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Spherical functions on Euclidean space
Journal of Functional Analysis, 2006 We study spherical functions on Euclidean spaces from the viewpoint of Riemannian symmetric spaces. Here the Euclidean space En=G/K where G is the semidirect product Rn⋅K of the translation group with a closed subgroup K of the orthogonal group O(n).
Joseph A Wolf
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Synthese, 1977
Philosophers of past times have claimed that the answer to the question, Is visual space Euclidean?, can be answered by a priori or purely philosophical methods. Today such a view is presumably held only in remote philosophical backwaters. It would be generally agreed that one way or another the answer is surely empirical, but the answer might be ...
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Philosophers of past times have claimed that the answer to the question, Is visual space Euclidean?, can be answered by a priori or purely philosophical methods. Today such a view is presumably held only in remote philosophical backwaters. It would be generally agreed that one way or another the answer is surely empirical, but the answer might be ...
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On characterization of Euclidean spaces
Applied Mathematics and Computation, 2007Let \(\mathcal{E}\) be a Euclidean plane with Euclidean norm \(\| \dots \| \). A bounded convex centrally symmetric subset \(K\) of \(\mathcal{E}\) with a non-empty interior defines a norm \(\| \dots \| _K\) by \(\| v \| _K = \left(\inf \{r : r v \in K\}\right)^{-1}\).
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G-Semidifferentiability in Euclidean Spaces
Journal of Optimization Theory and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
PAPPALARDO, MASSIMO, UDERZO A.
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Indivisibility of balls in Euclidean n-space
Topology and Its Applications, 1993 An open or closed ball in Euclidean n-space cannot be partitioned into k pairwise congruent sets if 2⩽ k ⩽
Eric K Van Douwen
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Embedding of trees in euclidean spaces
Graphs and Combinatorics, 1988It is proved that for any tree T the vertices of T can be placed on the surface of a sphere in \(R^ 3\) in such a way that adjacent vertices have distance 1 and nonadjacent vertices have distance less than 1. This improves an earlier result of the last three authors (to appear in Discrete and Computational Geometry).
Hiroshi Maehara +3 more
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THE EMBEDDING OF COMPACTA IN EUCLIDEAN SPACE
Mathematics of the USSR-Sbornik, 1970Recently the fundamental importance of the 1-ULC property of the complementary space in describing a given embedding in En has become clear. "Wild" embeddings in En are characterized by the absence of the 1-ULC property. In this paper "tame" and "wild" embeddings in En of arbitrary compacta in codimension at least 3 are defined.
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Spherical Submanifolds of a Euclidean Space
The Quarterly Journal of Mathematics, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Al-Odan, Haila, Deshmukh, Sharief
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A Representation of Hypergraphs in the Euclidean Space
IEEE Transactions on Computers, 1984This paper introduces a graph space that shows concisely the relative weights among combinations of vertices of a given hypergraph. (A hypergraph is a graph in which one edge may connect two or more vertices.) The hypergraph is represented by a collection of points in graph space such that the distance between vertices in graph space reflects the ...
Kunio Fukunaga +3 more
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