Spherical distributions of $N$ points with maximal distance sums are well spaced
نویسندگان
چکیده
منابع مشابه
Spherical Distribution of 5 Points with Maximal Distance Sum
In this paper, we mainly consider the problem of spherical distribution of 5 points, that is, how toconfigure 5 points on a sphere such that the mutual distance sum attains the maximum. It is conjecturedthat the sum of distances is maximal if 5 points form a bipyramid configuration in which case two pointsare positioned at two poles of the sphere and the other three are position...
متن کاملSums of Magnetic Eigenvalues Are Maximal on Rotationally Symmetric Domains
The sum of the first n ≥ 1 energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area) on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The...
متن کاملSpherical-Homoscedastic Distributions Spherical-Homoscedastic Distributions: The Equivalency of Spherical and Normal Distributions in Classification
Many feature representations, as in genomics, describe directional data where all feature vectors share a common norm. In other cases, as in computer vision, a norm or variance normalization step, where all feature vectors are normalized to a common length, is generally used. These representations and pre-processing step map the original data from R to the surface of a hypersphere Sp−1. Such re...
متن کاملFixed Points Theorems with respect to \fuzzy w-distance
In this paper, we shall introduce the fuzzyw-distance, then prove a common fixed point theorem with respectto fuzzy w-distance for two mappings under the condition ofweakly compatible in complete fuzzy metric spaces.
متن کاملComputing Maximal Layers of Points in Ef(n)
In this paper we present a randomized algorithm for computing the collection of maximal layers for a point set in E (k = f(n)). The input to our algorithm is a point set P = {p1, ..., pn} with pi ∈ E . The proposed algorithm achieves a runtime of O ( kn 2− 1 log k +logk (1+ 2 k+1 ) log n ) when P is a random order and a runtime of O(knk (k−1))/2 log n) for an arbitrary P . Both bounds hold in e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0365363-x