Introduction to metric spaces with dilations
英文摘要:
This paper gives a short introduction into the metric theory of spaces with dilations.
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Marius Buliga
This paper gives a short introduction into the metric theory of spaces with dilations.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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This article describes a structure that metric spaces can be equipped with so that they resemble normed vector spaces and examines necessary and sufficient conditions for the existence of such a structure on a general metric space.
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Two-point dilation-homogeneous metric spaces
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Analytic aspects of the dilation inequality for symmetric convex sets in Euclidean spaces
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$λ$-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.
Braided sets which are also spaces with dilations are presented and explored in this paper, in the general frame of emergent algebras arxiv:0907.1520. Examples of such spaces are the sub-riemannian symmetric spaces. Keywords: braided sets, quandles; emergent algebras; dilatation structures (spaces with dilations); sub-riemannian symmetric spaces.
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We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers~ -- heuristic algorithms that find models for CNF boolean formulas. Our algorithm was implemented and applied to the search of fractal surjective curves $γ\colon[0,1]\to[0,1]^d$ with minimal dilation $$ \sup_{t_1<t_2}\frac{\|γ(t_2)-γ(t_1)\|^d}{t_2-t_1}. $$ We report new results of that search in the case of Euclidean norm. We have found a new curve that we call "YE", a self-similar (monofractal) plane curve of genus $5\times 5$ with dilation $5\frac{43}{73}=5.5890\ldots$. In di…
We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a condensed way. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, it coincides with the Naimark Dilation and only one rotation matrix is computed, when the process is non-stationary, a set of rotation matrices are computed. In particular, the peri…
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