Zobrazeno 1 - 10 of 26 pro vyhledávání: '"Mahler volume"'
1
Diskretisierung, Subspace Concentration und Polarität
Autor: Freyer, Ansgar
The subject of this thesis is the volume of convex bodies K in R^n. Specifically, we investigate the volume vol(K) in the context of three different branches of convex geometry. In the first part of the thesis, we compare the volume of K to the numbe
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2
General Affine Invariances Related to Mahler Volume
Autor: Yiming Zhao, Dongmeng Xi
Publikováno v: International Mathematics Research Notices. 2022:14151-14180
General affine invariances related to Mahler volume are introduced. We establish their affine isoperimetric inequalities by using a symmetrization scheme that involves a total of $2n$ elaborately chosen Steiner symmetrizations at a time. The necessit
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::846be976a25ac3f46fc87fd995e14c4c
https://doi.org/10.1093/imrn/rnab118
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3
Akademický článek
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4
The Mahler Conjecture in Two Dimensions via the Probabilistic Method
Autor: Matthew Tointon
Publikováno v: The American Mathematical Monthly. 125:820-828
The "Mahler volume" is, intuitively speaking, a measure of how "round" a centrally symmetric convex body is. In one direction this intuition is given weight by a result of Santalo, who in the 1940s showed that the Mahler volume is maximized, in a giv
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fabfa3d33d840ae6aa56adc603fc7559
https://doi.org/10.1080/00029890.2018.1503511
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5
Approximate Polytope Membership Queries
Autor: Guilherme D. da Fonseca, David M. Mount, Sunil Arya
Publikováno v: STOC
SIAM Journal on Computing
SIAM Journal on Computing, 2018, 47 (1), pp.1-51. ⟨10.1137/16M1061096⟩
SIAM Journal on Computing, Society for Industrial and Applied Mathematics, 2018, 47 (1), pp.1-51. ⟨10.1137/16M1061096⟩
In the polytope membership problem, a convex polytope $K$ in $\mathbb{R}^d$ is given, and the objective is to preprocess $K$ into a data structure so that, given any query point $q \in \mathbb{R}^d$, it is possible to determine efficiently whether $q
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f495c749d7a19914c8688279d3961c9b
https://doi.org/10.1137/16m1061096
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6
PARALLEL SECTIONS HOMOTHETY BODIES WITH MINIMAL MAHLER VOLUME IN ℝn
Autor: Youjiang Lin, Gangsong Leng
Publikováno v: Bulletin of the Korean Mathematical Society. 51:1023-1029
In the paper, we define a class of convex bodies in R n –parallelsections homothety bodies, and for some special parallel sections homoth-ety bodies, we prove that n-cubes have the minimal Mahler volume. 1. IntroductionThe well-known Mahler’s co
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https://doi.org/10.4134/bkms.2014.51.4.1023
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8
Origin-symmetric bodies of revolution with minimal Mahler volume in ℝ^3-a new proof
Autor: Gangsong Leng, Youjiang Lin
Publikováno v: Journal of Mathematical Inequalities. :375-404
In (22), Meyer and Reisner proved the Mahler conjecture for rovelution bodies. In this paper, using a new method, we prove that among origin-symmetric bodies of revolution in R 3 , cylinders have the minimal Mahler volume. Further, we prove that amon
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https://doi.org/10.7153/jmi-08-28
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9
Akademický článek
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