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Unified Framework for the Propagation of ContinuousTime Enclosures for Parametric Nonlinear ODEs
"... Abstract This paper presents a framework for constructing and analyzing enclosures of the reachable set of nonlinear ordinary differential equations (ODEs) using continuoustime setpropagation methods. The focus is on convex enclosures that can be characterized in terms of their support functions. ..."
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Abstract This paper presents a framework for constructing and analyzing enclosures of the reachable set of nonlinear ordinary differential equations (ODEs) using continuoustime setpropagation methods. The focus is on convex enclosures that can be characterized in terms of their support functions
ORBITS OF MOST ACTION ON A CONVEX BILLIARD TABLE
"... ABSTRACT. Of concern are the trajectories of a ball bouncing inside a convex enclosure. The ball is treated as a mass point but the Coriolis force is not neglected. Thus between bounces a trajectory is a circular arc of given radius. At a bounce the angles of incidence and reflection are equal. Comp ..."
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ABSTRACT. Of concern are the trajectories of a ball bouncing inside a convex enclosure. The ball is treated as a mass point but the Coriolis force is not neglected. Thus between bounces a trajectory is a circular arc of given radius. At a bounce the angles of incidence and reflection are equal
Minimum Enclosures with Specified Angles
, 1994
"... Given a convex polygon P , an menvelope is a convex msided polygon that contains P . Given any convex polygon P , and any sequence of m 3 angles A = hff 1 ; ff 2 ; : : : ; ff m i, we consider the problem of computing the minimum area menvelope for P whose counterclockwise sequence of exterior an ..."
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Cited by 2 (0 self)
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Given a convex polygon P , an menvelope is a convex msided polygon that contains P . Given any convex polygon P , and any sequence of m 3 angles A = hff 1 ; ff 2 ; : : : ; ff m i, we consider the problem of computing the minimum area menvelope for P whose counterclockwise sequence of exterior
Enclosure method for the pLaplace equation
, 2014
"... We study the enclosure method for the pCalderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón that involves the pLaplace equation. The method allows one to reconstruct the convex hull of inclusions in the nonlinear model by using exponentially ..."
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Cited by 1 (1 self)
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We study the enclosure method for the pCalderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón that involves the pLaplace equation. The method allows one to reconstruct the convex hull of inclusions in the nonlinear model by using
The Herglotz wave function, the Vekua transform and the enclosure method
 Hiroshima Math. J
"... Abstract. This paper gives applications of the enclosure method introduced by the author to typical inverse obstacle and crack scattering problems in two dimensions. Explicit extraction formulae of the convex hull of unknown polygonal soundhard obstacles and piecewise linear cracks from the far fi ..."
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Cited by 11 (8 self)
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Abstract. This paper gives applications of the enclosure method introduced by the author to typical inverse obstacle and crack scattering problems in two dimensions. Explicit extraction formulae of the convex hull of unknown polygonal soundhard obstacles and piecewise linear cracks from the far
3D Vertical Ray Shooting and 2D Point Enclosure, Range Searching, and Arc Shooting Amidst Convex Fat Objects
 COMPUT. GEOM. THEORY APPL
, 1995
"... We present a new data structure for a set of n convex simplyshaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting  preprocess a set K of n nonintersecting convex simplyshaped flat objects in 3space, ..."
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Cited by 20 (4 self)
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, whose xyprojections are fat, for efficient vertical ray shooting queries, (ii) point enclosure  preprocess a set C of n convex simplyshaped fat objects in the plane, so that the k objects containing a query point p can be reported efficiently, (iii) boundedsize range searching  preprocess a set
Approximation Algorithms for a Triangle Enclosure Problem
"... Given a set S of n points in the plane, we want to find a triangle, with vertices in S, such that the number of points of S enclosed by it is maximum. A solution can be found by considering all () n 3 triples of points in S. We show that, by considering only triangles with at least 1, 2, or 3 vertic ..."
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vertices on the convex hull of S, we obtain various approximation algorithms that run in o(n3) time. 1
Rigorous enclosures of ellipsoids and directed cholesky factorizations
, 2009
"... This paper discusses the rigorous enclosure of an ellipsoid by a rectangular box, its interval hull, providing a convenient preprocessing step for constrained optimization problems. A quadratic inequality constraint with a positive definite Hessian defines an ellipsoid. The Cholesky factorization ca ..."
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Cited by 3 (0 self)
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This paper discusses the rigorous enclosure of an ellipsoid by a rectangular box, its interval hull, providing a convenient preprocessing step for constrained optimization problems. A quadratic inequality constraint with a positive definite Hessian defines an ellipsoid. The Cholesky factorization
Computing Slope Enclosures by Exploiting a Unique Point of Inflection
, 2007
"... Using slope enclosures may provide sharper bounds for the range of a function than using enclosures of the derivative. Hence, slope enclosures may be useful in verifying the assumptions for existence tests or in algorithms for global optimization. Previous papers by Kolev and Ratz show how to comput ..."
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Cited by 3 (2 self)
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to compute slope enclosures for convex and concave functions. In this paper, we generalize these formulas and show how to obtain slope enclosures for a function that has exactly one point of inflection or whose derivative has exactly one point of inflection.
The heat radiation problem: threedimensional analysis for arbitrary enclosure geometries
 Journal of Applied Mathematics
"... This paper gives very significant and uptodate analytical and numerical results to the threedimensional heat radiation problem governed by a boundary integral equation. There are two types of enclosure geometries to be considered: convex and nonconvex geometries. The properties of the integral op ..."
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Cited by 2 (1 self)
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This paper gives very significant and uptodate analytical and numerical results to the threedimensional heat radiation problem governed by a boundary integral equation. There are two types of enclosure geometries to be considered: convex and nonconvex geometries. The properties of the integral
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