منابع مشابه
Löwner-john Ellipsoids
Before giving the mathematical description of the Löwner-John ellipsoids and pointing out some of their far-ranging applications, I briefly illuminate the adventurous life of the two eminent mathematicians, by whom the ellipsoids are named: Charles Loewner (Karel Löwner) and Fritz John. Karel Löwner was born into a Jewish family in Lány, a small town about 30 km west of Prague, in 1893. Due to ...
متن کاملVOLUME INEQUALITIES FOR Lp-JOHN ELLIPSOIDS AND THEIR DUALS
In this paper, we establish some inequalities among the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual, which are the strengthened version of known results. We also prove inequalities among the polar of the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual. 2000 Mathematics Subject Classification. 52A40, 52A20.
متن کاملExperiments on random packings of ellipsoids.
Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25:1:0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We ha...
متن کاملNonexistence of Skew Loops on Ellipsoids
We prove that every C closed curve immersed on an ellipsoid has a pair of parallel tangent lines. This establishes the optimal regularity for a phenomenon first observed by B. Segre. Our proof uses an approximation argument with the aid of an estimate for the size of loops in the tangential spherical image of a spherical curve. A skew loop is a C closed curve without parallel tangent lines imme...
متن کاملOn the Kobayashi-Royden metric for ellipsoids
The Kobayashi indicatrix (infinitesimal unit ball) of a domain in IE n is known to be a biholomorphic invariant. In particular, if a domain is biholomorphic to a ball, then the indicatrix is the ball. Until the recent deep results of Lempert [4], it was not known to what extent the indicatrix characterizes the domain. Sibony had shown earlier that the indicatrix of any pseudoconvex circular dom...
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2020
ISSN: 1674-7216
DOI: 10.1360/scm-2019-0639