In this short communication, we observe that the Graphical Traveling Salesman Polyhedron is the intersection of the positive orthant with the Minkowski sum of the Symmetric Traveling Salesman Polytope and the polar of the metric cone. This follows trivially from known facts. There are two reasons why we find this observation worth communicating none-the-less: It is very surprising; it helps to ...

In this paper we consider the problem of computing control invariant sets for linear controlled systems with constraints on the input and on the states. We focus in particular on the complexity of the computation of the N-step operator, given by the Minkowski addition of sets, that is the basis of many of the iterative procedures for obtaining control invariant sets. Set inclusions conditions f...

Tropical geometry is used to develop a new approach to the theory of discriminants and resultants in the sense of Gel'fand, Kapranov and Zelevinsky. The tropical A-discriminant, which is the tropicalization of the dual variety of the projective toric variety given by an integer matrix A, is shown to coincide with the Minkowski sum of the row space of A and the tropicalization of the kernel of A...

Virtualization technology has been widely applied across a broad range of contemporary datacenters. While constructing a datacenter, architects have to choose a Virtualization Application Solution (VAS) to maximize performance as well as minimize cost. However, the performance of a VAS involves a great number of metric concerns, such as virtualization overhead, isolation, manageability, consoli...

The nofit polygon an important tool in the area of irregular shape stock cutting problems. It provides efficient handling of the geometric characteristics of the problem. The paper presents a new algorithmic procedure for deriving this tool. Abstract The nofit polygon is a powerful and effective tool for handling the geometric requirements of solution approaches to irregular cutting and packing...

Prompted by the development of algorithms for analysing geometric tolerancing, this article describes a method to determine the Minkowski sum for 3-dimension polytopes. This purposed method is based exclusively on intersection operations on normal cones, using the properties of the normal fan of a Minkowski sum obtained by common refinement of the normal fans of the operands. It can be used to ...

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in t...

In this paper we review the existing linear and quadratic complexity (upper) bounds on the values of the positive roots of polynomials and their impact on the performance of the Vincent-Akritas-Strzeboński (VAS) continued fractions method for the isolation of real roots of polynomials. We first present the following four linear complexity bounds (two “old” and two “new” ones, respectively): Cau...

Grasping and fixturing are concerned with immobilizing objects. Most prior work in this area uses a small number of contacts that is sufficient for force closure. However, for delicate objects or surfaces such as glass or bone (in medical applications), a larger number of contacts can be used to reduce the forces needed at each contact to resist applied wrenches. We focus on the problem of choo...

Appendectomy is the most common surgery in the world. Pain, bloat and nausea are the most side effects after appendectomy that leads to high morbidity and dissatisfaction in these patients. Herbal therapy is one the treatment .This study conducted aimed to investigate the effect of super mint on pain, nausea and bloat of patients undergoing of appendectomy. This study was a double-blind clinica...