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Two Conjectures on Convex Curves
, 2002
"... In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of . Namely, we show i) that the tangent developable of any convex curve in has degree 4 and ii) construct an example of 4 tange ..."
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Cited by 4 (0 self)
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In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of . Namely, we show i) that the tangent developable of any convex curve in has degree 4 and ii) construct an example of 4
Asymptotic approximation of convex curves
 Arch. Math
, 1994
"... Abstract. L. Fejes Tóth gave asymptotic formulae as n → ∞ for the distance between a smooth convex disc and its best approximating inscribed or circumscribed polygons with at most n vertices, where the distance is in the sense of the symmetric difference metric. In this paper these formulae are ext ..."
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Cited by 13 (3 self)
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Abstract. L. Fejes Tóth gave asymptotic formulae as n → ∞ for the distance between a smooth convex disc and its best approximating inscribed or circumscribed polygons with at most n vertices, where the distance is in the sense of the symmetric difference metric. In this paper these formulae
Discriminants of convex curves are homeomorphic
 PROC. OF THE AMS 126
, 1998
"... For a given real generic curve γ: S1 → Pn let Dγ denote the ruled hypersurface in Pn consisting of all osculating subspaces to γ of codimension 2. In this short note we show that for any two convex real projective curves γ1: S1 → Pn and γ2: S1 → Pn the pairs (Pn, Dγ1) and (Pn, Dγ2) are homeomorphic ..."
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Cited by 1 (0 self)
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For a given real generic curve γ: S1 → Pn let Dγ denote the ruled hypersurface in Pn consisting of all osculating subspaces to γ of codimension 2. In this short note we show that for any two convex real projective curves γ1: S1 → Pn and γ2: S1 → Pn the pairs (Pn, Dγ1) and (Pn, Dγ2
On An Evolution Problem For Convex Curves
"... In this paper, we will investigate a new curvature flow for closed convex plane curves which shortens the length of the evolving curve but expands the area it bounds and makes the curve more and more circular during the evolution process, and the final shape of the evolving curve will be a circle (a ..."
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In this paper, we will investigate a new curvature flow for closed convex plane curves which shortens the length of the evolving curve but expands the area it bounds and makes the curve more and more circular during the evolution process, and the final shape of the evolving curve will be a circle
A Method For Convex Curve Approximation
 European Journal of Operational Research
, 1997
"... . In this paper, a new sandwich method is introduced to approximate a convex curve in IR 2 . This method requires only function evaluation and the solution of a finite number of scalar optimization problems. A quadratic convergence property of the method is established, that is, the total number o ..."
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Cited by 8 (0 self)
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. In this paper, a new sandwich method is introduced to approximate a convex curve in IR 2 . This method requires only function evaluation and the solution of a finite number of scalar optimization problems. A quadratic convergence property of the method is established, that is, the total number
On two conjectures concerning convex curves
 Internat. J. Math. vol
"... Abstract. In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP 3. Namely, we show that i) the tangent developable of any convex curve in RP 3 has degree 4 and ii) construct ..."
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Cited by 9 (0 self)
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Abstract. In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP 3. Namely, we show that i) the tangent developable of any convex curve in RP 3 has degree 4 and ii
ON YOUNG HULLS OF CONVEX CURVE IN R 2n
, 1996
"... Abstract. For a convex curve in an evendimensional affine space we introduce a series of convex domains (called Young hulls) describe their structure and give a formulas fo the volume of the biggest of these domains. ..."
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Abstract. For a convex curve in an evendimensional affine space we introduce a series of convex domains (called Young hulls) describe their structure and give a formulas fo the volume of the biggest of these domains.
Convex curves moving translationally in the plane
 J. Differential Equations
"... We show that a nontrivial homothetic selfsimilar solution can happen only when F (k) = k α or F (k) = −k −α. We also derive a parametric representation of a translational selfsimilar solution. A translational selfsimilar solution may have selfintersections but can not be a simple closed curve f ..."
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Cited by 5 (1 self)
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We show that a nontrivial homothetic selfsimilar solution can happen only when F (k) = k α or F (k) = −k −α. We also derive a parametric representation of a translational selfsimilar solution. A translational selfsimilar solution may have selfintersections but can not be a simple closed curve
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Results 1  10
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160,905