Results 51 to 60 of about 5,495,109 (374)
Equiangular Subspaces in Euclidean Spaces [PDF]
Discrete & Computational Geometry, 2018 A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in $\mathbb{R}^n$ was studied extensively for the last 70 years. In this paper, we study analogous questions for $k$-dimensional subspaces.
Balla, Igor, Sudakov, Benny
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Super parallel immersions in Euclidean space
International Journal of Mathematics and Mathematical Sciences, 2002 Two submanifolds of Euclidean n-space En are called super parallel if the affine normal spaces are homothetic at the corresponding points. Characterizations are given for the action of conformal transformation on super parallel mates.
Tarek Fathy Mersal +1 more
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1-mean and 1-medoid 2-clustering problem with arbitrary cluster sizes: Complexity and approximation [PDF]
Yugoslav Journal of Operations Research, 2023 We consider the following 2-clustering problem. Given N points in Euclidean space, partition it into two subsets (clusters) so that the sum of squared distances between the elements of the clusters and their centers would be minimum.
Pyatkin Artem V.
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Notes on Euclidean de Sitter space [PDF]
, 2002 We discuss issues relating to the topology of Euclidean de Sitter space. We show that in (2+1) dimensions, the Euclidean continuation of the`causal diamond', i.e the region of spacetime accessible to a timelike observer, is a three-hemisphere.
A. Strominger +8 more
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Exploring quaternionic Bertrand curves: involutes and evolutes in $ \mathbb{E}^{4} $
AIMS MathematicsThis study investigated the concepts of (0, 2)-involute and (1, 3)-evolute curves associated with quaternionic Bertrand curves within the context of four-dimensional Euclidean space.
Ayman Elsharkawy +3 more
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On geometry on a two-dimensional plane in a five-dimensional pseudo-Euclidean space of index two [PDF]
E3S Web of ConferencesThe study of the geometry of surfaces having a codimension greater than one in multidimensional spaces is one of the most difficult problems in geometry. When the multidimensional geometry under consideration has a pseudo-Euclidean metric, its complexity
Mamadaliev Botirjon +2 more
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Approximating persistent homology in Euclidean space through collapses [PDF]
Applicable Algebra in Engineering, Communication and Computing, 2014 The Čech complex is one of the most widely used tools in applied algebraic topology. Unfortunately, due to the inclusive nature of the Čech filtration, the number of simplices grows exponentially in the number of input points.
M. B. Botnan, Gard Spreemann
semanticscholar +1 more source
Random walks in Euclidean space
, 2015 Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way.
Arnol'd +10 more
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Orthogonal embeddings of graphs in Euclidean space
Electronic Journal of Graph Theory and Applications, 2019 Let G = (V, E) be a simple connected graph. An injective function f : V → Rn is called an n-dimensional (or n-D) orthogonal labeling of G if uv, uw ∈ E implies that (f(v) − f(u)) ⋅ (f(w) − f(u)) = 0, where ⋅ is the usual dot product in Euclidean space.
Wai Chee Shiu, Richard M. Low
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The space of clouds in an Euclidean space
, 2002 27 pages ...
Hausmann, Jean-Claude +1 more
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