Ohlin-Type Theorem for Convex Set-Valued Maps
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DOI: 10.1007/s00025-020-01292-3
Abstract: A counterpart of the Ohlin theorem for convex set-valued maps is proved. An application of this result to obtain some inclusions related to convex set-valued maps in an alternative unified way is presented. In particular… read more here.
Keywords: valued maps; set valued; theorem convex; convex set ... See more keywords
The convex set containing two-qutrit maximally entangled states
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DOI: 10.1007/s11128-018-2159-4
Abstract: We construct the convex set $$\mathcal{M}$$M of two-qutrit states, and the subset $$\mathcal{P}\subset \mathcal{M}$$P⊂M. We characterize the extremal points of rank one and rank two of $$\mathcal{M}$$M. We further show that the extremal points of… read more here.
Keywords: conjecture; set containing; convex set; two qutrit ... See more keywords
The semi-E cone convex set-valued map and its applications
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DOI: 10.1007/s11590-017-1169-y
Abstract: In this paper, firstly, a new notion of the semi-E cone convex set-valued map is introduced in locally convex spaces. Secondly, without any convexity assumption, we investigate the existence conditions of the weakly efficient element… read more here.
Keywords: convex set; set valued; valued map; semi cone ... See more keywords
Finding a maximal element of a non-negative convex set through its characteristic cone: an application to finding a strictly complementary solution
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DOI: 10.1007/s40314-016-0324-x
Abstract: In order to express a polyhedron as the Minkowski sum of a polytope and a polyhedral cone, Motzkin (Beiträge zur Theorie der linearen Ungleichungen. Dissertation, University of Basel, 1936) devised a homogenization technique that translates… read more here.
Keywords: maximal element; convex set; convex; non negative ... See more keywords
Non-probabilistic polygonal convex set model for structural uncertainty quantification
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DOI: 10.1016/j.apm.2020.07.025
Abstract: Abstract In this paper, a general polygonal convex set model and clustering polygonal convex set model are proposed for more reasonably quantifying non-probabilistic uncertainties. Firstly, through the principal component analysis of uncertain samples, a new… read more here.
Keywords: non probabilistic; set model; polygonal convex; convex set ... See more keywords
ON THE INTEGRAL FORMULAS OF CROFTON AND HURWITZ RELATIVE TO THE VISUAL ANGLE OF A CONVEX SET
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DOI: 10.1112/s0025579319000202
Abstract: We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that… read more here.
Keywords: visual angle; integral formulas; crofton hurwitz; convex set ... See more keywords