Robust linear semi-infinite programming duality under uncertainty

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then establish that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and sufficient for robust duality. In other words, the robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with affinely parameterized data uncertainty, we establish that robust duality is easily satisfied under a Slater type constraint qualification. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-infinite linear inequalities.

Effect of commercial amino acids on iron nutrition of tomato plants grown under lime-induced iron deficiency

The objective of this work was to study the effect of root and foliar application of two commercial products containing amino acids from plant and animal origin on iron (Fe) nutrition of tomato seedlings cultivated in two nutrient media: lime and normal nutrient solutions. In the foliar-application experiment, each product was sprayed with 0.5 and 0.7 mL L–1 2, 7, 12, and 17 d after transplanting. In the root application experiment, 0.1 and 0.2 mL L–1 of amino acids products were added to the nutrient solutions. In both experiments, untreated control plants were included as well. Foliar and root application of the product containing amino acids from animal origin caused severe plant-growth depression and nonpositive effects on Fe nutrition were found. In contrast, the application of the product from plant origin stimulated plant growth. Furthermore, significantly enhanced root and leaf FeIII-chelate reductase activity, chlorophyll concentration, leaf Fe concentration, and FeII : Fe ratio were found in tomato seedlings treated with the product from plant origin, especially when the amino acids were directly applied to the roots. These effects were more evident in plants developed under lime-induced Fe deficiency. The positive results on Fe uptake may be related to the action of glutamic acid, the most abundant amino acid in the formulation of the product from plant origin.

Oleic acid modulates mRNA expression of liver X receptor (LXR) and its target genes ABCA1 and SREBP1c in human neutrophils

Purpose: Regulation of liver X receptors (LXRs) is essential for cholesterol homeostasis and inflammation. The present study was conducted to determine whether oleic acid (OA) could regulate mRNA expression of LXRα and LXRα-regulated genes and to assess the potential promotion of oxidative stress by OA in neutrophils. Methods: Human neutrophils were treated with OA at different doses and LXR target gene expression, oxidative stress production, lipid efflux and inflammation state were analyzed. Results: We describe that mRNA synthesis of both LXRα and ABCA1 (a reverse cholesterol transporter) was induced by OA in human neutrophils. This fatty acid enhanced the effects of LXR ligands on ABCA1 and LXR expression, but it decreased the mRNA levels of sterol regulatory element-binding protein 1c (a transcription factor that regulates the synthesis of triglycerides). Although OA elicited a slight oxidative stress in the short term (15–30 min) in neutrophils, it is unlikely that this is relevant for the modulation of transcription in our experimental conditions, which involve longer incubation time (i.e., 6 h). Of physiological importance is our finding that OA depresses intracellular lipid levels and that markers of inflammation, such as ERK1/2 and p38 mitogen-activated protein kinase phosphorylation, were decreased by OA treatment. In addition, 200 μM OA reduced the migration of human neutrophils, another marker of the inflammatory state. However, OA did not affect lipid peroxidation induced by pro-oxidant agents. Conclusions: This work presents for the first time evidence that human neutrophils are highly sensitive to OA and provides novel data in support of a protective role of this monounsaturated acid against the activation of neutrophils during inflammation.