A general framework for the construction of piecewise-polynomial local interpolants of minimum degree

In this paper we consider the problem of designing piecewise polynomial local interpolants of non-uniformly spaced data. We provide a constructive approach that, for any assigned degree of polynomial reproduction, continuity order, and support width, allows for generating the fundamental spline functions of minimum degree having the desired properties. Finally, the proposed construction is extended to handle open sets of data and to the case of multiple knots.     

Catalytic Transfer Hydrogenation and Acid Reactions of Furfural and 5-(Hydroxymethyl)furfural over Hf-TUD-1 Type Catalysts

Heterogeneous catalysis, which has served well the petrochemical industry, may valuably contribute towards a bio-based economy by sustainably enabling selective reactions to renewable chemicals. Carbohydrate-containing matter may be obtained from various widespread sources and selectively converted to furanic platform chemicals: furfural (Fur) and 5-(hydroxymethyl)furfural (Hmf). Valuable bioproducts may be obtained from these aldehydes via catalytic transfer hydrogenation (CTH) using alcohols as H-donors under relatively moderate reaction conditions. Hafnium-containing TUD-1 type catalysts were the first of ordered mesoporous silicates explored for the conversion of Fur and Hmf via CTH/alcohol strategies. The materials promoted CTH and acid reactions leading to the furanic ethers. The bioproducts spectrum was broader for the reaction of Fur than of Hmf. A Fur reaction mechanism based on literature data was discussed and supported by kinetic modelling. The influence of the Hf loading and reaction conditions (catalyst load, type of alcohol H-donor, temperature, initial substrate concentration) on the reaction kinetics was studied. The reaction conditions were optimized to maximize the yields of 2-(alkoxymethyl)furan ethers formed from Fur; up to 63% yield was reached at 88% Fur conversion, 4 h/150 °C, using Hf-TUD-1(75), which was a stable catalyst. The Hf-TUD-1(x) catalysts promoted the selective conversion of Hmf to bis(2-alkoxymethyl)furan; e.g., 96% selectivity at 98% Hmf conversion, 3 h/170 °C for Hf-TUD-1(50).     

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.     

Initiation mechanisms in copolymerization: Reaction of t-butoxyl radicals with co-monomers ethyl vinyl ether and methyl methacrylate

The radical trapping technique employing 1,1,3,3-tetramethyl-1,3-dihydro-1H-isoindol-2-yloxyl as a scavenger has been used to investigate the reaction of t-butoxyl radicals with mixtures of ethyl vinyl ether and methyl methacrylate. The range of identified products includes those from both addition and hydrogen abstraction with both monomers, head addition with ethyl vinyl ether, and some second monomer addition products. Relative rate constants have been obtained for various pairs of constituent reactions. t-Butoxyl radicals add to ethyl vinyl ether one to two times faster than to methyl methacrylate, depending on which monomer is in excess. The ratio is less than 1 in nonolefinic solvents and as high as 6 in t-butanol. This solvent effect is thought to be due to the radicals complexing to either methyl methacrylate or t-butanol (H-bonding), thereby increasing its electrophilic character. © 1997 John Wiley & Sons, Inc.     

Restricted rotations and stereodynamics of aziridine-2-methanol derivatives

‘Gear-like’ rotations of simple C-C bonds have been observed in some aziridine methanol derivatives. These restricted rotations have been studied by dynamic and multinuclear magnetic resonance experiments, and the barrier for rotations of Csp³-Csp³ and Csp³-Csp² bonds have been calculated. The role of an intramolecular hydrogen bond on the stereodynamics has also been demonstrated.     

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.     

Pt-Cu / ZSM-5 for removal of nitrates from drinking water

Removal of nitrates from drinking water by catalytic hydrogenation over ZSM-5 supported Pt-Cu catalysts was studied. Bimetallics Pt-Cu were prepared by ion exchange of copper on a parent monometallic platinum catalyst. Monometallic platinum catalysts are inactive for nitrate reduction, while Pt-Cu bimetallic catalysts are active for nitrate removal. In the bimetallic catalyst, the role of copper is probably to reduce nitrate according to a redox reaction. The addition of copper to Pt catalysts decreases the production of ammonium ions     

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.