In many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. This paper defines a new inverse problem, called “inverse feasible problem”. For a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

in many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. this paper defines a new inverse problem, called “inverse feasible problem”. for a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

The complex of Ce(III), [ Ce (PHENSC) (H 0) ] (C10 ) , was synthesized using the PHENSC, a hexadentate ligand,2,9-diformyl-1,lO- Phenanthroline bis (semicarbazone), and characterized by X-ray diffraction. The cerium atom has an unusual coordination number of ten involving six donor atoms of the planar ligand in the equatorial plane and four oxygen atoms from four axial water molecules. The...

An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cu...

A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. One can represent the boundary of a ballpolyhedron as the union of vertices, edges, and faces defined in a rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a standard ba...

Alexandrov’s Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of some convex polyhedron. Recent work by Bobenko and Izmestiev describes a differential equation whose solution is the polyhedron corresponding to a given metric. We describe an algorithm based on this differential equation to compute the pol...

How much of the combinatorial structure of a pointed polyhedron is contained in its vertex-facet incidences? Not too much, in general, as we demonstrate by examples. However, one can tell from the incidence data whether the polyhedron is bounded. In the case of a polyhedron that is simple and “simplicial,” i.e., a d-dimensional polyhedron that has d facets through each vertex and d vertices on ...

Methods are given for unifyin:: and extending previous work on detecting intersections of suitably preprocessed polyhedra. New upper bounds of O(log n) and O\log* IZ I are given on plane-polyhedron and polyhedron-polyhedron intersection problems.