On the internal stepsize of an extrapolation algorithm for IVP in ODE

We propose an extrapolation algorithm for initial value problems in ordinary differential equations. In the algorithm, an appropriately chosen stepsizeH is divided into smaller stepsizes by a sequence and a new stopping rule is proposed. The sequences applied to the algorithm are Romberg {2,4,8,16,32,...}, Bulirsch {2,4,6,8,16...} and Harmonic {2,4,6,8,10,12,...} types. The proposed algorithm is compared numerically with the algorithm introduced by Stoer. In view of the accuracy of numerical solutions, the relatively small number of calculations, the stability and reliability of the algorithm, we found that the algorithm with the Romberg sequence is the best.     

Bis(pentafluorophenyl) disulfide as a hydrogen abstractor and an electron acceptor from the resulting radical intermediate

The pentafluorobenzenethiyl radical is an efficient hydrogen abstractor from an activated methylene or methine group and bis(pentafluorophenyl) disulfide is an efficient electron acceptor from the resulting radical intermediate. Thus benzyl-OTBS ether was easily converted into the corresponding pinacol, and 2-phenyl-1,3-dioxanes are converted into the monobenzoates of diols.     

Synthesis of the LMN-ring fragment of the Caribbean ciguatoxin C-CTX-1

Ciguatoxin C-CTX-1 was isolated as a principal causative toxin of ciguatera seafood poisoning in the Caribbean Sea, and is structurally classified as a ladder-shaped polycyclic ether. In this Letter, we report the synthesis of the tricyclic LMN-ring system of C-CTX-1. SmI₂-mediated reductive cyclization efficiently constructed the seven-membered M-ring with the axially oriented 1,3-dimethyl structure.     

Activity evaluation of carbon paste electrodes loaded with pt nanoparticles prepared in different radiolytic conditions

Three Pt-based catalysts prepared in different radiolytic conditions and supported on graphite powder were packed into a carbon paste electrode configuration. They were compared to each other, to the commercial (Pt) deposited on activated carbon powder (Johnson Matthey) and to pure Vulcan XC-72 for their respective abilities toward the hydrogen evolution reaction (HER). The Tafel parameters were determined for all these electrodes. From the I–V curves and their quantitative treatment, the following order of activity emerged unambiguously and reads: (PtCO)₂ (fcc structure) > (PtCO)₁ (Chini cluster) > (Pt)_neat > (Pt)_JM (Johnson Matthey) ≫ (Vulcan XC-72). As expected, all the Pt-loaded electrodes were more efficient than Vulcan XC-72. The classification appears to be linked with the mean nanoparticle size, and for comparable sizes, with the surface morphology of the materials. The results and the stability of the electrodes suggest that the small particle sizes and the good dispersity on the carbon support were maintained during the HER.     

Multi-iron wells-Dawson heteropolytungstates. Electrochemical probing of siderophoric behavior in sandwich-type complexes

The demetalation process of 10 multi-iron Wells-Dawson polyoxometalates is studied by cyclic voltammetry and controlled potential coulometry. Eight sandwich-type complexes (alphaalphaalphaalpha-Na(16)[(NaOH(2))(2)(Fe(III))(2)(X(2)W(15)O(56))(2)], alphaalphabetaalpha-Na(14)[(NaOH(2))(Fe(III)OH(2))(Fe(III))(2)(X(2)W(15)O(56))(2)], alphabetabetaalpha-Na(12)[(Fe(III)OH(2))(2)(Fe(III))(2)(X(2)W(15)O(56))(2)], and alphabetabetaalpha-Na(14)[(Mn(II)OH(2))(2)(Fe(III))(2)(X(2)W(15)O(56))(2)] (where X = P(V) or As(V))) and two monomeric complexes (alpha-Na(11)[(P(2)(Fe(III)Cl)(2)(Fe(III)OH(2))W(15)O(59))] and alpha-Na(11)[(As(2)(Fe(III)Cl)(2)Fe(III)OH(2))W(15)O(59))]) were selected for this study. All 10 complexes show Fe(III) waves which are well-separated from the redox activity of the W(VI) centers. At room temperature and under mild conditions, iron release from the complexes is observed upon reduction of the Fe(III) centers. This release is controlled by the ionic strength of the medium, the nature and concentration of the anions present in the supporting electrolyte, and by the pH of the solution. This behavior parallels those described for most siderophores which depend on the same parameters.     

Synthesis of (±)‐Kempa‐6,8‐dien‐3‐ol (=(2aRS,3SR,4aSR,7RS,7aSR,10bSR,10cSR)‐2,2a,3,4,4a,5,6,7,7a,8,10b,10c‐Dodecahydro‐2a,7,10,10c‐tetramethylnaphth[2,18‐cde]azulen‐3‐ol)

The synthesis of kempa‐6,8‐dien‐3β‐ol ( 4a ), as a synthetic leading model of the natural product 4b , was carried out starting from intermediate 12 , the synthetic route of which has been developed previously (Scheme 1). The conversion of 12 to the model compound 4a involved the elaboration of three structure modifications by three processes, Tasks A, B, and C (see Scheme 2). Task A was achieved by epoxy‐ring opening of 41 with Me₃SiCl (Scheme 9), and Task B being performed by oxidation at the 13‐position, followed by hydrogenation, and then epimerization (Schemes 4 and 5). The removal of the 2‐OH group from 12 (Task C) was achieved via 30b according to Scheme 6, whereby 30b was formed exclusively from 30a / 31a 1 : 1 (Scheme 7). In addition, some useful reactions from the synthetic viewpoint were developed during the course of the present experiments.     

Fabrication of mesoporous ZnO nanosheets from precursor templates grown in aqueous solutions

Mesoporous ZnO nanosheets were successfully prepared by pyrolytic transformation of zinc carbonate hydroxide hydrate, Zn₄CO₃(OH)₆·H₂O. The nanosheets were initially formed as assemblies on glass substrates during chemical bath deposition (CBD) in aqueous solutions of urea and zinc acetate dihydrate, zinc chloride, zinc nitrate hexahydrate, or zinc sulfate heptahydrate at 80°C. It was key to induce heterogeneous nucleation of Zn₄CO₃(OH)₆·H₂O by promoting a gradual hydrolysis reaction of urea and controlling the degree of supersaturation of zinc hydroxide species. Morphology of Zn₄CO₃(OH)₆·H₂O was largely influenced by the anions present in the CBD solutions. The Zn₄CO₃(OH)₆·H₂O nanosheets were transformed into wurtzite ZnO by heating at 300°C in air without losing the microstructural feature.     

On-line measurement of intramolecular carbon isotope distribution of acetic acid by continuous-flow isotope ratio mass spectrometry

Molecular and intramolecular carbon isotope measurements of acetic acid present in natural environments have been performed by off-line procedures. The off-line method is complicated and time-consuming and requires micromolar to millimolar amounts of sample. This limits geochemical isotopic studies, especially at the intramolecular level, on acetic acid present in natural samples. Here, we examine an on-line measurement of intramolecular carbon isotope distribution of acetic acid using continuous-flow isotope ratio mass spectrometry (CF-IRMS) coupled with an on-line pyrolysis system. This is achieved by measurement of the respective carbon isotope ratios of CH4 and CO2 produced by on-line pyrolysis of acetic acid. Results for authentic standards of pure acetic acid demonstrated the practicality of this on-line method, although the carbon isotope ratio of the methyl group could not be determined directly. The precision of the carbon isotope measurements was 0.4 per thousand (1sigma). The carbon isotope distribution determined by the on-line method was identical to that determined by the conventional off-line method within analytical error. The advantages of the on-line method compared with the conventional off-line method are that it is less laborious, requires less analytical time (less than one hour per sample) and, most importantly, uses smaller sample sizes (ca. 10 nanomole). An application of this on-line method to natural geochemical samples will provide an insight into the geochemical cycle of acetic acid.     

The satellite-shaped Co-15 Polyoxotungstate, [Co6(H2O)30{Co9Cl2(OH)3(H2O)9(beta-SiW8O31)3}]5-

The 15-cobalt-substituted polyoxotungstate [Co(6)(H(2)O)(30){Co(9)Cl(2)(OH)(3)(H(2)O)(9)(beta-SiW(8)O(31))(3)}](5-) (1) has been characterized by single-crystal XRD, elemental analysis, IR, electrochemistry, magnetic measurements, and EPR. Single-crystal X-ray analysis was carried out on Na(5)[Co(6)(H(2)O)(30){Co(9)Cl(2)(OH)(3)(H(2)O)(9)(beta-SiW(8)O(31))(3)}].37H(2)O, which crystallizes in the hexagonal system, space group P6(3)/m, with a = 19.8754(17) A, b = 19.8754(17) A, c = 22.344(4) A, alpha= 90 degrees, beta = 90 degrees, gamma = 120 degrees, and Z = 2. The trimeric polyanion 1 has a core of nine Co(II) ions encapsulated by three unprecedented (beta-SiW(8)O(31)) fragments and two Cl(-) ligands. This central assembly {Co(9)Cl(2)(OH)(3)(H(2)O)(9)(beta-SiW(8)O(31))(3)}(17-) is surrounded by six antenna-like Co(II)(H(2)O)(5) groups resulting in the satellite-like structure 1. Synthesis of 1 is accomplished in a simple one-pot procedure by interaction of Co(II) ions with [gamma-SiW(10)O(36)](8-) in aqueous, acidic NaCl medium (pH 5.4). Polyanion 1 was studied by cyclic voltammetry as a function of pH. The current intensity of its Co(II) centers was compared with that of free Co(II) in solution. Our results suggest that 1 keeps its integrity in solution. Magnetic susceptibility results show the presence of both antiferro- and ferromagnetic coupling within the (Co(II))(9) core. A fully anisotropic Ising model has been employed to describe the exchange-coupling and yields g = 2.42 +/- 0.01, J(1) = 17.0 +/- 1.5 cm(-1), and J(2) = -13 +/- 1 cm(-(1). Variable frequency EPR studies reveal an anisotropic Kramer's doublet.     

Trans-cis Photoisomerization of 1-Methyl-4-(4′-hydroxystyryl)pyridinium in inclusion complexes ofβ-cyclodextrin and its derivatives

The effects of -cyclodextrin (-CyD), heptakis(2,6-di-O-methyl)--cyclodextrin (DMCyD) and heptakis(2,3,6-tri-O-methyl)--cyclodextrin (TMCyD) ontrans-cis photoisomerization of 1-ethyl-4-(4-hydroxystyryl)pyridinium (POH) have been studied in aqueous solutions. The ratio of [cis]/[trans] for POH in the photostationary state at pH 8.54 was remarkably reduced by the presence of CyD or DMCyD. The reduction of the [cis]/[trans] ratio in the photostationary state was explained in terms of the shift of the equilibrium of POH ₊ ^trans PO _trans + H^– toward PO _trans formation. The binding constants of CyD and DMCyD for PO _trans were 2.00- and 1.36-fold larger than those for POH ₊ ^trans , respectively. The binding constants of TMCyD for both species are much smaller than those of CyD and DMCyD. This result indicates that PO _trans , which has a betain structure, forms stable complexes with CyD and DMCyD with its hydrophobic parts inside and the charged parts outside the CyD cavities.