Proper Efficiency in Vector Optimization on Real Linear Spaces

In this paper, we use an algebraic type of closure, which is called vector closure, and through it we introduce some adaptations to the proper efficiency in the sense of Hurwicz, Benson, and Borwein in real linear spaces without any particular topology. Scalarization, multiplier rules, and saddle-point theorems are obtained in order to characterize the proper efficiency in vector optimization with and without constraints. The usual convexlikeness concepts used in such theorems are weakened through the vector closure.     

Determination of rotenone residues in raw honey by solid-phase extraction and high-performance liquid chromatography

A method for determining residues of the insecticide rotenone in raw-honey by high-performance liquid chromatography (HPLC) is described. To extract the residues, organic solvents such as ethyl acetate, n-hexane/dichloromethane and solid-phase extraction with octadecylsilane cartridges or Florisil packed columns were tested. Determination was carried out by reversed-phase HPLC using acetonitrile-buffer phosphate (pH 7) (60:40, v/v) as mobile phase and detection at 210 nm. Although the data showed that the two extraction methods were able to isolate the pesticide residues, the extraction on octadecylsilane cartridges was preferred due to its simplicity and higher recovery. Recoveries depended strongly on the fortification level for the two extraction procedures. Practical determination limits of 0.015 mg/kg were obtained. In the analysis of honeys, from beehives treated with rotenone at therapeutical doses for 1 month, residual amounts below 0.2 mg/kg were found.     

Inhibition of Bacterial Adhesion and Biofilm Formation by Seed-Derived Ethanol Extracts from Persea americana Mill

The increase in antibiotic resistance demands innovative strategies to combat microorganisms. The current study evaluated the antibacterial and antivirulence effects of ethanol extracts from Persea americana seeds obtained by the Soxhlet (SE) and maceration (MaE) methods. The UHPLC-DAD-QTOF analysis showed mainly the presence of polyphenols and neolignan. Ethanol extracts were not cytotoxic to mammalian cells (CC₅₀ > 500 µg/mL) and displayed a moderate antibacterial activity against Pseudomonas aeruginosa (IC₅₀ = 87 and 187 µg/mL) and Staphylococcus aureus (IC₅₀ = 144 and 159 µg/mL). Interestingly, no antibacterial activity was found against Escherichia coli. SE and MaE extracts were also able to significantly reduce the bacterial adhesion to A549 lung epithelial cells. Additionally, both extracts inhibited the biofilm growth at 24 h and facilitated the release of internal cell components in P. aeruginosa, which might be associated with cell membrane destabilization. Real-time PCR and agarose electrophoresis gel analysis indicated that avocado seed ethanol extracts (64 µg/mL) downregulated virulence-related factors such as mexT and lasA genes. Our results support the potential of bioproducts from P. americana seeds as anti-adhesive and anti-biofilm agents.     

Attractor minimal sets for cooperative and strongly convex delay differential systems

We study the skew-product semiflow induced by a family of convex and cooperative delay differential systems. Under some monotonicity assumptions, we obtain an ergodic representation for the upper Lyapunov exponent of a minimal subset. In addition, when eventually strong convexity at one point is assumed and there exist two completely strongly ordered minimal subsets K₁?_CK₂, we show that K₁ is an attractor subset which is a copy of the base. The long-time behaviour of every trajectory strongly ordered with K₂ is then deduced. Some examples of application of the theory are shown.     

Stability and extensibility results for abstract skew-product semiflows

In this paper we present new stability and extensibility results for skew-product semiflows with a minimal base flow. In particular, we describe the structure of uniformly stable and uniformly asymptotically stable sets admitting backwards orbits and the structure of omega-limit sets. As an application, the occurrence of almost periodic and almost automorphic dynamics for monotone non-autonomous infinite delay functional differential equations is analyzed.     

On Approximate Solutions in Vector Optimization Problems Via Scalarization

This work deals with approximate solutions in vector optimization problems. These solutions frequently appear when an iterative algorithm is used to solve a vector optimization problem. We consider a concept of approximate efficiency introduced by Kutateladze and widely used in the literature to study this kind of solutions. Necessary and sufficient conditions for Kutateladze’s approximate solutions are given through scalarization, in such a way that these points are approximate solutions for a scalar optimization problem. Necessary conditions are obtained by using gauge functionals while monotone functionals are considered to attain sufficient conditions. Two properties are then introduced to describe the idea of parametric representation of the approximate efficient set. Finally, through scalarization, characterizations and parametric representations for the set of approximate solutions in convex and nonconvex vector optimization problems are proved and the obtained results are applied to Pareto problems. AMS Classification:90C29, 49M37 This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194.     

Some remarks on an ODE-solver of Kirchgraber

Summary Kirchgraber derived in 1988 an integration procedure (called the LIPS-code) for long-term prediction of the solutions of equations which are perturbations of systems having only periodic solutions. His basic idea is to use the Poincaré map to define a new system which can be integrated with large step-size; the method is specially successful when the period is close to the unperturbed one. Obviously the size of the perturbation modifies the period and therefore affects the precision of the algorithm. In this paper we propose a double modification of Kirchgraber's code: to use a first-order approximation of the perturbed period instead of the unperturbed one, and a scheme specially designed for integration of orbits instead of the Runge-Kutta method. We show that this new code permits a spectacular improvement in accuracy and computation time.