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equations on the Euclidean space with a
, 2005
"... equations on the Euclidean space with a scattering metric by ..."
Averages on annuli of Euclidean space
, 2009
"... We study the range of validity of differentiation theorems and ergodic theorems for R d actions, for averages on “thick spheres” of Euclidean space. ..."
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We study the range of validity of differentiation theorems and ergodic theorems for R d actions, for averages on “thick spheres” of Euclidean space.
Reasoning with Lines in the Euclidean Space
"... The main result of this paper is to show that the problem of instantiating a finite and pathconsistent constraint network of lines in the Euclidean space is NPcomplete. Indeed, we already know that reasoning with lines in the Euclidean space is NPhard. In order to prove that this problem is NPcomp ..."
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The main result of this paper is to show that the problem of instantiating a finite and pathconsistent constraint network of lines in the Euclidean space is NPcomplete. Indeed, we already know that reasoning with lines in the Euclidean space is NPhard. In order to prove that this problem
Sphere Rigidity in the Euclidean Space
, 2008
"... In this article, we prove new stability results for almostEinstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almostumbilic hypersurfaces and new characterizations of geodesic spheres. ..."
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In this article, we prove new stability results for almostEinstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almostumbilic hypersurfaces and new characterizations of geodesic spheres.
Spherical Functions on Euclidean Space
, 2005
"... We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space E n = G/K where G is the semidirect product R n · K of the translation group with a closed subgroup K of the orthogonal group O(n). We give exact parameterizations of the space ..."
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Cited by 3 (0 self)
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We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space E n = G/K where G is the semidirect product R n · K of the translation group with a closed subgroup K of the orthogonal group O(n). We give exact parameterizations of the space
ON HOMOGENEOUS COVERINGS OF EUCLIDEAN SPACES
"... Abstract. The notion of a homogeneous covering of a given set is introduced and examined. Some homogeneous coverings of a Euclidean space, consisting of pairwise congruent geometric figures (spheres, hyperplanes, etc.), are constructed using the method of transfinite induction. ..."
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Abstract. The notion of a homogeneous covering of a given set is introduced and examined. Some homogeneous coverings of a Euclidean space, consisting of pairwise congruent geometric figures (spheres, hyperplanes, etc.), are constructed using the method of transfinite induction.
Approximate Decidability in Euclidean Spaces
, 2001
"... We study concepts of decidability (recursivity) for subsets of Euclidean spaces R k within the framework of approximate computability (type two theory of effectivity) . A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F. Hausdorff& ..."
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We study concepts of decidability (recursivity) for subsets of Euclidean spaces R k within the framework of approximate computability (type two theory of effectivity) . A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F. Hausdorff
Polyharmonic submanifolds in Euclidean spaces
"... Abstract. B.Y. Chen introduced biharmonic submanifolds in Euclidean spaces and raised the conjecture ”Any biharmonic submanifold is minimal”. In this article, we show some affirmative partial answers of generalized Chen’s conjecture. Especially, we show that the triharmonic hypersurfaces with consta ..."
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Abstract. B.Y. Chen introduced biharmonic submanifolds in Euclidean spaces and raised the conjecture ”Any biharmonic submanifold is minimal”. In this article, we show some affirmative partial answers of generalized Chen’s conjecture. Especially, we show that the triharmonic hypersurfaces
Euclidean space Rn:
"... Abstract — Given a sphere of radius r> 1 in the ndimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a point in a bigger sphere. For growin ..."
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Abstract — Given a sphere of radius r> 1 in the ndimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a point in a bigger sphere
On the coverings of an ellipsoid in the Euclidean space
 IEEE TRANS. INFORM. THEORY
, 2004
"... The thinnest coverings of ellipsoids are studied in the Euclidean spaces of an arbitrary dimension. Given any ellipsoid, the main goal is to find itsentropy, which is the logarithm of the minimum number of the balls of radius needed to cover this ellipsoid. A tight asymptotic bound on theentropy i ..."
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Cited by 2 (2 self)
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The thinnest coverings of ellipsoids are studied in the Euclidean spaces of an arbitrary dimension. Given any ellipsoid, the main goal is to find itsentropy, which is the logarithm of the minimum number of the balls of radius needed to cover this ellipsoid. A tight asymptotic bound on the
Results 11  20
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8,529