Minimal sets of foliations on complex projective spaces

Dedicated to René Thom with admiration.     

Extending the applicability of Newton’s method using nondiscrete induction

We extend the applicability of Newton’s method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Ptak. We obtain new sufficient convergence conditions for Newton’s method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F.A.Potra, V.Ptak, Sharp error bounds for Newton’s process, Numer. Math., 34 (1980), 63–72, and F.A.Potra, V.Ptak, Nondiscrete Induction and Iterative Processes, Research Notes in Mathematics, 103. Pitman Advanced Publishing Program, Boston, 1984. Under the same computational cost as before, we provide: weaker sufficient convergence conditions; tighter error estimates on the distances involved and more precise information on the location of the solution. Numerical examples are also provided in this study.     

Formation of C-C and C-O bonds and oxygen removal in reactions of alkanediols, alkanols, and alkanals on copper catalysts

This study reports evidence for catalytic deoxygenation of alkanols, alkanals, and alkanediols on dispersed Cu clusters with minimal use of external H(2) and with the concurrent formation of new C-C and C-O bonds. These catalysts selectively remove O-atoms from these oxygenates as CO or CO(2) through decarbonylation or decarboxylation routes, respectively, that use C-atoms present within reactants or as H(2)O using H(2) added or formed in situ from CO/H(2)O mixtures via water-gas shift. Cu catalysts fully convert 1,3-propanediol to equilibrated propanol-propanal intermediates that subsequently form larger oxygenates via aldol-type condensation and esterification routes without detectable involvement of the oxide supports. Propanal-propanol-H(2) equilibration is mediated by their chemisorption and interconversion at surfaces via C-H and O-H activation and propoxide intermediates. The kinetic effects of H(2), propanal, and propanol pressures on turnover rates, taken together with measured selectivities and the established chemical events for base-catalyzed condensation and esterification reactions, indicate that both reactions involve kinetically relevant bimolecular steps in which propoxide species, acting as the base, abstract the α-hydrogen in adsorbed propanal (condensation) or attack the electrophilic C-atom at its carbonyl group (esterification). These weakly held basic alkoxides render Cu surfaces able to mediate C-C and C-O formation reactions typically catalyzed by basic sites inherent in the catalyst, instead of provided by coadsorbed organic moieties. Turnover rates for condensation and esterification reactions decrease with increasing Cu dispersion, because low-coordination corner and edge atoms prevalent on small clusters stabilize adsorbed intermediates and increase the activation barriers for the bimolecular kinetically relevant steps required for both reactions.     

Matrix-free laser desorption/ionization of ions landed on plasma-treated metal surfaces

We report new experiments in which laser desorption/ionization time-of-flight mass spectrometry (LDI-TOF-MS) was applied to detection and characterization of gramicidin S and IgG pentapeptide (DSDPR) that were reactively landed on plasma-treated stainless steel surfaces. The distributions of [M + H](+), [M + Na](+) and [M + K](+) ion species in LDI-TOF for gramicidin S and IgG pentapeptide (DSDPR) were found to be markedly different from those in conventional MALDI-TOF spectra of the same samples. LDI-TOF mass spectra showed a strong preference for [M + K](+) adducts even in the presence of a large excess of sodium cations, or following surface treatment with trifluoroacetic acid. Alkali metal cations (K(+) and Cs(+)) can be exchanged in reactively landed peptide samples to provide the corresponding cationized peptide ions by LDI. Multiple charged trypsin cations were reactively landed into a layer of 2-(4-hydroxyphenylazo)benzoic acid and ionized by LDI. The ionization mechanisms for LDI of surface-deposited peptides are briefly discussed. Copyright (c) 2008 John Wiley & Sons, Ltd.     

The Influence of Spin-Orbit Interaction on the Electron-Phonon Coupling in Tl-Rich Cubic AuCu3-Type Superconductors: Comparison with La3Tl

In this work, the role of spin-orbit coupling (SOC) in ATl₃ (A = Ca, Y, La, and Th) and La₃Tl is investigated by theoretical investigation of their structural, electronic, elastic, mechanical, phonon, and electron–phonon interaction properties. The effect of SOC on the electronic band structures of these compounds is that some of the degeneracies at the high symmetry points that would exist in a scalar relativistic calculation without SOC are removed by considering this coupling. The replacement of La and Tl atoms in LaTl₃ increases the value of the density of states at the Fermi level N($E_{\mathrm{F}}$) by a factor of 2.1. Furthermore, this replacement makes almost all phonon modes in La₃Tl softer than those in LaTl₃. Both softer phonon modes and higher N($E_{\mathrm{F}}$) make the electron–phonon interaction in La₃Tl much stronger than in LaTl₃. The presence of SOC increases the $T_{\mathrm{c}}$ values of LaTl₃ by 34% (from 1.151 to 1.542 K) and of ThTl₃ by 65% (from 0.479 to 0.793 K), resulting in good agreement with the corresponding experimental values of 1.63 and 0.87 K. The inclusion of SOC also improves the agreement with the experiment for $T_{\mathrm{c}}$ values of CaTl₃, YTl₃, and La₃Tl.