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A Problem in Enumerating Extreme Points
, 2002
"... We describe the central problem in developing an efficient algorithm for enumerating the extreme points of a convex polytope specified by linear constraints, and discuss a conjecture for its solution. ..."
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We describe the central problem in developing an efficient algorithm for enumerating the extreme points of a convex polytope specified by linear constraints, and discuss a conjecture for its solution.
Enumerating Extreme Points in Higher Dimensions
, 1995
"... We consider the problem of enumerating all extreme points of a given set P of n points in d dimensions. We present an algorithm with O(n) space and O(nm) time where m is the number of extreme points of P . We also present an algorithm to compute the depth of each point of the given set of n poi ..."
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Cited by 14 (0 self)
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We consider the problem of enumerating all extreme points of a given set P of n points in d dimensions. We present an algorithm with O(n) space and O(nm) time where m is the number of extreme points of P . We also present an algorithm to compute the depth of each point of the given set of n
SECTION 2.1: Extreme Points
, 2010
"... Show by example that the set of extreme points of a nonempty compact set need not be closed. Hint: Consider a line segment C1 = { (x1, x2, x3)  x1 = 0, x2 = 0, −1 ≤ x3 ≤ 1} and a circular disk C2 = { (x1, x2, x3)  (x1 −1) 2 +x 2 2 ≤ 1, x3 = 0} , and verify that the set conv(C1 ∪ C2) is compact ..."
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Show by example that the set of extreme points of a nonempty compact set need not be closed. Hint: Consider a line segment C1 = { (x1, x2, x3)  x1 = 0, x2 = 0, −1 ≤ x3 ≤ 1} and a circular disk C2 = { (x1, x2, x3)  (x1 −1) 2 +x 2 2 ≤ 1, x3 = 0} , and verify that the set conv(C1 ∪ C2
Extreme points in triangular UHF algebras
 3391–3400, MR 1407493 (97m:47058), Zbl 0883.47035
, 1997
"... Abstract. We examine the strongly extreme point structure of the unit balls of triangular UHF algebras. The semisimple triangular UHF algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal. In contrast to this, f ..."
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Cited by 2 (1 self)
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Abstract. We examine the strongly extreme point structure of the unit balls of triangular UHF algebras. The semisimple triangular UHF algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal. In contrast to this
ON THE EXTREME POINTS OF CLASSES OF UNIVALENT FUNCTIONS
"... Let H(D) denote the set of all analytic functions in the unit 6its p:{z€Cl lzl=l). Equipped with the usual topology of locally uniform convergence II(D) is a locally convex topological vector space. A function f(B is called an extreme point of a subset BcH(D) if it cannot be written as a proper conv ..."
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Let H(D) denote the set of all analytic functions in the unit 6its p:{z€Cl lzl=l). Equipped with the usual topology of locally uniform convergence II(D) is a locally convex topological vector space. A function f(B is called an extreme point of a subset BcH(D) if it cannot be written as a proper
EXTREME POINTS RELATED TO MATRIX ALGEBRAS
"... Abstract. Let A denote the set {a ∈ Mn ∣∣a ≥ 0, tr(a) = 1}, St(Mn) the set of all states on Mn, and PS(Mn) the set of all pure states on Mn. We show that there are onetoone correspondences between A and St(Mn), and between the set of all extreme points of A and PS(Mn). We find a necessary and su ..."
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Abstract. Let A denote the set {a ∈ Mn ∣∣a ≥ 0, tr(a) = 1}, St(Mn) the set of all states on Mn, and PS(Mn) the set of all pure states on Mn. We show that there are onetoone correspondences between A and St(Mn), and between the set of all extreme points of A and PS(Mn). We find a necessary
ON CLOSED CONVEX HULLS AND THEIR EXTREME POINTS
"... Abstract. In this paper, the new subclass denoted by Sp(α, β, ξ, γ) of pvalent holomorphic functions has been introduced and investigate the several properties of the class Sp(α, β, ξ, γ). In particular we have obtained integral representation for mappings in the class Sp(α, β, ξ, γ) and determine ..."
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) and determined closed convex hulls and their extreme points of the class Sp(α, β, ξ, γ). 1.
Extremal point methods for Robin capacity
 Comp. Meth. Funct. Th
"... Abstract. The Robin capacity δ(A) of a compact, nonempty set A ⊂ ∂Ω with respect to a domain Ω ⊂ C ̂ containing ∞ is defined by δ(A) = δ(A,Ω) = exp lim z→∞−R(z) + log z where R(z) = R(z,∞) is the fundamental solution of a mixed boundary value problem with pole at ∞, where Dirichlet conditions ..."
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Cited by 1 (0 self)
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. For this purpose the conformal invariant δ(A) / cap(∂Ω) is related to other moduli of the given configuration like harmonic measure or conformal modulus. Then an effective extremal point discretization for these moduli based on Menke points is derived. If Ω is analytically bounded, the discretizations presented
Robust wide baseline stereo from maximally stable extremal regions
 In Proc. BMVC
, 2002
"... The widebaseline stereo problem, i.e. the problem of establishing correspondences between a pair of images taken from different viewpoints is studied. A new set of image elements that are put into correspondence, the so called extremal regions, is introduced. Extremal regions possess highly desir ..."
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Cited by 1016 (35 self)
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The widebaseline stereo problem, i.e. the problem of establishing correspondences between a pair of images taken from different viewpoints is studied. A new set of image elements that are put into correspondence, the so called extremal regions, is introduced. Extremal regions possess highly de
Results 11  20
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9,372