Comparing stage-scenario with nodal formulation for multistage stochastic problems

To solve real life problems under uncertainty in Economics, Finance, Energy, Transportation and Logistics, the use of stochastic optimization is widely accepted and appreciated. However, the nature of stochastic programming leads to a conflict between adaptability to reality and tractability. To formulate a multistage stochastic model, two types of formulations are typically adopted: the so-called stage-scenario formulation named also formulation with explicit non-anticipativity constraints and the so-called nodal formulation named also formulation with implicit non-anticipativity constraints. Both of them have advantages and disadvantages. This work aims at helping the scholars and practitioners to understand the two types of notation and, in particular, to reformulate with the nodal formulation a model that was originally defined with the stage-scenario formulation presenting this implementation in the algebraic language GAMS. In addition, this work presents an empirical analysis applying the two formulations both without any further decomposition to perform a fair comparison. In this way, we show that the difficulties to implement the model with the nodal formulation are somehow reworded making the problem tractable without any decomposition algorithm. Still, we remark that in some other applications the stage-scenario formulation could be more helpful to understand the structure of the problem since it allows to relax the non-anticipativity constraints.

     

Skin permeation of cacalol, cacalone and 6-epi-cacalone sesquiterpenes from a nanoemulsion

The objective of the present study was to investigate the transdermal permeation of cacalol (1) and a mixture of cacalone (2) and 6-epi-cacalone (3) in comparison with diclofenac acid (4) delivered from the same characterized nanoemulsion using Franz diffusion cells (formulae I, II and III). Results show that de Kp, J, Q24, PI and P2 were higher for the acid diclofenac nanoemulsion than for the natural products nanoemulsions. As for the differences between the formulations I and II, with the natural products, Q24, the quantity extracted from skin and P2 were higher in the mixture of 2 and 3 nanoemulsion compared with the corresponding nanoemulsion of 1. In conclusion, the low permeability of the natural products nanoemulsions in comparison with that of diclofenac acid has the potential for development for drugs with local and systemic applications, respectively.     

Cycloisomerization of dienes and enynes catalysed by a modified ruthenium carbene species

Cycloisomerization is a totally atom economic procedure which converts dienes and enynes into cyclic molecules. Modification of Grubbs' 2nd generation catalysts by reaction with dimethylformamide provides a new species able to catalyse this transformation. Selection of suitable conditions allowed high yields and selectivity. Studies performed in order to identify the catalytic species point to a non-carbenic ruthenium complex that has lost the phosphine. No hydride signals appeared. In addition, the reaction works with enynes and the new species catalyses efficiently crossed cyclotrimerizations of alkynes with diynes.     

Medium-sized and strained heterocycles from non-catalysed and gold-catalysed conversions of β-carbolines

2-Allyl-1-vinyl-β-carbolines and dihydropyrrolo-β-carbolines react with activated internal alkynes through novel rearrangement reactions leading to complex polycyclic structures. Favored reaction pathways depend on reaction conditions and on the presence of gold catalysts. In particular, upon reaction with 2 equiv. of the alkyne, new hexacyclic structures 10 are formed with total stereocontrol.     

Electrochemical anion sensing using electrodes chemically modified with Au(I)–Cu(I) heterotrimetallic alkynyl cluster complexes containing ferrocenyl groups

A novel family of electrochemical anion sensors operating in aqueous media, based on the heterometallic Au(I)–Cu(I) [{Au₃Cu₂(C₂R)₆}Au₃(PPh₂C₆H₄PPh₂)₃](PF₆)₂ (L1, R = Fc; L2, R = C₆H₄Fc) alkynyl cluster complexes, is presented. Upon attachment to graphite and gold electrodes, these compounds exhibit a well-defined, essentially reversible, solid-state electrochemistry in contact with aqueous media, based on ferrocenyl-centered oxidation processes involving anion insertion, leading to distinctive pH-independent electrochemical responses for fluoride, chloride, bromide, perchlorate, bicarbonate, carbonate, phosphate, hydrogen phosphate, dihydrogen phosphate, and nitrate anions. Cluster-modified electrodes can be used as potentiometric sensors as a result of the reversible, diffusion-controlled electrochemistry obtained for the anion-assisted electrochemical oxidation of L1 and L2.     

Electrochemistry for conservation science

Voltammetry of microparticles, an electrochemical methodology based on the record of the voltammetric response of sparingly soluble solids mechanically transferred to the surface of inert electrodes in contact with suitable electrolytes, is able to provide significant analytical information in the fields of conservation and restoration of cultural goods. Using this methodology, identification, speciation, and relative and absolute quantification of analytes from works of art samples can be achieved. Applications to the analysis of organic and inorganic pigments in paints, fibbers, ceramic materials as well as alteration compounds in paintings and metallic artifacts are reviewed.     

Al3Li4(BH4)13: A Complex Double‐Cation Borohydride with a New Structure

The new double‐cation Al–Li–borohydride is an attractive candidate material for hydrogen storage due to a very low hydrogen desorption temperature (～70 °C) combined with a high hydrogen density (17.2 wt %). It was synthesised by high‐energy ball milling of AlCl₃ and LiBH₄. The structure of the compound was determined from image‐plate synchrotron powder diffraction supported by DFT calculations. The material shows a unique 3D framework structure within the borohydrides (space group=P‐43n, a=11.3640(3) Å). The unexpected composition Al₃Li₄(BH₄)₁₃ can be rationalized on the basis of a complex cation [(BH₄)Li₄]³⁺ and a complex anion [Al(BH₄)₄]^?. The refinements from synchrotron powder diffraction of different samples revealed the presence of limited amounts of chloride ions replacing the borohydride on one site. In situ Raman spectroscopy, differential scanning calorimetry (DSC), thermogravimetry (TG) and thermal desorption measurements were used to study the decomposition pathway of the compound. Al–Li–borohydride decomposes at ～70 °C, forming LiBH₄. The high mass loss of about 20 % during the decomposition indicates the release of not only hydrogen but also diborane.     

Vapour pressures,osmotic and activity coefficients for binary mixtures containing (1-ethylpyridinium ethylsulfate + several alcohols) at T = 323.15 K

Osmotic coefficients of binary mixtures containing several primary and secondary alcohols (1-propanol, 2-propanol, 1-butanol, 2-butanol, and 1-pentanol) and the pyridinium-based ionic liquid 1-ethylpyridinium ethylsulfate were determined at T = 323.15 K using the vapour pressure osmometry technique. From the experimental results, vapour pressure and activity coefficients can be determined. For the correlation of osmotic coefficients, the extended Pitzer model modified by Archer, and the modified NRTL (MNRTL) model were used, obtaining deviations lower than 0.017 and 0.047, respectively. The mean molal activity coefficients and the excess Gibbs free energy for the binary mixtures studied were determined from the parameters obtained with the extended Pitzer model modified by Archer.     

Un modelo de difusión anisótropa para el estudio del tráfico urbano

In order to design or redesign urban transportation networks, the employment of mathematical models is very useful for predicting the effects of possible modifications of implementing. Such models allow the determination of vehicular flows and travel times for every link of the network from the knowledge of its inherent features and the corresponding traffic demand. They are based on a phenomenological law of the social collective behavior of the drivers called Wardrop principle. It is an optimization problem, in general, very demanding from the computational point of view.In order to accelerate the computation process, in this paper, a continuum model for the urban traffic is proposed. The fundamental assumption behind this theory is that the variation of network properties is small in close regions when compared with the full system. Accordingly, it is possible to use continuous functions for representing travel times or vehicular flows. Essentially, the problem is formulated as a system of non-linear anisotropic diffusion (differential) equations that can be conveniently solved by means of the finite element method. The efficiency of the proposed model is studied by means of a comparison with results obtained with the classical optimization approach. As shown, the results are similar although the computation times are significantly reduced.     

Ion-pair association and acid-base equilibria in nonaqueous capillary electrophoresis of weakly basic compounds

CE in nonaqueous media was used to study the migrating behavior of two weakly basic s-triazine pesticides and one of their metabolites. The target pesticides were selected to be representative for each of the two main groups: propazine and deethylatrazine for the chloro-s-triazines group and ametryn for the methylthio-s-triazines group. To elucidate the phenomena involved, systematic studies were carried out in the different organic media studied. Absolute mobilities were determined in 50% v/v methanol (MeOH)/ACN by extrapolation of the effective mobilities to zero ionic strength in the presence of different concentrations of perchloric acid. Conductivity measurements performed in MeOH and 50 and 20% v/v methanol/ACN permitted the evaluation of the associations of the components of the BGE. The effects of ionic strength on the actual mobilities of the compounds were determined in the presence of perchloric acid and SDS in different organic media. Two different ion-pair equilibria were considered: one due to the presence of perchlorate anions present in the BGE and second that from the added dodecyl sulfate anions. Bearing in mind that these weakly basic compounds can exhibit ion-pair and acid-base equilibria, the acid-base and ion-pair parasite reaction coefficients were determined. Finally, the effects of ionic strength, ion-pair interactions and acid-base properties on the effective electrophoretic mobilities of the analytes are discussed.