Solving (1, q) KdV gravity

In this paper we explicitly compute the correlation functions of the (1, q) series of the KdV hierarchy i.e. models with q − 1 primary fields. We also find from algebraic considerations a ghost number conservation law for the (1, q) models. All the results in this paper follow from the algebraic properties of the KdV hierarchy without using any extraneous information from a field theory interpretation. We find the interesting result that some correlation functions vanish even when they conserve ghost number. This is an indication for further selection rules.     

On a Generalization of Szász–Mirakjan–Kantorovich Operators

In this paper we introduce and study a sequence of positive linear operators acting on suitable spaces of measurable functions on [0,+∞[, including L ^p ([0,+∞[) spaces, 1 ≤ p < +∞, as well as continuous function spaces with polynomial weights. These operators generalize the Szász–Mirakjan–Kantorovich operators and they allow to approximate (or to reconstruct) suitable measurable functions by knowing their mean values on a sequence of subintervals of [0,+∞[ that do not constitute a subdivision of it. We also give some estimates of the rates of convergence by means of suitable moduli of smoothness.     

3-Quasi-Sasakian manifolds

We correct the results in section 6 of [B. Cappelletti Montano, A. De Nicola, G. Dileo, 3-Quasi-Sasakian manifolds, Ann. Global Anal. Geom. 33 (2008), 397–409], concerning the corrected energy of the Reeb distribution of a compact 3-quasi-Sasakian manifold. The results are slightly different than what was originally claimed and they are obtained by using results in [B. Cappelletti Montano, A. De Nicola, G. Dileo, The geometry of a 3-quasi-Sasakian manifold, Int. J. Math., to appear, arXiv:0801.1818], where the geometry of these manifolds is more deeply investigated. The online version of the original article can be found under doi:.     

Building and testing correlations for the estimation of one‐electron reduction potentials of a diverse set of organic molecules

We describe and evaluate a method for computationally predicting reduction potentials of a diverse group of organic molecules by linearly correlating calculated lowest unoccupied molecular orbital energies with ground state reduction potentials measured in acetonitrile. The approach is shown to provide a unique combination of extreme computational simplicity and excellent accuracy across a diverse range of organic structures and a wide window of reduction potentials. A disparate set of molecules (74 compounds belonging to six distinct structural families, comprised of molecules containing C, H, N, O, F, Cl, and Br, with functional groups including esters, ketones, halides, nitriles, quinones, alkenes, arenes, heteroarenes, and pyridinium and higher benzologs, all containing conjugated pi systems, spanning a 3.5‐V range of reduction potentials) was used to build the correlations. This methodology was found to be computationally inexpensive compared with other approaches and to permit the useful prediction of reduction potentials of additional molecules of diverse structural types not included in the families used to determine the correlation parameters. The effects of varying the basis set used in the B3LYP electronic structure calculations and including solvent (compared with calculations in gas phase) were also examined. It was found that the inclusion of a continuum solvent model in the calculations was required for accurate results, particularly when including cationic species in the correlations (although when only neutral molecules were examined, reasonable results could even be obtained in vacuo). Several of the best correlations were used to predict the reduction potentials of seven much larger and structurally diverse chromophores that were not included in the correlation data set. Strong correlations (r² values > 0.99) with very good predictive abilities (root mean square deviation < 60 mV) were found. This extremely simple and computationally efficient entirely closed‐shell methodology is proven robust and useful for the design of new molecules capable of participating in redox processes, including electron transfer reactions. Copyright © 2015 John Wiley & Sons, Ltd.     

Inelastic magnetic X-ray scattering from highly correlated electron systems: La1.2Sr1.8Mn2O7, La0.7Sr0.3MnO3 and Fe3O4

Magnetic Compton profiles have been measured for the colossal magnetoresistance manganites La_1.2Sr_1.8Mn₂O₇ and La_0.7Sr_0.3MnO₃, and for magnetite Fe₃O₄, along various crystallographic directions, over a wide range of temperatures and magnetic fields. The experimental results are interpreted via first-principles computations for the double layer manganite, La_1.2Sr_1.8Mn₂O₇, and by using a simple model involving atomic d-orbitals and free electrons for the other two compounds. For all three materials a preference for the occupation of e_g orbitals is found, particularly, for orbitals of dx²−y² symmetry. An itinerant electron contribution is adduced at all temperatures in magnetite; such a contribution also appears in La_1.2Sr_1.8Mn₂O₇, but it is present only at low temperatures in La_0.7Sr_0.3MnO₃.     

The magnetic hyperfine interaction of iron atoms isolated in a xenon matrix in the presence of an external magnetic field

The Mössbauer effect has been used to measure the magnetic hyperfine interaction of isolated ⁵⁷Fe atoms in solid xenon with an applied external magnetic field. A field dependent Mössbauer absorption spectrum is observed. The ground state of these iron atoms is a triplet, which is split in the external field. The Mössbauer spectrum was analyzed taking into consideration relaxation effects. For an applied external field of 28 kOe an internal magnetic field at the ⁵⁷Fe nucleus of 700± 15 kOe was observed (external field included).     

Hydrogen and deuterium exchange on Pt(111) and its poisoning by carbon monoxide studied by surface sensitive high-pressure techniques

Catalytic hydrogen/deuterium exchange on a platinum (111) single crystal and its poisoning with carbon monoxide was studied using scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), sum frequency generation vibrational spectroscopy (SFG), and mass spectrometry under reaction conditions at pressures in the mTorr to atmospheric range. At 298 K and in the presence of 200 mTorr of hydrogen and 20 mTorr of deuterium the surface is catalytically active, producing HD with activation energy of approximately 5.3 kcal/mol. Addition of 5 mTorr of CO stops the reaction completely. In situ STM images reveal an ordered surface structure of chemisorbed CO. At 353 K the addition of 5 mTorr of CO slows the reaction by 3 orders of magnitude, but HD production continues with an activation energy of 17.4 kcal/mol. Changes in coverage and adsorption site of CO were followed by XPS and SFG up to a temperature of 480 K. From these data, a CO dominated, mobile and catalytically active surface model is proposed.     

Temperature-dependent orbital degree of freedom of a bilayer manganite by magnetic compton scattering

We have measured temperature-dependent magnetic Compton profiles (MCPs) from a single crystal of La1.2Sr1.8Mn2O7. The MCPs, which involved the scattering of circularly polarized x rays, are in general related to the momentum density of all the unpaired spins in the system. Nevertheless, we show that when the x-ray scattering vector lies along the [110] direction, the number of magnetic electrons of a specific symmetry, i.e., d electrons of x(2)-y(2) symmetry, yield a distinct signature in the MCP, allowing us to monitor substantial changes in the occupancy of the dx(2)(-y(2)) states over the investigated temperature range of 5-200 K. This study indicates that magnetic Compton scattering can provide a powerful window on the properties of specific magnetic electrons in complex materials.     

Momentum-resolved charge excitations in a prototype one-dimensional mott insulator

We report momentum-resolved charge excitations in a one-dimensional (1D) Mott insulator studied using high resolution inelastic x-ray scattering over the entire Brillouin zone for the first time. Excitations at the insulating gap edge are found to be highly dispersive (momentum dependent) compared to excitations observed in two-dimensional Mott insulators. The observed dispersion in 1D cuprates ( SrCuO2 and Sr2CuO3) is consistent with charge excitations involving holons which is unique to spin-1/2 quantum chain systems. These results point to the potential utility of momentum-resolved inelastic x-ray scattering in providing valuable information about electronic structure of strongly correlated insulators.