Erratum to “Unique continuation results for Ricci curvature and applications” [J. Geom. Phys. 58 (2008) 179–207]

Corrections are given to some of the proofs of the paper mentioned in the title.     

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.     

One-pot Double Suzuki Couplings of Dichloropyrimidines

An effective one-pot, regioselective double Suzuki coupling of 2,4-dichloropyrimidine has been developed, which enables the quick and efficient synthesis of diarylated pyrimidines. The choice of solvent proved critical to the success of this reaction sequence, with alcoholic solvent mixtures affording much greater reactivity and correspondingly lower temperatures than the use of polar aprotic solvents.     

Synthesis of copolyimides based on room temperature ionic liquid diamines

Block copolyimides based on aromatic dianhydrides and diamines copolymerized with diamino room temperature ionic liquid (RTIL) monomers were synthesized over a range of compositions. Specifically, two diamino RTILs, 1,3‐di(3‐aminopropyl) imidazolium bis[(trifluoromethyl)sulfonyl] imide ([DAPIM] [NTf₂]) and 1,12‐di[3‐(3‐aminopropyl) imidazolium] dodecane bis[(trifluoromethyl) sulfonyl] imide ([C₁₂ (DAPIM)₂] [NTf₂]₂) were synthesized using a Boc protection method. The two RTILs were reacted with 2,2‐bis(3,4‐carboxylphenyl) hexafluoropropane dianhydride (6FDA) to produce 6FDA‐RTILs oligomers that formed the RTIL component for the block copolyimides. The oligomers were reacted with 6FDA and m‐phenylenediamine (MDA) at oligomer concentration from 6.5 to 25.8 mol % to form block copolyimides. Increasing the concentration of the 6FDA‐RTIL oligomer in the block copolyimides resulted in a decrease in the thermal degradation temperature, glass transition temperature and an increase in the density. The gas permeability of the RTIL based block copolyimide decreased but the ideal permeability selectivity for CO₂/CH₄ gas pair increased relative to the pure 6FDA‐MDA. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 4036–4046, 2010     

Determination of the mineral composition of fresh bovine milk from the milk-producing areas located in the State of Sergipe in Brazil and evaluation employing exploratory analysis

In this work, the mineral composition of fresh bovine milk obtained from the milk-producing areas of the Brazilian State of Sergipe was examined. A dry-ashed digestion method and the ICP OES technique were used for the quantification of mineral elements (e.g., Ca, Mg, K, Na, P, Sr and Zn) in 27 samples of milk collected from properties located in milk-producing areas around Nossa Senhora da Glória. The following ranges of values (% m/v) were obtained: 0.063 to 0.117 for Ca; 0.060 to 0.114 for P; 0.024 to 0.064 for Na; and 0.087 to 0.164 for K. The ranges of values (mg L^− 1) for the other mineral elements were also found: 0.68 to 1.89 for Sr; 2.46 to 5.73 for Zn; and 54.2 to 109.9 for Mg. Additionally, the exploratory evaluation of the 27 milk samples was performed using principal component analysis (PCA) involving seven variables dealing with the effect of different management systems (conventional and organic) on milk composition. The results show that there are indeed differences between the mineral composition of milk from properties that use organic practices and those that use conventional management practices.     

Synthesis and Properties of Porphyrin Nanotubes

Discrete π‐conjugated zinc porphyrin nanotubes are investigated as molecular analogues of carbon nanotubes. These porphyrin nanotubes have a diameter of 2.4 nm (Zn–Zn distance) and lengths of up to 3.6 nm, measured to the van der Waals surfaces of the outer β‐pyrrole hydrogen atoms, or 4.5 nm measured to the para hydrogen atoms of the aryl groups. We explore three different strategies for synthesizing these nanotubes. The first two strategies use a template to achieve direct or sequential stave‐joining, respectively, and proceed via linear oligomers that pre‐define the length of the nanotube. These strategies are applied to synthesize porphyrin nanotubes containing 12‐ or 18‐porphyrin subunits, with ethynylene (C₂) or butadiynylene (C₄) links between the 6‐porphyrin nanorings. The third strategy involves the covalent stacking of pre‐formed 6‐porphyrin nanorings to form a 12‐porphyrin nanotube, without using a template to guide this coupling reaction. The nanotubes show strongly red‐shifted absorption spectra and low fluorescence quantum yields, indicating structural rigidity and extensive π‐conjugation.     

Stereoselective C-X and regioselective C-H activation to,and selective C(sp2)-C(sp3) reductive elimination from,platinum compounds with thiophene-derived ligands

Several thiophene-based N^C ligands were synthesized. Strategically, a bromide was incorporated on the 2-position of the thiophene ring. When allowed to react with the platinum tetramethyl dimer, [Pt₂Me₄(µ-SMe₂)₂], platinum(IV) platinacycles were formed by oxidative addition of the C(sp²)-X bond. These platinum(IV) compounds were characterized by NMR and HRMS. The platinum (IV) compounds were subsequently subjected to thermolysis. A series of reactions occurred, including selective C-C reduction elimination and selective C-H oxidative addition, giving mixtures of platinum(II) products with varying degrees of regioselectivity.     

A Divergent Synthetic Route to the Vallesamidine and Schizozygine Alkaloids: Total Synthesis of (+)‐Vallesamidine and (+)‐14,15‐Dehydrostrempeliopine

The total synthesis of representative members of the schizozygine alkaloids, (+)‐vallesamidine and (+)‐14,15‐dehydrostrempeliopine, were completed from a late‐stage divergent intermediate. The synthesis took advantage of efficient nitro‐group reactions with the A/B/C ring skeleton constructed concisely on a gram scale through an asymmetric Michael addition, nitro‐Mannich/lactamisation, Tsuji–Trost allylation, and intramolecular C?N coupling reaction. Other key features of the synthesis are a novel [1,4] hydride transfer/Mannich‐type cyclisation to build ring E and a diastereoselective ring‐closing metathesis reaction to construct ring D. This approach gave access to a late‐stage C14,C15 alkene divergent intermediate that could be simply transformed into (+)‐vallesamidine, (+)‐14,15‐dehydrostrempeliopine, and potentially other schizozygine alkaloids and unnatural derivatives.