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Symmetric spaces and convex cones
"... We recall some notation and basic facts concerning convex cones in Lie algebras. An excellent source of reference is the monograph [5], which tells the story of convex cones and their relation to Lie semigroups. A wedge W in a finite dimensional real vector space is a topologically closed ..."
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We recall some notation and basic facts concerning convex cones in Lie algebras. An excellent source of reference is the monograph [5], which tells the story of convex cones and their relation to Lie semigroups. A wedge W in a finite dimensional real vector space is a topologically closed
On measures of size for convex cones
"... Abstract. By using an axiomatic approach we formalize the concept of size index for closed convex cones in the Euclidean space R n . We review a dozen of size indices disseminated through the literature, commenting on the advantages and disadvantages of each choice. Mathematics Subject Classificati ..."
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Abstract. By using an axiomatic approach we formalize the concept of size index for closed convex cones in the Euclidean space R n . We review a dozen of size indices disseminated through the literature, commenting on the advantages and disadvantages of each choice. Mathematics Subject
Geometric Tomography of Convex Cones
 DISCRETE COMPUT GEOM (2009) 41: 61–76
, 2009
"... The parallel Xray of a convex set K ⊂ Rn in a direction u is the function that associates to each line l, parallel to u, the length of K ∩ l. The problem of finding a set of directions such that the corresponding Xrays distinguish any two convex bodies has been widely studied in geometric tomogr ..."
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tomography. In this paper we are interested in the restriction of this problem to convex cones, and we are motivated by some applications of this case to the covariogram problem. We prove that the determination of a cone by parallel Xrays is equivalent to the determination of its sections from a different
CONVEX CONES IN SCREW SPACES
"... This work examines different screw systems and analyzes the possible subsets spanned by the various choices of a screw basis when the intensities of the wrenches, applied on the screws of the basis, are not allowed to change sign. Such sets arise in cable robotics and grasping. Convex screw spaces ..."
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Cited by 1 (0 self)
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This work examines different screw systems and analyzes the possible subsets spanned by the various choices of a screw basis when the intensities of the wrenches, applied on the screws of the basis, are not allowed to change sign. Such sets arise in cable robotics and grasping. Convex screw spaces
SPHERICAL CAPS IN A CONVEX CONE
"... Abstract. We show that a compact embedded hypersurface with constant ratio of mean curvature functions in a convex cone C ⊂ Rn+1 is part of a hypersphere if it has a point where all the principal curvatures are positive and if it is perpendicular to ∂C. 1. ..."
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Abstract. We show that a compact embedded hypersurface with constant ratio of mean curvature functions in a convex cone C ⊂ Rn+1 is part of a hypersphere if it has a point where all the principal curvatures are positive and if it is perpendicular to ∂C. 1.
Representing Sets of Orientations as Convex Cones
"... AbstractIn a wide range of applications the orientation of a rigid body does not need to be restricted to one given orientation, but can be given as a continuous set of frames. We address the problem of defining such sets and to find simple tests to verify if an orientation lies within a given set ..."
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set. The unit quaternion is used to represent the orientation of the rigid body and we develop three different sets of orientations that can easily be described by simple constraints in quaternion space. The three sets discussed can also be described as convex cones in R 3 defined by different norms
Multispectral and hyperspectral image analysis with convex cones
 IEEE Trans. Geosci. Remote Sens
, 1999
"... Abstract—A new approach to multispectral and hyperspectral image analysis is presented. This method, called convex cone analysis (CCA), is based on the fact that some physical quantities such as radiance are nonnegative. The vectors formed by discrete radiance spectra are linear combinations of non ..."
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Cited by 43 (0 self)
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Abstract—A new approach to multispectral and hyperspectral image analysis is presented. This method, called convex cone analysis (CCA), is based on the fact that some physical quantities such as radiance are nonnegative. The vectors formed by discrete radiance spectra are linear combinations
On Homogeneous Convex Cones, Carathéodory Number, And Duality Mapping
 Mathematics of Operations Research
, 1999
"... Using three simple examples, we answer three questions related to homogeneous convex cones, the Carath'eodory number of convex cones and selfconcordant barriers for convex cones. First, we show that if the convex cone is not homogeneous then the duality mapping does not have to be an involutio ..."
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Cited by 4 (3 self)
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Using three simple examples, we answer three questions related to homogeneous convex cones, the Carath'eodory number of convex cones and selfconcordant barriers for convex cones. First, we show that if the convex cone is not homogeneous then the duality mapping does not have
Results 1  10
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1,203