A Dissection of Rhombic Triacontahedron
A Dissection of Two Rhombic Dodecahedra of the Second Kind to a Cube
A dual proof of the upper bound conjecture for convex polytopes.
A dyadic view of rational convex sets
Let be a subfield of the field of real numbers. Equipped with the binary arithmetic mean operation, each convex subset of becomes a commutative binary mode, also called idempotent commutative medial (or entropic) groupoid. Let and be convex subsets of . Assume that they are of the same dimension and at least one of them is bounded, or is the field of all rational numbers. We prove that the corresponding idempotent commutative medial groupoids are isomorphic iff the affine space ...
A finite calculus approach to Ehrhart polynomials.
A fixed point theorem in a Hausdorff topological vector space
In this paper, we will give a new fixed point theorem for lower semicontinuous multimaps in a Hausdorff topological vector space.
A further generalization of Ky Fan's maximal inequality and its applications
A Gallai-Type Transversal Problem in the Plane.
A general approach to dual characterizations of solvability of inequality systems with applications.
A General Approach to the Notion of Silov Boundary.
A general geometric construction for affine surface area
Let K be a convex body in and B be the Euclidean unit ball in . We show that , where as(K) respectively as(B) is the affine surface area of K respectively B and , are general families of convex bodies constructed from K,B satisfying certain conditions. As a corollary we get results obtained in [M-W], [Schm], [S-W] and [W].
A general notion of extreme subset
A general theory of polyhedral sets and the corresponding T-complexes [Book]
A generalization of branch weight centroids
A Generalization of Dehn-Sommerville Relations to Simple Stratified Spaces.
A Generalization of Hadwiger's Transversal Theorem to Intersecting Sets.
A generalization of the Cauchy-Schwarz inequality.
A generalization of the Erdös-Szekeres convex n-gon theorem.
A geometric approach to correlation inequalities in the plane
By elementary geometric arguments, correlation inequalities for radially symmetric probability measures are proved in the plane. Precisely, it is shown that the correlation ratio for pairs of width-decreasing sets is minimized within the class of infinite strips. Since open convex sets which are symmetric with respect to the origin turn out to be width-decreasing sets, Pitt’s Gaussian correlation inequality (the two-dimensional case of the long-standing Gaussian correlation conjecture) is derived...
A Geometric Inequality and the Complexity of Computing Volume.