Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Piotr Mankiewicz"'
Publikováno v:
ESI preprints.
Autor:
Piotr Mankiewicz
Publikováno v:
Bulletin of the Polish Academy of Sciences Mathematics. 60:285-294
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d4fc6cc28dfce424177e662a9cd249a9
https://doi.org/10.4064/ba60-3-8
https://doi.org/10.4064/ba60-3-8
Publikováno v:
Discrete & Computational Geometry. 41:257-272
We introduce a quantitative parameter measuring m-neighbourliness of symmetric convex polytopes in ℝk . We discuss this parameter for random polytopes generated by subgaussian vectors and show its stability properties.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::492f5ee78fd79924088bf5a9e1d49414
https://doi.org/10.1007/s00454-008-9092-8
https://doi.org/10.1007/s00454-008-9092-8
Publikováno v:
Discrete & Computational Geometry. 38:29-50
We consider polytopes in ${\Bbb R}^n$ that are generated by N vectors in ${\Bbb R}^n$ whose coordinates are independent subgaussian random variables. (A particular case of such polytopes are symmetric random $\pm 1$ polytopes generated by N independe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bd81f39f3ca187c9e1c42b7cfa8f314f
https://doi.org/10.1007/s00454-007-1326-7
https://doi.org/10.1007/s00454-007-1326-7
Publikováno v:
Israel Journal of Mathematics. 153:45-60
The structure of low dimensional sections and projections of symmetric convex bodies is studied. For a symmetric convex bodyB ⊂ ℝ n , inequalities between the smallest diameter of rank l projections ofB and the largest in-radius ofm-dimensional s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::68a2ebbc134c0329aff2f096e7a49e26
https://doi.org/10.1007/bf02771778
https://doi.org/10.1007/bf02771778
Publikováno v:
Studia Mathematica. 159:315-335
The geometry of random projections of centrally symmetric convex bodies inR N is studied. It is shown that if for such a bodyK the Euclidean ballB N 2 is the ellipsoid of minimal volume containing it and a random n-dimensional projection B = PH (K) i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d4ae6191d36b510189e3558ff43c906f
https://doi.org/10.4064/sm159-2-10
https://doi.org/10.4064/sm159-2-10
Autor:
Stanislaw J. Szarek, Piotr Mankiewicz
Publikováno v:
Studia Mathematica. 155:51-66
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::147171c4b4baa39e4969ffda72c8a028
https://doi.org/10.4064/sm155-1-4
https://doi.org/10.4064/sm155-1-4
Publikováno v:
Comptes Rendus Mathematique. 335:345-350
Let K be a symmetric convex body in R N for which B 2 N is the ellipsoid of minimal volume. We provide estimates for the geometric distance of a ‘typical’ rank n projection of K to B 2 n , for 1⩽ n N . Known examples show that the resulting est
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d9357c090a4815aa4dd7afe0746ee25e
https://doi.org/10.1016/s1631-073x(02)02476-7
https://doi.org/10.1016/s1631-073x(02)02476-7
Autor:
Piotr Mankiewicz, Carsten Schütt
Publikováno v:
Journal of Approximation Theory. 111(1):139-142
''Almost exact'' estimates for the Delone triangulation numbers are given. In particularlimn->~del"n"-"[email protected]=0.0585498....
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da7dec9889a6825331d3068298e298f2
Autor:
Piotr Mankiewicz, Carsten Schütt
Publikováno v:
Journal of Approximation Theory. 107:268-280
We give a simple proof of an estimate for the approximation of the Euclidean ball by a polytope with a given number of vertices with respect to the volume of the symmetric difference metric and relatively precise estimate for the Delone triangulation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::085a3ae7b54c3dc0189174b1993e329f
https://doi.org/10.1006/jath.2000.3509
https://doi.org/10.1006/jath.2000.3509