We consider a polyhedron intersected by a two-term disjunction, and we characterize the polyhedron resulting from taking its closed convex hull. This generalizes an earlier result of Conforti, Wolsey and Zambelli on split disjunctions. We also recover as a special case the valid inequalities derived by Judice, Sherali, Ribeiro and Faustino for linear complementarity problems.

In this note we calculate the number of crepant valuations of an isolated canonical singularity 0 ∈ X : (f = 0) ⊂ Cn, which is assumed to be nondegenerate with respect to its Newton polyhedron, in terms of weightings and the Newton polyhedron of f .

The solution of the Chinese postman problem using matching theory is given. The convex hull of integer solutions is described as a linear programming polyhedron. This polyhedron is used to show that a good algorithm gives an optimum solution. The algorithm is a specialization of the more general b-matching blossom algorithm. Algorithms for finding Euler tours and related problems are also discu...

We prove that it is strongly NP-complete to decide whether a given orthogonal polyhedron has a (nonoverlapping) edge unfolding. The result holds even when the polyhedron is topologically convex, i.e., is homeomorphic to a sphere, has faces that are homeomorphic to disks, and where every two faces share at most one edge.

In (1) x is an m + n vector, b is an integer m-vector, c an m + n vector, and A an m X (m + n) integer matrix containing an m X m identity matrix. A is assumed to be rearranged and partitioned into an m X m optimal basis matrix B for the noninteger problem and a collection of nonbasic columns forming the matrix N with A = (B,N). An alternative form of (1) that is useful here for geometric inter...

this article is devoted to kamāl al-dīn al-fārsī’s (d. 1319) additions to some remarks contained in book xiii of al-ṭūsī’s taḥrīr uṣūl al-handasa, concerning the construction of a semi-regular polyhedron inscribed into a sphere using the movement as a way for the construction. this treatise is one treatise among ten found in a codex preserved at the bibliothèque nationale de tunis.