On the hausdorff dimensions of distance sets
WebIn mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a … Web17 de abr. de 2024 · We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances { x − y : y ∈ A} has full …
On the hausdorff dimensions of distance sets
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Web20 de jun. de 2024 · We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors … WebThe Mumford–Shah functional is a functional that is used to establish an optimality criterion for segmenting an image into sub-regions. An image is modeled as a piecewise-smooth function. The functional penalizes the distance between the model and the input image, the lack of smoothness of the model within the sub-regions, and the length of the boundaries …
Web16 de dez. de 2024 · We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient dimensions. In... Global Survey. In just 3 minutes help us understand how you see arXiv. Web7 de abr. de 2024 · Keich (1999) showed that the sharp gauge function for the generalized Hausdorff dimension of Besicovitch sets in is between and by refining an argument of Bourgain (1991). It is not known whether the iterated logarithms in …
Web31 de mai. de 2024 · We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors … Web23 de mai. de 2024 · Editorial introduction. On distance sets, box-counting and Ahlfors-regular sets, Discrete Analysis 2024:9, 22 pp. A well-known problem of Falconer, a sort of continuous analogue of the Erdős distinct-distance problem, asks how large the Hausdorff dimension of a Borel subset of R d needs to be before the set of distances between …
Web16 de dez. de 2024 · In dimensions $d=2$ or $3$, we obtain the first explicit estimates for the dimensions of distance sets of general Borel sets of dimension $d/2$; for example, we show that the set of...
WebIn mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. … filma24 spider man no way homeWebMinkowski and Hausdorff dimensions In this chapterwe will deÞne the Minkowski andHausdorffdimensionsof a set and will compute each in a few basic examples. We will then prove Billings-leyÕs Lemma and the Law of Large Numbers. These allow us to deal with more sophisticated examples: sets deÞned in terms of digit frequencies, ran- grounds for referral to scraWeb10 de dez. de 2010 · On the Hausdorff dimension of pinned distance sets. 01 March 2024. Pablo Shmerkin. Improved Bounds for Metric Capacitated Covering Problems. 15 December 2024. Sayan Bandyapadhyay. Covering compact metric spaces greedily. 08 May 2024. J. H. Rolfes & F. Vallentin. grounds for redundancyWebClick on the article title to read more. filma 24 puss in boots last wishWeb2 de mar. de 2024 · The existence of Arnoux–Rauzy IETs with two different invariant probability measures is established in [].On the other hand, it is known (see []) that all Arnoux–Rauzy words are uniquely ergodic.There is no contradiction with our Theorem 1.1, since the symbolic dynamical system associated with an Arnoux–Rauzy word is in … filma24 top gunWebOn the Hyperbolic Hausdorff Dimension of the Boundary of a Basin of Attraction for a Holomorphic Map and of Quasirepellers . × Close Log In. Log in with Facebook Log in with Google. or. Email. Password. Remember me on this computer. or reset password. Enter the email address you signed up with and we'll ... grounds for redundancy philippinesWeb17 de mar. de 2016 · In this paper, we replace the Hausdorff dimension on the left hand side of the first inequality above by the lower Minkowski dimension and replace the Lebesgue measure of the set of translates by a Hausdorff measure on a set of sufficiently large ... On the Hausdorff dimensions of distance sets, Mathematika 32 (1985), … grounds for redundancy in jamaica