TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

Arbitrage-Free Conditions and Hedging Strategies for Markets with Penalty Costs on Short Positions

We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficient conditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate a contingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedure for obtaining perfect hedging strategies.

Effects of Black Leaf Streak Disease and Sigatoka Disease on fruit quality and maturation process of bananas produced in the subtropical conditions of southern Brazil

Banana fruits are harvested at the green-mature stage (pre-climacteric) in order to allow sufficient time for transport and marketing. The time between the harvest and the initiation of the natural ripening process is called green life (GL), which is closely correlated to physiological age. Sigatoka Disease (SD: also called yellow Sigatoka) and Black Leaf Streak Disease (BLSD; also called black Sigatoka) are the main foliar diseases affecting banana production. The aim of this work was to investigate the influence of these diseases on banana GL and postharvest behavior in subtropical conditions (southeastern Brazil). The results showed that both diseases shortened the banana's GL when compared to control bananas of the same physiological age. Moreover, fruits from infested plots showed higher values of CO2 (+100% for SD and +300% for BLSD) and C2H4 production (+30% for SD and +60% for BLSD) at the climacteric peak. BLSD caused 40% reduction in fruit weight. Fruits from plants with a high degree of SD or BLSD undergo an altered maturation process. (C) 2011 Elsevier Ltd. All rights reserved.