Smoothing of rational m-ropes

In a recent paper, Gallego, González and Purnaprajna showed that rational 3-ropes can be smoothed. We generalise their proof, and obtain smoothability of rational m-ropes for m ≥ 3.     

Rapid and efficient method for the quantification of lychnopholide in rat plasma by liquid chromatography–tandem mass spectrometry for pharmacokinetic application

Lychnopholide is a sesquiterpene lactone usually obtained from Lychnophora and Eremanthus species and has pharmacological activities that include anti‐inflammatory and anti‐tumor. Lychnopholide isolated from Eremanthus matogrossenssis was analyzed in this study. The aims of this study were to develop and validate an analytical methodology by LC‐MS/MS and to quantify lychnopholide in rat plasma. Chromatographic separation was achieved on a C₁₈ column using isocratic elution with the mobile phase consisting of methanol and water (containing 0.1% formic acid) at a flow rate of 0.4 mL/min. The detection was performed in multiple‐reaction monitoring mode using electrospray ionization in positive mode. The method validation was performed in accordance with regulatory guidelines and the results met the acceptance criteria. The linear range of detection was 10–200 ng/mL (r > 0.9961). The intra‐ and inter‐day assay variability were <6.2 and <11.7%, respectively. The extraction recovery was approximately 63% using liquid–liquid extraction with chloroform. Lychnopholide was detected in plasma up to 60 min after intravenous administration in rats. This rapid and sensitive method for the analysis of the sesquiterpene lactone lychnopholide in rat plasma can be applied to pharmacokinetic studies of this compound. Copyright © 2016 John Wiley & Sons, Ltd.     

A Few Remarks About the Hilbert Scheme of Smooth Projective Curves

We discuss two conjectures by Francesco Severi and Joe Harris about the irreducibility and the dimension of the Hilbert scheme parameterizing smooth projective curves of given degree and genus.     

A Jahn–Teller analysis of K3 and Rb3 in the electronic states 1E′ and 1E″

The potential energy surfaces (PES) of the Jahn–Teller distorted doublet 1²E′ (1B₂/1A₁) ground state and 1²E″ (2B₁/1A₂) excited state of alkali metal trimers (K₃, Rb₃) are studied with three high-level computational chemistry methods whose results are compared: single-reference coupled cluster, equation-of-motion coupled cluster and multi-reference second-order Rayleigh–Schrödinger perturbation theory. The doubly degenerate E electronic state interacts with the twofold degenerate vibrational e mode. We use the E ⊗ e Jahn–Teller effect theory to analyze in detail one- and two-dimensional cuts of the PES as a function of the symmetry-adapted internal coordinates Q_s, Q_x and Q_y and we extract the associated Jahn–Teller parameters. Spin-orbit coupling is accounted for by means of the Effective-Core-Potential-LS technique and spin-orbit splitting constants are extracted. We also provide the geometries, the binding energies and tentative vibronic spectra for the 1²E″ ← 1²E′ transitions.     

Thermodynamics of Hydrogen Adsorption on Metal‐Organic Frameworks

Interaction between adsorbed hydrogen and the coordinatively unsaturated Mg²⁺ and Co²⁺ cationic centres in Mg‐MOF‐74 and Co‐MOF‐74, respectively, was studied by means of variable‐temperature infrared (VTIR) spectroscopy. Perturbation of the H₂ molecule by the cationic adsorbing centre renders the H? H stretching mode IR‐active at 4088 and 4043 cm^?1 for Mg‐MOF‐74 and Co‐MOF‐74, respectively. Simultaneous measurement of integrated IR absorbance and hydrogen equilibrium pressure for spectra taken over the temperature range of 79–95 K allowed standard adsorption enthalpy and entropy to be determined. Mg‐MOF‐74 showed ΔH⁰=?9.4 kJ mol^?1 and ΔS⁰=?120 J mol^?1 K^?1, whereas for Co‐MOF‐74 the corresponding values of ΔH⁰=?11.2 kJ mol^?1 and ΔS⁰=?130 J mol^?1 K^?1 were obtained. The observed positive correlation between standard adsorption enthalpy and entropy is discussed in the broader context of corresponding data for hydrogen adsorption on cation‐exchanged zeolites, with a focus on the resulting implications for hydrogen storage and delivering.     

Thermodynamics of Carbon Dioxide Adsorption on the Protonic Zeolite H‐ZSM‐5

Adsorption of carbon dioxide on H‐ZSM‐5 zeolite (Si:Al=11.5:1) was studied by means of variable‐temperature FT‐IR spectroscopy, in the temperature range of 310–365 K. The adsorbed CO₂ molecules interact with the zeolite Brønsted‐acid OH groups bringing about a characteristic red‐shift of the O? H stretching band from 3610 cm^?1 to 3480 cm^?1. Simultaneously, the ν₃ mode of adsorbed CO₂ is observed at 2345 cm^?1. From the variation of integrated intensity of the IR absorption bands at both 3610 and 2345 cm^?1, upon changing temperature (and CO₂ equilibrium pressure), the standard adsorption enthalpy of CO₂ on H‐ZSM‐5 is ΔH⁰=?31.2(±1) kJ mol^?1 and the corresponding entropy change is ΔS⁰=?140(±10) J mol^?1 K^?1. These results are discussed in the context of available data for carbon dioxide adsorption on other protonic, and also alkali‐metal exchanged, zeolites.     

Sulphur speciation of PM10 samples by XANES spectroscopy

Sulphur K-edge X-ray absorption near edge structure (XANES) spectroscopy was used to identify sulphur compounds in PM10 samples collected simultaneously at two sites with different environmental situations in the province of Trieste (NE of Italy), during summer and winter seasons respectively. The first site is an industrial site located near a steel mill plant and the second is a coastal site. The sulphur speciation at the industrial site has shown the presence of the following sulphur compounds in both seasons: organic compounds (thiophenes or Polycyclic Aromatic Sulphur Heterocycles — PAHs) and sulphates while in the winter season sulphites were also present. In the coastal site organic compounds (thiophenes or PASHs) and sulphate were found during winter season, moreover bisulphates were found during summer season. Relative percentages of the different sulphur compounds have shown that sulphate is the most abundant form of sulphur in the industrial site samples during both seasons and in the coastal site sample collected during the winter season (> 98%); in the coastal site sample collected during the summer season the relative percentages of bisulphate and sulphate were around 40% and 60% respectively.      

Qregularity and an extension of the Evans-Griffiths criterion to vector bundles on quadrics

Here we define the concept of Qregularity for coherent sheaves on a smooth quadric hypersurface Q_n⊂Pⁿ⁺¹. In this setting we prove analogs of some classical properties. We compare the Qregularity of coherent sheaves on Q_n with the Castelnuovo-Mumford regularity of their extension by zero in Pⁿ⁺¹. We also classify the coherent sheaves with Qregularity −∞. We use our notion of Qregularity in order to prove an extension of the Evans-Griffiths criterion to vector bundles on quadrics. In particular, we get a new and simple proof of Knörrer’s characterization of ACM bundles.     

Metal-directed self-assembly of cavitand frameworks

The self-assembly between bidentate cavitand ligands and mono/dinuclear metal precursors to give cavitand frameworks has been explored. For this purpose, two new cavitands bearing AB and AC phenylpyridyl moieties at the upper rim have been synthesized. A series of self-assembled molecular dimers featuring fac-Re(CO)(3)Br as metal corners have been prepared and characterized. Two possible dimeric structures (C-shaped and S-shaped) are possible when AB cavitand 2 is used in the self-assembly reaction; only one is obtained in the case of AC cavitand 3. In addition, the self-assembly of AB-dibridged cavitand 2 with dinuclear Pd/Pt metal precursors 5a and 5b has been studied. At this level of complexity, the self-assembly can lead to more than one structure. Several different final structures have been envisioned and their formation analyzed in silico and in solution. Out of the three possible cyclic structures (dimer, trimer, and tetramer), only the entropically favored dimer 6a (6b) is formed, as predicted from molecular modeling and demonstrated by PGSE NMR experiments.