Transmission line failure in power systems prop-agate non-locally, making the control of resulting outages extremely difficult. In Part II this paper, we continue study localizability transmission networks and characterize impact cut set outages. We establish a Simple Path Criterion, showing that propagation pattern due to bridge outages, special case failures, are fully determined by positions...

Providing a fresh and cool airflow in underground mines is one of the main concerns during mining. Destruction of support systems, the presence of undesirable objects in the airway and distortion of airflow are the parameters involved that would result in pressure loss, which would affect the ventilation network. There are a lot of research works about the ventilation network planning that cons...

This paper presents an algorithm to obtain lower bounds for the Split Delivery Vehicle Routing Problem. An extended formulation over a large set of variables is provided and valid inequalities are identified. The algorithm combines column and cut generation and was able to improve the lower bound for almost all instances tested.

Let G = (V, E) be a graph with positive edge weights and let V’ c V. The min VI-cut prohlenl is to find a minimum weight set E’ E E such that no two nodes of V’ occur in the same component of G’ = (V, E\E’). Our main results are two new structural theorems for optimal solutions to the min V-cut problem when G is planar. The first theorem establishes for the first time a close connection between...

Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has at most n times a polylogarithmic number of edges, where the exponent of the logarithmic factor depends on k. In the case where C consists of convex sets, we improve this bound to O(n log n). If in addition k = 2, the ...

Abstract. A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we introduce the concepts of neutrosophic rough Sets and investigate some of its properties. Further as the charact...

We propose a branch and cut algorithm for the Pallet Loading Problem. The 0-1 formulation proposed by Beasley for cutting problems is adapted to the problem, adding new constraints and new procedures for variable reduction. We then take advantage of the relationship between this problem and the maximum independent set problem to use the partial linear description of its associated polyhedron. F...

Fuzzy relations on the same domain are classified according to the equality of families of cut sets. This equality of fuzzy relations is completely characterized, not only for unit interval valued fuzzy relations, but more generally, for fuzzy relations whose domain is a (complete) lattice. Similar results for fuzzy sets in general are considered in [12]. Applications of the results for fuzzy c...