023 at "Demonstratio Mathematica"
DOI: 10.1515/dema-2022-0228
Abstract: Abstract We prove that if a self-affine arc γ ∈ R 2 \gamma \in {{\mathbb{R}}}^{2} does not satisfy weak separation condition, then it is a segment of a parabola or a straight line. If a… read more here.
Keywords: jordan; structure self; jordan arcs; self affine ... See more keywords
Topological Properties of a Class of Higher-dimensional Self-affine Tiles
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DOI: 10.4153/s0008439519000237
Abstract: Abstract We construct a family of self-affine tiles in $\mathbb{R}^{d}$ ( $d\geqslant 2$ ) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in $\mathbb{R}^{2}$ , and… read more here.
Keywords: class higher; affine tiles; properties class; self affine ... See more keywords