Polyenoid systems (or polyenoids) are trees which can be embedded in a hexagonal lattice and represent CnHn+2 polyene hydrocarbons. Complete mathematical solutions in terms of summations and in terms of a generating function are deduced for the numbers of polyenoids when overlapping edges and/or vertices are allowed. Geometrically planar polyenoids (without overlapping vertices) are enumerated ...

We consider the problem of the joint mission planning with a team of heterogeneous physical agents. The type of missions that we consider are composed of a set of spatially distributed tasks that need to be selected and assigned to the agents for dealing with them. A plan consists of a set of directives specifying who does what, where, when, and for how long. The aim is to optimize system-level...

This study considers the problem of determining operation and maintenance schedules for a containership equipped with components during its sailing according to a pre-determined navigation schedule. The operation schedule, which specifies work time of each component, determines the due-date of each maintenance activity, and the maintenance schedule specifies the actual start time of each mainte...

Bone is a common site for cancer metastasis. To create space for their growth, cancer cells stimulate bone resorbing osteoclasts. Cytokine RANKL is a key osteoclast activator, while osteoprotegerin (OPG) is a RANKL decoy receptor and an inhibitor of osteoclastogenesis. Consistently, systemic application of OPG decreases metastatic tumor burden in bone. However, OPG produced locally by cancer ce...

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MP...

A formal de nition of morphological operators in (max,min)algebra is introduced and their relevant properties from an algebraic viewpoint are stated. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them has not yet been undertaken in the morphological literature. It is shown in particular that one of their fundamental prop...

A typical linear water wave problem is a boundary-value problem involving partial differential equations and boundary conditions. Such a problem is usually solved by applying a sequence of mathematical arguments, and it would be helpful if some or all of the successive steps in this sequence could be given a physical interpretation. In the author’s experience this is generally not possible. Ill...

Petroleum Allocation is an important link for the integration of Petroleum Supply Chain at PETROBRAS as it is responsible for refining the strategic supply planning information to be used at the operation levels. In this work we describe how mathematical programming is being used to solve the Petroleum Allocation Problem and we show the effectiveness of a local search method by optimization to ...