Insertion of lattice-valued and hedgehog-valued functions

Problems of inserting lattice-valued functions are investigated. We provide an analogue of the classical insertion theorem of Lane [Proc. Amer. Math. Soc. 49 (1975) 90-94] for L-valued functions where L is a ?-separable completely distributive lattice (i.e. L admits a countable join-dense subset which is free of completely join-irreducible elements). As a corollary we get an L-version of the Katětov-Tong insertion theorem due to Liu and Luo [Topology Appl. 45 (1992) 173-188] (our proof is different and much simpler). We show that ?-separable completely distributive lattices are closed under the formation of countable products. In particular, the Hilbert cube is a ?-separable completely distributive lattice and some join-dense subset is shown to be both order and topologically isomorphic to the hedgehog J(ω) with appropriately defined topology. This done, we deduce an insertion theorem for J(ω)-valued functions which is independent of that of Blair and Swardson [Indian J. Math. 29 (1987) 229-250]. Also, we provide an iff criterion for inserting a pair of semicontinuous function which yields, among others, a characterization of hereditarily normal spaces.     

Determination of the entropy of formation of the Pt(111)∣ perchloric acid solution interface. Estimation of the entropy of adsorbed hydrogen and OH species

The entropy of formation of the interface between a Pt(111) electrode and a 0.1-M HClO₄ solution is calculated here for the first time from the temperature dependence of total charge vs potential curves following a thermodynamic analysis based on the electrocapillary equation. From this quantity, the absolute entropies of specifically adsorbed species (hydrogen and OH) can be estimated. The present method is an alternative treatment of data that overcomes some of the limitations involved in the approach that uses a generalized isotherm. However, it requires additional experimental data: the temperature coefficient of the potential of zero total charge of the working electrode and the temperature coefficient of the reference electrode. Comparison of the results obtained by both approaches shows that, for hydrogen adsorption, the agreement is reasonable, but the differences are larger for OH adsorption, thus showing the limitations inherent in the treatment based on the generalized isotherm. Dedicated to Professor Oleg Petrii on the occasion of his 70th birthday on August 24, 2007.     

Time and work generalised precedence relationships in project scheduling with pre-emption: An application to the management of Service Centres

In this paper we present an application of project scheduling concepts and solution procedures for the solution of a complex problem that comes up in the daily management of many company Service Centres. The real problem has been modelled as a multi-mode resource-constrained project scheduling problem with pre-emption, time and work generalised precedence relationships with minimal and maximal time lags between the tasks and due dates. We present a complete study of work GPRs which includes proper definitions, a new notation and all possible conversions amongst them. Computational results that show the efficiency of the proposed hybrid genetic algorithm and the advantages of allowing pre-emption are also presented.     

Characterizing efficiency without linear structure: a unified approach

In this paper, we study a general optimization problem without linear structure under a reflexive and transitive relation on a nonempty set E, and characterize the existence of efficient points and the domination property for a subset of E through a generalization of the order-completeness condition introduced earlier. Afterwards, we study the abstract optimization problem by using generalized continuity concepts and establish various existence results. As an application, we extend and improve several existence results given in the literature for an optimization problem involving set-valued maps under vector and set criteria. The work of the first author was partially supported by CONICYT-Chile through FONDECYT 107-0689 and FONDAP-Matemáticas Aplicadas II; whereas that of the second and third author were supported in part by Ministerio de Educación y Ciencia (Spain), project MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06.     

Solid-phase synthesis of biaryl cyclic peptides by borylation and microwave-assisted intramolecular Suzuki-Miyaura reaction

Miyaura borylation and Suzuki-Miyaura cross-coupling have been combined to set up an efficient strategy for the solid-phase synthesis of biaryl cyclic peptides. The Miyaura borylation was the key step in obtaining the linear peptidyl resin precursor containing both the boronate and the halogenated derivative of an aromatic amino acid. The Suzuki-Miyaura macrocyclization was performed under microwave irradiation leading to biaryl cyclic peptides of different ring sizes.     

TPD study of NO decomposition on Rh(111) by dynamic Monte Carlo simulation

The kinetics of NO desorption and its decomposition on Rh(111) surfaces have been simulated by using a dynamic Monte Carlo method. During the simulations, we used a triangular lattice that mimics the Rh(111) phase. NO decomposition was studied at low pressure and temperatures ranging from 120 to 1000 K. The present analysis incorporates recent experimental evidence showing that N₂ production occurs either from the classical N + N recombination step or by the formation and successive decay of an (N–NO)* intermediate species. Moreover, N₂ and NO desorption rates are enhanced and the NO dissociation rate is inhibited by coadsorbed NO, N, and O species as nearest neighbors. These effects are taken into account in this study, along with the experimental adsorption, desorption, dissociation, and diffusion rates of the reactants. Our simulations are consistent with the experimental results of TPD spectra and can explain the formation of two peaks, δ-N₂ and β-N₂, as a natural consequence of the reaction mechanism herein proposed. Comparisons with different mechanisms used by other authors are also made.     

Rheological properties for inelastic Maxwell mixtures under shear flow

The Boltzmann equation for inelastic Maxwell models is considered to determine the rheological properties in a granular binary mixture in the simple shear flow state. The transport coefficients (shear viscosity and viscometric functions) are exactly evaluated in terms of the coefficients of restitution, the (reduced) shear rate and the parameters of the mixture (particle masses, diameters and concentration). The results show that in general, for a given value of the coefficients of restitution, the above transport properties decrease with increasing shear rate.     

Characterization of taste-active fractions in red wine combining HPLC fractionation, sensory analysis and ultra performance liquid chromatography coupled with mass spectrometry detection

Five Tempranillo wines exhibiting marked differences in taste and/or astringency were selected for the study. In each wine the non-volatile extract was obtained by freeze-drying and further liquid extraction in order to eliminate remaining volatile compounds. This extract was fractionated by semipreparative C18-reverse phase-high performance liquid chromatography (C18-RP-HPLC) into nine fractions which were freeze-dried, reconstituted with water and sensory assessed for taste attributes and astringency by a specifically trained sensory panel. Results have shown that wine bitterness and astringency cannot be easily related to the bitter and astringent character of the HPLC fractions, what can be due to the existence of perceptual and physicochemical interactions. While the bitter character of the bitterest fractions may be attributed to some flavonols (myricetin, quercetin and their glycosides) the development of a sensitive UPLC-MS method to quantify astringent compounds present in wines has made it possible to demonstrate that proanthocyanidins monomers, dimers, trimers and tetramers, both galloylated or non-galloylated are not relevant compounds for the perceived astringency of the fractions, while cis-aconitic acid, and secondarily vainillic, and syringic acids and ethyl syringate, are the most important molecules driving astringency in two of the fractions (F5 and F6). The identity of the chemicals responsible for the astringency of the third fraction could be assigned to some proanthocyanidins (higher than the tetramer) capable to precipitate with ovalbumin.     

Synthesis of ferrocene-substituted 2-azetidinones.

The photochemical reaction of alkoxychromium(0)carbene complexes and ferrocene mono- and disubstituted imines formed 2-azetidinones having one or two ferrocene moieties in good yields. Yields decrease when the carbene moiety bears an aminoferrocene moiety attached to the carbene carbon, while complex 9 having the ferrocene directly bonded to the carbene carbon was totally inert in these reactions. Access to beta-lactams with the ferrocene tethered to the C3 position through a methylene group was gained using the lithium enolate derived from ethyl 3-ferrocenylpropanoate. The reaction of this enolate produced two unexpected processes. Thus, 2-azetidinone 15 having an hydroxyl group at the C3 position was obtained together with the expected beta-lactam 14, by reaction of the lithium enolate of ethyl 3-ferrocenylpropenoate and imine 1. Additionally, unsaturated amide 17 was obtained by base-promoted Hoffmann-like breakage of the beta-lactam ring formed in the reaction of the same enolate and imine 2. Oxidation of the anion at the C3 of the 2-azetidinone ring on compound 14, as well as the sterically driven ring-breakage of the C3 anion derived from the nonisolated 2-azetidinone 18, should be responsible for this behavior.