An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains

We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p–Laplacian operator and subcritical nonlinearities satisfying Ambrosetti–Rabinowitz type conditions. Using Morse theory and a cohomological local splitting as in Degiovanni et al. (Commun Contemp Math 12:475–486, 2010), we prove the existence of a nontrivial weak solution for all (real) values of the eigenvalue parameter. Our result is new even in the semilinear case p = 2 and complements some recent results obtained in Autuori et al. (Adv Anal Equ 18:1–48, 2013).     

A clustering approach for scenario tree reduction: an application to a stochastic programming portfolio optimization problem

This paper deals with the problem of scenario tree reduction for stochastic programming problems. In particular, a reduction method based on cluster analysis is proposed and tested on a portfolio optimization problem. Extensive computational experiments were carried out to evaluate the performance of the proposed approach, both in terms of computational efficiency and efficacy. The analysis of the results shows that the clustering approach exhibits good performance also when compared with other reduction approaches.     

A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.     

Aflatoxin M1 determination in cheese by liquid chromatography-tandem mass spectrometry

A new method for determining aflatoxin M1 (AFM1) in cheese by liquid chromatography-tandem mass spectrometry has been developed. Two methodologies were compared for sample extraction. The first one involves sample extraction with dichloromethane for hard, aged cheese or acetone for fresh cheese and includes a preliminary matrix solid-phase dispersion-extraction step before solid-phase extraction (SPE) clean-up by a Carbograph-4 cartridge. The second method uses a water/methanol solution (90:10, v/v) extraction at 150 degrees C before clean-up. The average recoveries of AFM1 from samples spiked at levels of 0.25-0.45 microg/kg, were 81-92% and the precision (RSD) ranged from 3 to 7% with the first method, whilst the average recoveries were 79-84%, and RSD ranged from 7 to 15% for the second method. Due to different matrix effect, the quantification limits were 0.019-0.025 microg/kg in the first case and 0.048-0.143 microg/kg in the second one, depending on cheese typology.     

Infinite dimensional duality and applications

The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example, we find the Lagrange multiplier associated to a general elastic–plastic torsion problem.     

A sensitive confirmatory method for aflatoxins in maize based on liquid chromatography/electrospray ionization tandem mass spectrometry

A liquid chromatography/electrospray ionization tandem mass spectrometry (LC/ESI-MS/MS) method for measurement of aflatoxins B1, B2, G1, and G2 in maize is described. Aflatoxins (AFs) were extracted from 1 g samples by using tri-portions of acetonitrile/water (80:20, v/v) (10 + 7 + 7 mL), and 2/5 of the extract diluted to 500 mL by water was cleaned up with a 100 mg Carbograph-4 cartridge. After the addition of the internal standard AFM1, the final extract was analyzed by LC/ESI-MS/MS in positive ion mode using multiple reaction monitoring with a triple-quadrupole instrument. A C(18) column thermostatted at 45 degrees C with a mobile phase gradient of acetonitrile/water with 2 mmol/L ammonium formate was used. Although the matrix suppression effect was negligible, quantitation was achieved by an external calibration procedure using matrix-matched standard solutions to improve accuracy. Sample recoveries at four spiking levels ranged from 81 to 101% (relative standard deviation (RSD) 相似文献   

Mukaiyama-Michael vinylogous additions to nitroalkenes under solvent-free conditions

The first Mukaiyama-Michael vinylogous reaction of a dioxinone-derived silyl ether to nitroalkenes is reported. The conjugate addition is performed in absence of any catalyst under solvent-free conditions, proceeding with satisfactory efficiency with variously substituted nitroalkenes.     

Synthesis and Antioxidative Properties of 1,2,3,4-Tetrahydropyridine Derivatives with Different Substituents in 4-Position

Natural products are an excellent source of inspiration for the development of new drugs. Among them, betalains have been extensively studied for their antioxidant properties and potential application as natural food dyes. Herein, we describe the seven-step synthesis of new betalamic acid analogs without carboxy groups in the 2- and 6-position with an overall yield of ~70%. The Folin–Ciocalteu assay was used to determine the antioxidant properties of protected intermediate 21. Additionally, the five-step synthesis of betalamic acid analog 35 with three ester moieties was performed. Using NMR techniques, the stability of the obtained compounds towards oxygen was analyzed.