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<i>Dysosma xishuiensis</i> (Berberidaceae), a new species from Guizhou, China, based on morphological and molecular evidence. [PDF]
PhytoKeysHuang L +6 more
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International Journal of Computational Geometry & Applications, 1996
The task of finding the largest empty ellipsoid defined by a set of n point sites in Rd is investigated. It is shown that this can be solved by enumerating the facets of the convex hull of the sites projected onto a manifold in R[d(d+3)/2]. While O(n[d(d+3)/4]) time is required in the worst case, it is found that O(nd) suffices on average for ...
Dwyer, Rex A., Eddy, William F.
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The task of finding the largest empty ellipsoid defined by a set of n point sites in Rd is investigated. It is shown that this can be solved by enumerating the facets of the convex hull of the sites projected onto a manifold in R[d(d+3)/2]. While O(n[d(d+3)/4]) time is required in the worst case, it is found that O(nd) suffices on average for ...
Dwyer, Rex A., Eddy, William F.
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Proceedings of the London Mathematical Society, 2005
The authors show that associated with each convex body \(K\) that contains the origin in its interior is a family of ellipsoids \(E_pK\), the \(L_p\) John ellipsoids of \(K\). For origin-symmetric \(K\) the ellipsoid \(E_{\infty}K\) turns out to be the classical John ellipsoid. This is the largest (in volume) ellipsoid that can be squeezed inside \(K\).
Lutwak, Erwin +2 more
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The authors show that associated with each convex body \(K\) that contains the origin in its interior is a family of ellipsoids \(E_pK\), the \(L_p\) John ellipsoids of \(K\). For origin-symmetric \(K\) the ellipsoid \(E_{\infty}K\) turns out to be the classical John ellipsoid. This is the largest (in volume) ellipsoid that can be squeezed inside \(K\).
Lutwak, Erwin +2 more
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Ellipsoidal geoidal undulations (ellipsoidal Bruns formula): case studies
Journal of Geodesy, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ardalan, A. A., Grafarend, E. W.
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Circumscribing an Ellipsoid about the Intersection of Two Ellipsoids
Canadian Mathematical Bulletin, 1968An ellipsoid G is associated uniquely with a positive definite matrix A viaNote that all ellipsoids discussed here are centred at 0. Given G1, and G2 we seek another ellipsoid circumscribed about G1 ∩ G2. It is easy to see that if and only if x'hx ≤ maxi x'aix for all vectors x.
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1999
Abstract In this chapter we present explicit results for low frequency scattering by a triaxial ellipsoid with semi-axes a 1 > a 2 > a 3 > 0. Results for rotationally symmetric ellipsoids are easily obtained by setting a 2 = a 3 (prolate spheroid) or a 1 = a 2 (oblate spheroid).
George Dassios, Ralph Kleinman
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Abstract In this chapter we present explicit results for low frequency scattering by a triaxial ellipsoid with semi-axes a 1 > a 2 > a 3 > 0. Results for rotationally symmetric ellipsoids are easily obtained by setting a 2 = a 3 (prolate spheroid) or a 1 = a 2 (oblate spheroid).
George Dassios, Ralph Kleinman
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2012
The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years.
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The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years.
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