Packing 10 or 11 unit squares in a square.
Packing and covering a unit equilateral triangle with equilateral triangles.
Packing lines, planes, etc.: Packings in Grassmannian spaces.
Packing of 180 equal circles on a sphere.
Packing unit squares in a rectangle.
Packing unit squares in squares: A survey and new results.
Packungen kongruenter Stäbchen mit konstanter Nachbarnzahl.
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
Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator
Let be a family of rational polytopes parametrized by inequations. It is known that the volume of is a locally polynomial function of the parameters. Similarly, the number of integral points in is a locally quasi-polynomial function of the parameters. Paul-Émile Paradan proved a jump formula for this function, when crossing a wall. In this article, we give an algebraic proof of this formula. Furthermore, we give a residue formula for the jump, which enables us to compute it.
Parallel methods in image recovery by projections onto convex sets
Parallel projection of matroid spheres
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.