Intersections of polynomial orbits, and a dynamical Mordell–Lang conjecture

We prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection, then the polynomials have a common iterate. We also prove a special case of a conjectured dynamical analogue of the Mordell–Lang conjecture. Mathematics Subject Classification (1991) Primary 14G25; Secondary 37F10, 11C08     

Unusual structures in some alkyl cyanoterphenyls

The phase behaviour of three alkyl cyanoterphenyls has been investigated with the particular objective of elucidating their unusual phase behaviour and determining the structure of the new, and so far uncharacterized, phase (E') appearing between the smectic A_d and the crystal E' phases. In the course of this work complications arose from the appearance of yet another phase which appears only on cooling but for which no characteristic X-ray diffraction pattern could be obtained. The E phase appears to have the orthorhombic symmetry characteristic of the E phase but has a complex temperature dependent packing in the c direction. This is driven by the competition between a density wave and an antiferroelectric pair ordering which results in a locked-in structure with a periodicity of three times that of the underlying density wave.     

Solution self-assembly and adsorption at the air-water interface of the monorhamnose and dirhamnose rhamnolipids and their mixtures

The self-assembly in solution and adsorption at the air-water interface, measured by small-angle neutron scattering, SANS, and neutron reflectivity, NR, of the monorhamnose and dirhamnose rhamnolipids (R1, R2) and their mixtures, are discussed. The production of the deuterium-labeled rhamnolipids (required for the NR studies) from a Pseudomonas aeruginosa culture and their separation into the pure R1 and R2 components is described. At the air-water interface, R1 and R2 exhibit Langmuir-like adsorption isotherms, with saturated area/molecule values of about 60 and 75 ?(2), respectively. In R1/R2 mixtures, there is a strong partitioning of R1 to the surface and R2 competes less favorably because of the steric or packing constraints of the larger R2 dirhamnose headgroup. In dilute solution (<20 mM), R1 and R2 form small globular micelles, L(1), with aggregation numbers of about 50 and 30, respectively. At higher solution concentrations, R1 has a predominantly planar structure, L(α) (unilamellar, ULV, or bilamellar, BLV, vesicles) whereas R2 remains globular, with an aggregation number that increases with increasing surfactant concentration. For R1/R2 mixtures, solutions rich in R2 are predominantly micellar whereas solutions rich in R1 have a more planar structure. At an intermediate composition (60 to 80 mol % R1), there are mixed L(α)/L(1) and L(1)/L(α) regions. However, the higher preferred curvature associated with R2 tends to dominate the mixed R1/R2 microstructure and its associated phase behavior.     

Nitrous oxide dimer: a new potential energy surface and rovibrational spectrum of the nonpolar isomer

The spectrum of nitrous oxide dimer was investigated by constructing new potential energy surfaces using coupled-cluster theory and solving the rovibrational Schro?dinger equation with a Lanczos algorithm. Two four-dimensional (rigid monomer) global ab initio potential energy surfaces (PESs) were made using an interpolating moving least-squares (IMLS) fitting procedure specialized to describe the interaction of two linear fragments. The first exploratory fit was made from 1646 CCSD(T)/3ZaP energies. Isomeric minima and connecting transition structures were located on the fitted surface, and the energies of those geometries were benchmarked using complete basis set (CBS) extrapolations, counterpoise (CP) corrections, and explicitly correlated (F12b) methods. At the geometries tested, the explicitly correlated F12b method produced energies in close agreement with the estimated CBS limit. A second fit to 1757 data at the CCSD(T)-F12b/VTZ-F12 level was constructed with an estimated fitting error of less than 1.5?cm(-1). The second surface has a global nonpolar O-in minimum, two T-shaped N-in minima, and two polar minima. Barriers between these minima are small and some wave functions have amplitudes in several wells. Low-lying rovibrational wave functions and energy levels up to about 150?cm(-1) were computed on the F12b PES using a discrete variable representation/finite basis representation method. Calculated rotational constants and intermolecular frequencies are in very close agreement with experiment.     

Synthesis and complexation properties of novel triazoyl-based ferrocenyl ligands

Two new ligand derivatives of ferrocene, namely N-4-[3,5-di-(2-pyridyl)-1,2,4-triazoyl]ferrocene carbimine (L1) and N-4-[3,5-di-(2-pyridyl)-1,2,4-triazoyl]ferrocene carbamide (L2), were synthesised in good yields by reacting the known compound 3,5-di-pyridine-2-yl-[1,2,4]triazol-4-ylamine (1) with ferrocenecarbaldehyde and chlorocarbonyl ferrocene, respectively. The structures of L1 and L2 were determined by X-ray crystallography. The complexation of L1 and L2 with Cu^I, Ag^I, Zn^II and Cd^II was studied by NMR and UV-vis spectroscopies, as well as by electrochemistry, with titrations used to determine metal:ligand stoichiometries. The cyclic voltammograms of L1 and L2 and their respective complexes indicated reversible one-electron transfers corresponding to the Fc^0/+ redox couple (Fc = ferrocene), with formal electrode potentials shifting to more positive values upon metal complexation.     

Selective catch and release of a synthetically useful phosphine ligand

The selective catch and release of the synthetically useful (o-biphenyl)(t-butyl)₂P from basic and non basic compounds, utilizing solid phase supported sulfonic acid sources is demonstrated.     

High-performance liquid chromatographic determination of 4-methylimidazole in sheep plasma and in ammoniated tall fescue hay

A method for 4-methylimidazole (4MI) extraction and quantitation in body fluids and forage samples was developed. The procedures involve ion-pair extraction of the compound with the quantitation done by ion-pair liquid chromatography. The results indicate that this high-performance liquid chromatographic method is sensitive, reproducible and more rapid than others that have been previously used. The mean recovery of 4MI from plasma and tall fescue (Festuca arundinacea) hay samples were above 95 and 85%, respectively. The versatility of the procedure makes it suitable for the determination of 4MI in body fluids and in forage samples.