High-temperature expansions to fifteenth order

High-temperature series expansions of the susceptibility and second moment to 15th order are calculated for zero external field on the linear chain (LC), plane square (PSQ), simple cubic (SC), and body-centered cubic (BCC) lattices. Checks for specific models against pertinent work in the literature are detailed.     

Novel light-fluorous TEMPO reagents and their application in oxidation reactions

The synthesis of two light-fluorous TEMPO derivatives is reported, along with their application in oxidation reactions.     

Independent dominating sets and hamiltonian cycles

A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r‐regular uniquely hamiltonian graphs when r > 22. This improves upon earlier results of Thomassen. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 233–244, 2007     

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Chitosan–sodium alginate encapsulated Co-doped ZrO<Subscript>2</Subscript>–MWCNTs nanocomposites for photocatalytic decolorization of organic dyes

Photocatalytic decolorization properties of cobalt doped-ZrO₂-multiwalled carbon nanotubes (Co–ZrO₂–MWCNTs) and chitosan–sodium alginate encapsulated Co–ZrO₂–MWCNTs (CS/Alg–Co–ZrO₂–MWCNTs) with varying weight percentage of Co–ZrO₂–MWCNTs are presented in this research paper. The Co–ZrO₂–MWCNTs was first synthesized through homogenous co-precipitation method and introduced into the chitosan–sodium sodium alginate (CS/Alg) biopolymer matrix. The bio-nanocomposites were characterized using X-ray powder diffraction, Fourier transform infrared spectroscopy, transmission electron microscopy, (UV–Vis)-spectroscopy and energy dispersive spectroscopy to obtain information on their structure, formation, morphology, size and elemental analysis. The photodecolorization efficiency of the samples was determined through their decolorization of trypan blue dye aqueous solution in 180 min. Recyclability of the catalysts was also assessed. The bio-nanocomposites experienced reduced band gap values with subsequent improvement in visible light activity compared to the uncapped Co–ZrO₂–MWCNTs. All the CS/Alg–Co–ZrO₂–MWCNTs exhibited higher photodecolorization activities than the uncapped Co–ZrO₂–MWCNTs. The most efficient catalyst (CS/Alg–40 % Co–ZrO₂–MWCNTs) with a band gap of 2.56 eV displayed 94 % decolorization efficiency of the dye. Though reusability of the catalyst is significant, its efficiency diminished consistently after each cycle.     

Perron's method for second order hyperbolic PDE. Part I

In parts I, II, and III combined of this paper, we define a notion of viscosity solution for these equations and existence is proved by a Perron-like method. Here, in part I, we prove useful identities, and a maximum-like principle for smooth sub(super) solutions of the standard wave equation. We define a new potential theoretic (P) notion of solution, subsolution and supersolution, and a related potential type (P) Cauchy problem for semilinear second order hyperbolic equations.     

Intermediates in asymmetric hydrogenation : The structure and 31P NMR spectra of rhodium enamide complexes containing 1R, 2R-trans-1,2-bis (diphenylphosphinomethyl) cyclo buta

Hydrogenation of bicyclo[2.2.1]heptadiene-1R,2R-(trans-1,2-bis(diphenylphosphinomethyl)cyclbutane rhodium (I) tetrafluoroborate in methanol gives a solvent adduct which reacts with N-acyldehydroamino acids and their esters to give air-unstable scarlet to yellow complexes. Effects of structure variation in the enamide on the ³¹P NMR spectra of these species are reported and discussed with reference to (a) the equilibrium between methanol and enamide complexes; (b) the ratio of diastereomeric enamide complexes formed; (c) the temperature dependence of this ratio; (d) the rate of complexation equilibria and (e) the structure of enamide complexes, which are normally bidentate with binding via the olefin and amide groups. In certain cases the complex may be terdentate and E-enamides bind through the olefin and carboxyl groups. Each mode of binding gives rise to characteristic ³¹P NMR spectra with regard to P-P and P-Rh coupling constants.