(Vapor + liquid) equilibrium data for (carbon dioxide + 1,1-difluoroethane) system at temperatures from (258 to 343) K and pressures up to about 8 MPa

Accurate thermo-physical data are of utmost interest for the development of new efficient refrigeration systems. Carbon dioxide (R744) and 1,1-difluoroethane (R152a) are addressed here. Isothermal (vapor + liquid) equilibrium data are reported herein for (R744 + R152a) binary system in the (258–343) K temperature range and in the (0.14 to 7.65) MPa pressure range. A reliable “static-analytic” method taking advantage of two online ROLSI? micro capillary samplers is used for all thermodynamic measurements. The data are correlated using our in-house ThermoSoft thermodynamic model using the Peng–Robinson equation of state, the Mathias–Copeman alpha function, the Wong–Sandler mixing rules, and the NRTL model.     

A Matrix-Valued Point Interactions Model

We study a matrix-valued Schrödinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that, away from a discrete set, its Lyapunov exponents do not vanish. For this we use a criterion by Gol’dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer matrices. Then we prove estimates on the transfer matrices which lead to the Hölder continuity of the Lyapunov exponents. After proving the existence of the integrated density of states of the operator, we also prove its Hölder continuity by proving a Thouless formula which links the integrated density of states to the sum of the positive Lyapunov exponents.     

EPR, NMR, and Thermodynamic Evidences for Forced Nuclear Spin–Electron Spin Interactions in the Case of 1-Phenyl-2-Methylpropyl-1,1-Dimethyl-2-Nitroxide (TIPNO) Attached to Permethylated β-Cyclodextrin

In a recent paper (Bardelang et al. in J Org Chem 71:7657–7667, 2006), the deep inclusion of the TIPNO (1-phenyl-2-methylpropyl-1,1-dimethylethyl-2-nitroxide) free radical attached to a permethylated β-cyclodextrin (TRIMEB) into its cavity was questioned. In the present paper it is shown that the results of X-band and W-band electron paramagnetic resonance (EPR) and ¹H nuclear magnetic resonance (NMR) studies of the TIPNO–TRIMEB in the presence of competitors of complexation (1-adamantanol, methyl orange and 1-adamantylamine) are consistent with a situation where the nitroxide is capping the small cavity entrance. The inclusion of the incoming guest was proven by ¹H NMR, whereas no changes in EPR spectra were noticed whatever the competitors’ concentrations. These observations are rationalized in terms of an equilibrium between a nitroxide-capped cyclodextrin (weak complex) and a non-self included form, both species involving competitors’ inclusion without significant EPR spectral changes. These results not only confirm our preliminary findings, but also point out to the peculiar role of the cyclodextrin methoxy crown of the primary rim stabilizing the appended guest by means of weak interactions.     

Localization for a Matrix-valued Anderson Model

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schrödinger operators, acting on $L^2(\mathbb R)\otimes \mathbb C^NWe study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr?dinger operators, acting on , for arbitrary N ≥ 1. We prove that, under suitable assumptions on the Fürstenberg group of these operators, valid on an interval , they exhibit localization properties on I, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the Fürstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters.      

Preconcentration of Rare Earth Elements in Seawater with Chelating Resin Having Fluorinated β‐Diketone Immobilized on Styrene Divinyl Benzene for their Determination by ICP‐OES

An analytical method has been developed for the preconcentration of rare earth elements (REEs) in seawater for their determination by inductively coupled plasma optical emission spectrometry (ICP‐OES). An indigenously synthesized chelating resin was used for the preconcentration of (REEs) which was based on immobilization of fluorinated β‐diketone group on solid support styrene divinyl benzene. Sample solutions (adjusted to optimized pH) were passed through a polyethylene column packed with 250 mg of the resin. Experimental conditions consisting of pH, sample flow rate, sample volume and eluent concentration were optimized. The established method has been applied for the preconcentration of light, medium and heavy REEs in coastal sea water samples for their subsequent determination by (ICP‐OES). Percentage recoveries of La, Ce, Nd, Sm, Eu, Gd, Dy, Er, Yb and Lu were ≥ 95%, a preconcentration factor of 200 times, and relative standard deviations < 5% were achieved.     

Naupliolide, a sesquiterpene lactone with a novel tetracyclic skeleton from Nauplius graveolens subsp. odorus

The aerial parts of Nauplius graveolens subsp. odorus (Schousb) Wikl. afforded a novel sesquiterpene lactone (1) named naupliolide together with the known 6,7,9,10-tetradehydroasteriscanolide 2 and asteriscunolides A-D 3a-d. The structure of compound 1 corresponds to a novel skeleton of 14,15-dimethyl-7,13-dioxotricyclic[6.4.0.0^9,11]dodeca-12,13-olide, and was established on the basis of spectroscopic methods including 2D-NMR. The coexistence of naupliolide 1 together with the structurally related sesquiterpene lactones asterisculolides A-D (3a-d) and 6,7,9,10-tetradehydroasteriscanolide 2, seems to indicate their biosynthetic relationship.     

A new fractional analytical approach via a modified Riemann–Liouville derivative

This work suggests a new analytical technique called the fractional homotopy perturbation method (FHPM) for solving fractional differential equations of any fractional order. This method is based on He’s homotopy perturbation method and the modified Riemann–Liouville derivative. The fractional differential equations are described in Jumarie’s sense. The results from introducing a modified Riemann–Liouville derivative in the cases studied show the high accuracy, simplicity and efficiency of the approach.