Transitions to the Fulde-Ferrell-Larkin-Ovchinnikov phases at low temperature in two dimensions

We explore the nature of the transition to the Fulde-Ferrell-Larkin- Ovchinnikov superfluid phases in the low temperature range in two dimensions, for the simplest isotropic BCS model. This is done by applying the Larkin-Ovchinnikov approach to this second order transition. We show that there is a succession of transitions toward ever more complex order parameters when the temperature goes to zero. This gives rise to a cascade with, in principle, an infinite number of transitions. Except for one case, the order parameter at the transition is a real superposition of cosines with equal weights. The directions of these wavevectors are equally spaced angularly, with a spacing which goes to zero when the temperature goes to zero. This singular behaviour in this T = 0 limit is deeply linked to the two-dimensional nature of the problem.     

2-Methoxy-6-oxo-1,4,5,6-tetrahydropyridine-3-carbonitriles: versatile starting materials for the synthesis of libraries with diverse heterocyclic scaffolds

Heterocyclic demonstration libraries for agrochemical screening were prepared from the common intermediates 2-methoxy-6-oxo-1,4,5,6-tetrahydropyridine-3-carbonitriles (1), using standard solution-phase techniques. A total of 18 screening libraries were prepared in good to excellent yields. Several members of these libraries were active in the first level of agrochemical screening, especially in the fungicide screen.     

Algorithmic complexity and entanglement of quantum states

We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its algorithmic complexity.     

Synthesis,structural characterization and cytotoxic activity of organotin derivatives of indomethacin

The synthesis, characterization and cytotoxic properties in vitro of tri‐n‐butyltin 1‐(4‐chlorobenzoyl)‐5‐methoxy‐2‐methyl‐1H‐indole‐3‐acetate ( 1 ), tri‐phenyltin 1‐(4‐chlorobenzoyl)‐5‐methoxy‐2‐methyl‐1H‐indole‐3‐acetate ( 2 ), tetra‐n‐butyltin[bis‐1‐(4‐chlorobenzoyl)‐5‐methoxy‐2‐methyl‐1H‐indole‐3‐acetato]distannoxane ( 3 ) and di‐n‐butyltin bis‐1‐(4‐chlorobenzoyl)‐5‐methoxy‐2‐methyl‐1H‐indole‐3‐acetate ( 4 ) are described. These compounds have been characterized by ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy in solution and ¹¹⁹Sn NMR in the solid state, infrared spectroscopy, elemental analysis and X‐ray diffraction for compound 1 . The growth inhibition effects of compounds 1–4 against the lung adenocarcinoma cell line SK‐LU‐1 as well as the cervical cancer cell line HeLa were determined. Compounds 1 and 2 exhibit cytotoxic activity, whereas compounds 3 and 4 are inactive. Copyright © 2008 John Wiley & Sons, Ltd.     

Suzuki cross‐coupling reaction of aryl and heterocyclic bromides and aromatic polybromides on a Pd(II)‐hydrotalcite catalyst

The Suzuki cross‐coupling reaction of various bromine‐containing substrates and phenylboronic acid in toluene at 90 °C on a Pd(AcO)₂Py₂ catalyst supported on an Mg? Al hydrotalcite, using K₂CO₃ as the base, was studied. The conversion and selectivity results obtained for many of the substrates were excellent and similar to those provided by more active or even homogeneous catalysts. The reactions of aryl polybromides and phenylboronic acid gave the corresponding polyaromatic compounds in variable yields depending on the particular substrate. Arylation occurred in a consecutive manner by substitution of the different Br atoms. ICP‐MS measurements of the palladium content of the catalyst performed prior to and after the reaction revealed that part of the metal is incorporated into the bulk solution; therefore, the catalytic process is not purely heterogeneous. Copyright © 2008 John Wiley & Sons, Ltd.     

Structural and electronic study of neutral,positive, and negative small rhodium clusters [Rhn,Rh, and Rh]

We have carried out a systematic study for the determination of the structure and the fundamental state of neutral and ionic small rhodium clusters [Rh_n, Rh, Rh (n = 5–10)] using ab initio Hartree‐Fock methods with a LANL2DZ basis set. A range of spin multiplicities is studied for each cluster. We present the bond lengths and angles and geometric configuration adopted for the clusters in its minimum energy conformation showing the differences when the clusters have different number of unpaired electrons. In addition, we report the vertical ionization potential and the adiabatic potential calculated by the Koopman's theorem. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2541–2547, 2010     

A multidimensional real Schwarz Lemma for the Hilbert metric

We present a real multidimensional version of the Schwarz Lemma on a bounded convex domain D of ℝ ⁿ endowed with the Hilbert metric. We provide as an application an extension of a Birkhoff’s Theorem on mappings contracting the Hilbert metric.     

Glycosyl-nucleoside fluorinated amphiphiles as components of nanostructured hydrogels

The synthesis of two novel glycosyl-nucleoside fluorinated amphiphiles (GNFs) derived from the 2H,2H,3H,3H-perfluoro-undecanoyl hydrophobic chain is described. The GNF amphiphiles, which feature either β-d-glucopyranosyl or β-d-lactopyranosyl moieties linked to a thymine base via a 1,2,3 triazole linker, were prepared using a ‘double click’ chemistry route. Surface tension measurements, gelation properties, and TEM studies show that GNFs spontaneously assemble into supramolecular structures. Similarly to their hydrocarbon analogues (GNLs), the GNFs have unique gelation properties in water. A minimum hydrogelation concentration of 0.1% (w/w), was determined in the case of the β-d-glucopyranosyl derivative. Cell viability studies indicate that fluorocarbon GNF 5 was not toxic for human cells (Huh7), whereas hydrocarbon analogue GNL is toxic above 100 μm.