Packing and covering a unit equilateral triangle with equilateral triangles.
Packing of 180 equal circles on a sphere.
Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment
Let be a Minkowski space with a unit ball and let be the Hausdorff metric induced by in the hyperspace of convex bodies (nonempty, compact, convex subsets of ℝ). R. Schneider [RSP] characterized pairs of elements of which can be joined by unique metric segments with respect to for the Euclidean unit ball Bⁿ. We extend Schneider’s theorem to the hyperspace over any two-dimensional Minkowski space.
Pairs of sets with convex union.
In this paper the notion of convex pairs of convex bounded subsets of a Hausdorff topological vector space is introduced. Criteria of convexity pair are proved.
Paraconvex analysis
Parallel methods in image recovery by projections onto convex sets
Parallel synchronous algorithm for nonlinear fixed point problems.
Parallelbeleuchtung konvexer Körper mit glatten Rändern
Parallelepipeds circumscribed about a convex body in 3-space.
Parallelograms inscribed in a curve having a circle as π/2-isoptic
Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.
Partial inflation of closed polygons in the plane.
Partitioning Arrangements of Lines, II: Applications.
Partitioning Euclidean Space.
p-convex functions in linear spaces
Penny-Packing and Two-Dimensional Codes.
Permanence of moment estimates for p-products of convex bodies
It is shown that two inequalities concerning second and fourth moments of isotropic normalized convex bodies in ℝⁿ are permanent under forming p-products. These inequalities are connected with a concentration of mass property as well as with a central limit property. An essential tool are certain monotonicity properties of the Γ-function.
Perturbations and approximations of support functions of convex bodies.
Piecewise Convex Curves and their Integral Representation
2000 Mathematics Subject Classification: 52A10.A convex arc in the plane is introduced as an oriented arc G satisfying the following condition: For any three of its points c1 < c2 < c3 the triangle c1c2c3 is counter-clockwise oriented. It is proved that each such arc G is a closed and connected subset of the boundary of the set FG being the convex hull of G. It is shown that the convex arcs are rectifyable and admit a representation in the natural parameter by the Riemann-Stieltjes integral...
Piecewise polynomial functions, convex polytopes and enumerative geometry
Planar anisotropy revisited
The paper concerns estimation of anisotropy of planar fibre systems using the relation between the rose of directions and the rose of intersections. The discussion about the properties of the Steiner compact estimator is based on both theoretical and simulation results. The approach based on the distribution of the Prokhorov distance between the estimated and true rose of directions is developed. Finally the curved test systems are investigated in both Fourier and Steiner compact analysis of anisotropy....