Discrete Optimization, ISSN 1572-5286, 2019, p. 100539

Let E denote the d-dimensional Euclidean space. The r-ball body generated by a given set in E is the intersection of balls of radius r centered at the points...

Gromov–Klee–Wagon problem | Kneser–Poulsen conjecture | Euclidean space | r-ball body | Uniform contraction | (intrinsic) volume of intersections of congruent balls

Gromov–Klee–Wagon problem | Kneser–Poulsen conjecture | Euclidean space | r-ball body | Uniform contraction | (intrinsic) volume of intersections of congruent balls

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2014, Volume 416, Issue 2, pp. 783 - 799

The ball number function is extended here to platonic bodies and corresponding generalized uniform distributions on platonic spheres are considered. A platonic...

Platonically generalized surface content | Disintegration of Lebesgue measure | Generalized method of indivisibles | Platonically generalized uniform distribution | Intersection percentage function | Platonically generalized radius | DISTRIBUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | CAVALIERI INTEGRATION | PERIMETER

Platonically generalized surface content | Disintegration of Lebesgue measure | Generalized method of indivisibles | Platonically generalized uniform distribution | Intersection percentage function | Platonically generalized radius | DISTRIBUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | CAVALIERI INTEGRATION | PERIMETER

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2018, Volume 327, pp. 260 - 273

A ball B-spline curve (BBSC) is a skeleton based solid model representation, which consists of a B-spline curve and a B-spline function serving as the...

Intersection | Newton’s method | Implicitization | Ball Bézier curve | Ball B-spline curve | Parameterization | Newton's method | MATHEMATICS, APPLIED | Ball Bezier curve | REVOLUTION | SURFACES | Computer science | Information science | Algorithms | Analysis | Visualization (Computers)

Intersection | Newton’s method | Implicitization | Ball Bézier curve | Ball B-spline curve | Parameterization | Newton's method | MATHEMATICS, APPLIED | Ball Bezier curve | REVOLUTION | SURFACES | Computer science | Information science | Algorithms | Analysis | Visualization (Computers)

Journal Article

Studia Scientiarum Mathematicarum Hungarica, ISSN 0081-6906, 2018, Volume 55, Issue 4, pp. 421 - 478

High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle....

Spherical | Convex bodies | Parasphere and hypersphere | Central symmetry of closed convex hulls of unions | Central symmetry of intersections | Closed convex sets with interior points | Characterizations of ball | Euclidean and hyperbolic spaces | Directly congruent copies | directly congruent copies | central symmetry of closed convex hulls of unions | MATHEMATICS | characterizations of ball | convex bodies | spherical | closed convex sets with interior points | central symmetry of intersections | parasphere and hypersphere

Spherical | Convex bodies | Parasphere and hypersphere | Central symmetry of closed convex hulls of unions | Central symmetry of intersections | Closed convex sets with interior points | Characterizations of ball | Euclidean and hyperbolic spaces | Directly congruent copies | directly congruent copies | central symmetry of closed convex hulls of unions | MATHEMATICS | characterizations of ball | convex bodies | spherical | closed convex sets with interior points | central symmetry of intersections | parasphere and hypersphere

Journal Article

Contributions to Discrete Mathematics, ISSN 1715-0868, 2017, Volume 12, Issue 2, pp. 146 - 157

The notions of ball hull and ball intersection of finite sets, important in Banach space theory, are extended from normed planes to generalized normed planes,...

gauge | MATHEMATICS | Davenport-Schinzel sequences | normed space | closed convex curves | ball intersection | SETS | ball hull | ALGORITHMS | (asymmetric) convex distance function | 2-center problem

gauge | MATHEMATICS | Davenport-Schinzel sequences | normed space | closed convex curves | ball intersection | SETS | ball hull | ALGORITHMS | (asymmetric) convex distance function | 2-center problem

Journal Article

Journal of Computational Chemistry, ISSN 0192-8651, 05/2012, Volume 33, Issue 13, pp. 1252 - 1273

Given a set of spherical balls, called atoms, in three‐dimensional space, its mass properties such as the volume and the boundary area of the union of the...

accessible area | offset‐volume | molecular surface | Lee‐Richards (accessible) surface | solvent accessible surface | beta‐shape | offset surface | molecular area | quasi‐triangulation | molecular volume | Voronoi diagram of spheres | offset‐area | beta‐complex | accessible volume | van der Waals area | van der Waals volume | offset-area | Lee-Richards (accessible) surface | offset-volume | beta-shape | quasi-triangulation | beta-complex | ALGORITHM | VORONOI-DIAGRAM | MOLECULAR VOLUMES | ATOMS | PROTEIN VOLUMES | COMPUTATION | SPHERES | CHEMISTRY, MULTIDISCIPLINARY | ACCESSIBLE SURFACE-AREAS | INTERSECTION | PROGRAM

accessible area | offset‐volume | molecular surface | Lee‐Richards (accessible) surface | solvent accessible surface | beta‐shape | offset surface | molecular area | quasi‐triangulation | molecular volume | Voronoi diagram of spheres | offset‐area | beta‐complex | accessible volume | van der Waals area | van der Waals volume | offset-area | Lee-Richards (accessible) surface | offset-volume | beta-shape | quasi-triangulation | beta-complex | ALGORITHM | VORONOI-DIAGRAM | MOLECULAR VOLUMES | ATOMS | PROTEIN VOLUMES | COMPUTATION | SPHERES | CHEMISTRY, MULTIDISCIPLINARY | ACCESSIBLE SURFACE-AREAS | INTERSECTION | PROGRAM

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 382, Issue 2, pp. 523 - 533

In this paper we show that there is no local equatorial characterization of bodies that embed in L p in odd dimensions for all p not even, 0 < p < ∞ . However,...

[formula omitted] embedding | Fourier transform | Convex bodies | Cosine transform | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX-BODIES | FOURIER-TRANSFORM | AFFINE | INTERSECTION BODIES | PROJECTIONS | ZONOIDS | L-p embedding

[formula omitted] embedding | Fourier transform | Convex bodies | Cosine transform | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX-BODIES | FOURIER-TRANSFORM | AFFINE | INTERSECTION BODIES | PROJECTIONS | ZONOIDS | L-p embedding

Journal Article

International Journal of Computational Geometry and Applications, ISSN 0218-1959, 08/2011, Volume 21, Issue 4, pp. 403 - 415

A collection C of balls in R-d is delta-inflantable if it is isometric to the intersection U boolean AND E of some d-dimensional affine subspace E with a...

disjoint unit ball | inflation | Geometric transversal | MATHEMATICS, APPLIED | NUMBER | THEOREM | R-D | LINE TRANSVERSALS | GEOMETRIC PERMUTATIONS | CONVEX-SETS | DISJOINT UNIT BALLS | BOUNDS | R-3 | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | Computational geometry | Algorithms | Collection | Intersections | Subspaces | Inflating | Recognition

disjoint unit ball | inflation | Geometric transversal | MATHEMATICS, APPLIED | NUMBER | THEOREM | R-D | LINE TRANSVERSALS | GEOMETRIC PERMUTATIONS | CONVEX-SETS | DISJOINT UNIT BALLS | BOUNDS | R-3 | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | Computational geometry | Algorithms | Collection | Intersections | Subspaces | Inflating | Recognition

Journal Article

Mechanism and Machine Theory, ISSN 0094-114X, 2011, Volume 46, Issue 1, pp. 67 - 81

The color-changing ball has two stable configurations. Its mechanism is a multiple loop and polygonal mechanism. This paper investigates the mechanism typology...

Singularity | Double-sliders | Mechanism topology | Kinematics | MOBILITY | METAMORPHIC MECHANISMS | DEVICE | ENGINEERING, MECHANICAL | Design engineering | Platforms | Simulation | Singularities | Linkage mechanisms | Topology | Intersections

Singularity | Double-sliders | Mechanism topology | Kinematics | MOBILITY | METAMORPHIC MECHANISMS | DEVICE | ENGINEERING, MECHANICAL | Design engineering | Platforms | Simulation | Singularities | Linkage mechanisms | Topology | Intersections

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 3/2017, Volume 182, Issue 3, pp. 709 - 729

We prove a randomized version of the generalized Urysohn inequality relating mean width to the other intrinsic volumes. To do this, we introduce a stochastic...

Rearrangement inequalities | Generalized Urysohn inequality | 52A40 | Wulff shape | Mean width | Primary 52A22 | Mathematics, general | Mathematics | Convex body | Minkowski symmetrization | Intersections of congruent balls | Steiner symmetrization | MATHEMATICS | RANDOM POLYTOPE

Rearrangement inequalities | Generalized Urysohn inequality | 52A40 | Wulff shape | Mean width | Primary 52A22 | Mathematics, general | Mathematics | Convex body | Minkowski symmetrization | Intersections of congruent balls | Steiner symmetrization | MATHEMATICS | RANDOM POLYTOPE

Journal Article

International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, 2018, Volume 99, Issue 1-4, pp. 461 - 474

Computer Numeric Control (CNC) milling lathes are used for pseudo-symmetric ornamental woodworking. A stereolithography (STL) part model is used for gouge-free...

Three-axis CNC milling lathe | STL sculptured surface machining | Toolpath planning optimisation | Overcutting | Undercutting | SURFACE MODELS | GENERALIZED CUTTER | ENGINEERING, MANUFACTURING | PATH GENERATION | AUTOMATION & CONTROL SYSTEMS | Algorithms | Mechanical engineering | Analysis | Machining | Milling (machining) | Computer simulation | Turning (machining) | Lithography | Triangles | Adaptive algorithms | Tools | Lathes | Intersections | Computer numerical control | Gouging

Three-axis CNC milling lathe | STL sculptured surface machining | Toolpath planning optimisation | Overcutting | Undercutting | SURFACE MODELS | GENERALIZED CUTTER | ENGINEERING, MANUFACTURING | PATH GENERATION | AUTOMATION & CONTROL SYSTEMS | Algorithms | Mechanical engineering | Analysis | Machining | Milling (machining) | Computer simulation | Turning (machining) | Lithography | Triangles | Adaptive algorithms | Tools | Lathes | Intersections | Computer numerical control | Gouging

Journal Article

Advances in Geometry, ISSN 1615-715X, 07/2017, Volume 17, Issue 3, pp. 347 - 354

We introduce successive radii in generalized Minkowski spaces (that is, with respect to gauges) and study some first properties. This is done via formulating...

gauge | 52A21 | containment problem | convex distance function | 52A40 | generalized Minkowski space | Minkowski functional | successive radii | ball intersection | Ball hull | 52A27 | INEQUALITIES | OUTER J-RADII | MATHEMATICS | SETS | DIAMETERS | INNER

gauge | 52A21 | containment problem | convex distance function | 52A40 | generalized Minkowski space | Minkowski functional | successive radii | ball intersection | Ball hull | 52A27 | INEQUALITIES | OUTER J-RADII | MATHEMATICS | SETS | DIAMETERS | INNER

Journal Article

Lithuanian Mathematical Journal, ISSN 0363-1672, 7/2011, Volume 51, Issue 3, pp. 440 - 449

The ball number function was recently defined in [W.-D. Richter, Continuous l n,p -symmetric distributions, Lith. Math. J., 49(1):93–108, 2009] for l n,p...

33B15 | 60D05 | semi-anti-norm | 28A75 | generalized method of indivisibles | thin-layer property | geometric measure representation | 53A35 | 51F99 | Mathematics | Statistics, general | 28A50 | disintegration of Lebesgue measure | ball number asymptotics | generalization of the circle number π | intersection percentage function | Algebra | coarea formula | Beta function | Mathematics, general | anti-norm | non-Euclidean surface content | 60E05 | generalization of the circle number pi | MATHEMATICS

33B15 | 60D05 | semi-anti-norm | 28A75 | generalized method of indivisibles | thin-layer property | geometric measure representation | 53A35 | 51F99 | Mathematics | Statistics, general | 28A50 | disintegration of Lebesgue measure | ball number asymptotics | generalization of the circle number π | intersection percentage function | Algebra | coarea formula | Beta function | Mathematics, general | anti-norm | non-Euclidean surface content | 60E05 | generalization of the circle number pi | MATHEMATICS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 66, Issue 4, pp. 914 - 925

The ball hull mapping β associates with each closed bounded convex set K in a Banach space its ball hull β ( K ) , defined as the intersection of all closed...

Semi-denting point | Intersections of balls | Ball hull mapping | [formula omitted]-convexity | Polyhedral norms | H-convexity | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | ball hull mapping | SETS | polyhedral norms | intersections of balls | semi-denting point

Semi-denting point | Intersections of balls | Ball hull mapping | [formula omitted]-convexity | Polyhedral norms | H-convexity | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | ball hull mapping | SETS | polyhedral norms | intersections of balls | semi-denting point

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2015, Volume 194, Issue 4, pp. 931 - 952

Let $$B\subset \mathbb {R}^N$$ B ⊂ R N , $$N\ge 3$$ N ≥ 3 , be the unit ball. We study the global bifurcation diagram of the solutions of $$\begin{aligned}...

Bifurcation diagram | Intersection number | 35J61 | Singular solution | 35B33 | 35B32 | Mathematics, general | Mathematics | 35J25 | Elliptic Dirichlet problem | Exponential growth | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SUPERCRITICAL GROWTH | GEOMETRY

Bifurcation diagram | Intersection number | 35J61 | Singular solution | 35B33 | 35B32 | Mathematics, general | Mathematics | 35J25 | Elliptic Dirichlet problem | Exponential growth | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SUPERCRITICAL GROWTH | GEOMETRY

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 11/2009, Volume 36, Issue 4, pp. 327 - 362

We provide a variety of classes of functions that can be realized as the mean curvature on the boundary of the standard n dimensional ball, n a parts per...

Morse theory | Intersection number | Morse inequalities | Critical points at infinity | Topological methods | Boundary operator | Morse lemma at infinity | Boundary mean curvature | YAMABE PROBLEM | EXISTENCE | SCALAR-CURVATURE | PERTURBATION RESULT | MATHEMATICS | MANIFOLDS | Studies | Geometry | Mathematics | International

Morse theory | Intersection number | Morse inequalities | Critical points at infinity | Topological methods | Boundary operator | Morse lemma at infinity | Boundary mean curvature | YAMABE PROBLEM | EXISTENCE | SCALAR-CURVATURE | PERTURBATION RESULT | MATHEMATICS | MANIFOLDS | Studies | Geometry | Mathematics | International

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 12/2018, Volume 60, Issue 4, pp. 967 - 980

The Kneser–Poulsen conjecture states that if the centers of a family of N unit balls in $${\mathbb E}^d$$ Ed are contracted, then the volume of the union...

52A20 | Computational Mathematics and Numerical Analysis | Volume of intersections of balls | 52A22 | Kneser–Poulsen conjecture | Alexander’s contraction | Mathematics | Blaschke–Santalo inequality | Combinatorics | Ball-polyhedra | Volume of unions of balls | Blaschke-Santalo inequality | MATHEMATICS | Kneser-Poulsen conjecture | Alexander's contraction | DISKS | VOLUME | COMPUTER SCIENCE, THEORY & METHODS

52A20 | Computational Mathematics and Numerical Analysis | Volume of intersections of balls | 52A22 | Kneser–Poulsen conjecture | Alexander’s contraction | Mathematics | Blaschke–Santalo inequality | Combinatorics | Ball-polyhedra | Volume of unions of balls | Blaschke-Santalo inequality | MATHEMATICS | Kneser-Poulsen conjecture | Alexander's contraction | DISKS | VOLUME | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2011, Volume 226, Issue 3, pp. 2629 - 2642

The intersection body of a ball is again a ball. So, the unit ball B d ⊂ R d is a fixed point of the intersection body operator acting on the space of all...

Intersection body | Radon transform | Convex body | Spherical harmonics | MATHEMATICS | BODIES

Intersection body | Radon transform | Convex body | Spherical harmonics | MATHEMATICS | BODIES

Journal Article

Studia Mathematica, ISSN 0039-3223, 2008, Volume 184, Issue 3, pp. 217 - 231

We extend Kahane-Khinchin type inequalities to the case p > -2. As an application we verify the slicing problem for the unit balls of finite-dimensional spaces...

Embedding in L | Slicing problem | Convex body | Kahane-Khinchin inequality | MATHEMATICS | CONSTANTS | CONVEX-BODIES | SPACES | DUAL MIXED VOLUMES | SLICING PROBLEM | SUBSPACES | INTERSECTION BODIES | BUSEMANN-PETTY PROBLEM

Embedding in L | Slicing problem | Convex body | Kahane-Khinchin inequality | MATHEMATICS | CONSTANTS | CONVEX-BODIES | SPACES | DUAL MIXED VOLUMES | SLICING PROBLEM | SUBSPACES | INTERSECTION BODIES | BUSEMANN-PETTY PROBLEM

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2019, Volume 356, p. 106813

We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches...

Discrete metric space | Intersection of balls | Tripod | Hyperconvex | Hyperbolic | Curvature inequality | MATHEMATICS | EXTENSIONS | Mathematics - Metric Geometry

Discrete metric space | Intersection of balls | Tripod | Hyperconvex | Hyperbolic | Curvature inequality | MATHEMATICS | EXTENSIONS | Mathematics - Metric Geometry

Journal Article

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