Generalized elementary functions

We use the theory of generalized linear differential equations to introduce new definitions of the exponential, hyperbolic and trigonometric functions. We derive some basic properties of these generalized functions, and show that the time scale elementary functions with Lebesgue integrable arguments represent a special case of our definitions.     

Niobium oxide solid catalyst: esterification of fatty acids and modeling for biodiesel production

Biodiesel can be obtained from fatty acid raw materials through esterification. The reactivity of lauric, palmitic, stearic, oleic, and linoleic fatty acids with methanol using powdered niobic acid as a heterogeneous catalyst was investigated in this work, both experimentally (in a batch reactor) and theoretically. A 2³ experimental design was used, with methanol/fatty acid molar ratio, catalyst concentration, and temperature as main factors. An empirical model demonstrated that temperature is the most important variable. Fourteen heterogeneous and 56 homogeneous‐like kinetic models were tested. A homogeneous‐like model considering zero order for all species and inhibition by water was the most adequate for experiments without catalyst. A homogeneous‐like model considering a second‐order reaction in relation to the fatty acid and no water inhibition was the most adequate for niobic acid catalyzed reaction. Molecular modeling confirmed the experimental results showing that the reactivity is directly related to the increase of unsaturated bonds and the reduction of carbon chain length. The polarity of the fatty acid is determinant in the reactivity. At the molecular level, reaction occurs between the HOMO orbital of methanol and LUMO orbitals of fatty acids and reactivity is higher when the energy difference between these orbitals is lower. Copyright © 2010 John Wiley & Sons, Ltd.     

Trust region affine scaling algorithms for linearly constrained convex and concave programs

We study a trust region affine scaling algorithm for solving the linearly constrained convex or concave programming problem. Under primal nondegeneracy assumption, we prove that every accumulation point of the sequence generated by the algorithm satisfies the first order necessary condition for optimality of the problem. For a special class of convex or concave functions satisfying a certain invariance condition on their Hessians, it is shown that the sequences of iterates and objective function values generated by the algorithm convergeR-linearly andQ-linearly, respectively. Moreover, under primal nondegeneracy and for this class of objective functions, it is shown that the limit point of the sequence of iterates satisfies the first and second order necessary conditions for optimality of the problem. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.The work of these authors was based on research supported by the National Science Foundation under grant INT-9600343 and the Office of Naval Research under grants N00014-93-1-0234 and N00014-94-1-0340.     

Building the Additive Utility Functions for CAD-UFRJ Evaluation Staff Criteria

This paper presents an application of the UTA method for building utility functions for the evaluation criteria defined by the Staff Evaluation Commission (CAD) of the Rio de Janeiro Federal University (UFRJ). Every year, the CAD-UFRJ gives the staff evaluation results for each Postgraduate Engineering Programme. However, the method used to generate the staff evaluation is assumed unknown. Trying to find the CAD-UFRJ preference structure, the evaluation results supplied by CAD-UFRJ are used to apply the UTA method. Some additional information obtained from the CAD-UFRJ data is incorporated in the optimal solutions analysis.     

Highly Stereoselective Synthesis of Natural‐Product‐Like Hybrids by an Organocatalytic/Multicomponent Reaction Sequence

In an endeavor to provide an efficient route to natural product hybrids, described herein is an efficient, highly stereoselective, one‐pot process comprising an organocatalytic conjugate addition of 1,3‐dicarbonyls to α,β‐unsaturated aldehydes followed by an intramolecular isocyanide‐based multicomponent reaction. This approach enables the rapid assembly of complex natural product hybrids including up to four different molecular fragments, such as hydroquinolinone, chromene, piperidine, peptide, lipid, and glycoside moieties. The strategy combines the stereocontrol of organocatalysis with the diversity‐generating character of multicomponent reactions, thus leading to structurally unique peptidomimetics integrating heterocyclic, lipidic, and sugar moieties.     

Role of the Polymer Matrix on the Photoluminescence of Embedded CdSe Quantum Dots

The photoluminescence (PL) of CdSe quantum dots (QDs) that form stable nanocomposites with polymer liquid crystals (LCs) as smectic C hydrogen‐bonded homopolymers from a family of poly[4‐(n‐acryloyloxyalkyloxy)benzoic acids] is reported. The matrix that results from the combination of these units with methoxyphenyl benzoate and cholesterol‐containing units has a cholesteric structure. The exciton PL band of QDs in the smectic matrix is redshifted with respect to QDs in solution, whereas a blueshift is observed with the cholesteric matrix. The PL lifetimes and quantum yield in cholesteric nanocomposites are higher than those in smectic ones. This is interpreted in terms of a higher order of the smectic matrix in comparison to the cholesteric one. CdSe QDs in the ordered smectic matrix demonstrate a splitting of the exciton PL band and an enhancement of the photoinduced differential transmission. These results reveal the effects of the structure of polymer LC matrices on the optical properties of embedded QDs, which offer new possibilities for photonic applications of QD–LC polymer nanocomposites.     

Separation and determination of <Superscript>90</Superscript>Sr in low- and intermediate-level radioactive wastes using extraction chromatography and LSC

A methodology for the determination of ⁹⁰Sr in low- and intermediate-level radioactive wastes from nuclear power plants is presented in this work. It is a part of a methodology developed for the sequential radiochemical separation of radionuclides difficult-to-measure directly by gamma spectrometry in these radioactive wastes. The separation procedure was carried out using precipitation and extraction chromatography with Sr Resin, from Eichrom and the ⁹⁰Sr was measured by liquid scintillation counting (LSC). Optimum conditions for the pretreatment, separation and LSC measurements were determined using simulated samples, which were prepared using standard solutions and carriers. The procedure showed to be rapid and achieved a good chemical yield, in the range 60–90%, and a detection limit of 6.0 × 10⁻⁴ Bq g⁻¹. The method was also tested by participation in a national intercomparison program, with aqueous samples, with good agreement of results.     

Thermochemistry of 2,2′-dipyridil N-oxide and 2,2′-dipyridil N,N′-dioxide. The dissociation enthalpies of the N−O bonds

In this paper, the first, second and mean (N?O) bond dissociation enthalpies (BDEs) were derived from the standard (p° = 0.1 MPa) molar enthalpies of formation, in the gaseous phase, ${\mathrm{\Delta }}_{\text{f}}{H}_{\text{m}}^{°}(\text{g})$, at T = 298.15 K, of 2,2′-dipyridil N-oxide and 2,2′-dipyridil N,N′-dioxide. These values were calculated from experimental thermodynamic parameters, namely from the standard (p° = 0.1 MPa) molar enthalpies of formation, in the crystalline phase, ${\mathrm{\Delta }}_{\text{f}}{H}_{\text{m}}^{°}(\text{cr})$, at T = 298.15 K, obtained from the standard molar enthalpies of combustion, ${\mathrm{\Delta }}_{\text{c}}{H}_{\text{m}}^{°}$, measured by static bomb combustion calorimetry, and from the standard molar enthalpies of sublimation, at T = 298.15 K, determined from Knudsen mass-loss effusion method.