A fast numerical procedure is presented for computing growth distances between a pair of polytopes in three dimensional space that move incrementally along specified smooth paths. The procedure carrys out the growth distance evaluations efficiently by predicting and verifying contact configurations between a pair of grown polytopes. In the prediction and verification the procedure uses vertex a...

evaluation of any irrigation system consists of analyzing the measurable performance of the system in real conditions as well as during the normal operation of the farm. irrigation evaluation is a management tool that allows the system manager to make the best use of what is available. unfortunately, in most regions of iran, after the implementation of irrigation systems their performance is no...

This article considers the question of how to succinctly approximate a multidimensional convex body by polytope. Given K unit diameter in Euclidean d -dimensional space (where is constant) and an error parameter ε > 0, objective determine polytope low combinatorial complexity whose Hausdorff distance from at most ε. By , we mean total number faces all dimensions. Classical constructions Dudl...

We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not always specialize to convex polytopes; however, in a number of cases where we can realize it, it produces interesting classes of polytopes. Thus we produce ...

We show that the problem of deciding membership in the moment polytope associated with a finite-dimensional unitary representation of a compact, connected Lie group is in NP ∩ coNP. This is the first non-trivial result on the computational complexity of this problem, which naively amounts to a quadratically-constrained program. Our result applies in particular to the Kronecker polytopes, and th...

The Singular Value Decomposition (SVD) is a longstanding standard for data approximation because it is optimal in the 2 and Frobenius norms. The SVD, nevertheless, suffers from many setbacks, including computational cost, loss of sparsity in the decomposition, and the inability to be updated easily when new information arrives. Additionally, the SVD provides limited information on data features...

In this paper, a combinational optimization algorithm is introduced to obtain the best size and location of Static Compensator (STATCOM) in power systems. Its main contribution is considering contingency analysis where lines outages may lead to infeasible solutions especially at peak loads and it commonly can be vanished by load-shedding. The objective of the proposed algorithm is firstly to pr...