Results 11 to 20 of about 93,156 (306)

Generalized Helicoidal Surfaces in Euclidean 5-space

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ...
Uçum Ali, Sakaki Makoto
doaj   +2 more sources

Normal curves in n-dimensional Euclidean space [PDF]

Advances in Difference Equations, 2018
In this paper, we give a generalization of normal curves to n-dimensional Euclidean space. Then we obtain a necessary and sufficient condition for a curve to be a normal curve in the n-dimensional Euclidean space. We characterize the relationship between
Özcan Bektaş
doaj   +2 more sources

On Sumsets in Euclidean Space

Journal of Number Theory, 2000
Some addition theorems for Lebesgue measurable sets and lattice subsets of Euclidean space \(\mathbb{R}^n\) are proved. Let \(P\) be an \(n\)-dimensional parallelepiped, \(A\) and \(B\) be non-empty measurable subsets of \(P\) such that the convex hull of \(A\) is \(P\). If \(S=A+B\), then \[ m(S)\geq 2^nm(B)+\min\{m(A),m(p\setminus B)\},\tag{Theorem 4}
Fainleib, A.S
openaire   +2 more sources

Space Complexity of Euclidean Clustering [PDF]

IEEE Transactions on Information Theory
The $(k, z)$-Clustering problem in Euclidean space $\mathbb{R}^d$ has been extensively studied. Given the scale of data involved, compression methods for the Euclidean $(k, z)$-Clustering problem, such as data compression and dimension reduction, have received significant attention in the literature.
Xiaoyi Zhu, Yuxiang Tian, Lingxiao Huang, Zengfeng Huang   +3 more
core   +7 more sources

A d-dimensional analyst's Travelling Salesman theorem for arbitrary sets in Euclidean space [PDF]

, 2021
In this thesis, we discuss recent progress on higher dimensional analogues to the Analyst’s Travelling Salesman Theorem (TST) of Peter Jones. The TST characterizes subsets of rectifiable curves in the plane, via a multiscale sum of β-numbers.
Hyde, Matthew
core   +1 more source

Minimal homogeneous submanifolds in euclidean spaces [PDF]

, 2002
We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex (intrisecally) homogeneous submanifold of a complex Euclidean space must be totally ...
Di Scala, Antonio Jose'
core   +1 more source

Special Smarandache Curves in the Euclidean Space [PDF]

, 2010
In this work, we introduce some special Smarandache curves in the Euclidean space. We study Frenet-Serret invariants of a special case.
Ali, Ahmad
core   +1 more source

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.
doaj   +1 more source

The Space of Clouds in Euclidean Space

Experimental Mathematics, 2004
We study the space {\small $\nua{m}{d}$} of clouds in {\small $\bbr^d$} (ordered sets of m points modulo the action of the group of affine isometries). We show that {\small $\nua{m}{d}$} is a smooth space, stratified over a certain hyperplane arrangement in {\small $\bbr^m$}.
Hausmann, Jean-Claude, Rodriguez, Eugenio   +1 more
openaire   +3 more sources

Minimal Immersions of Kahler manifolds into Euclidean Spaces [PDF]

, 2003
It is proved here that a minimal isometric immersion of a Kähler-Einstein or homogeneous Kähler-manifold into an Euclidean space must be totally ...
Di Scala, Antonio Jose'
core   +1 more source