Polynomial,rational and analytic first integrals for a family of 3-dimensional Lotka-Volterra systems

We extend the study of the integrability done by Leach and Miritzis (J Nonlinear Math Phys 13:535–548, 2006) on the classical model of competition between three species studied by May and Leonard (SIAM J Appl Math 29:243–256, 1975), to all real values of the parameters. Additionally, our results provide all polynomial, rational and analytic first integrals of this extended model. We also classify all the invariant algebraic surfaces of these models.     

Iododesilylation of TIPS-, TBDPS-, and TBS-substituted alkenes in connection with the synthesis of amphidinolides B/D

The C-Si bonds of triisopropylsilyl-substituted alkenes, 1,3-dienes, and related multifunctional substrates, as well as analogous C-TBDPS and C-TBS bonds, are readily and chemoselectively cleaved with NIS (or other sources of I(+), such as N-iodosaccharin, 1,3-diodohydantoin, and Ipy(2)BF(4)). The desired iodoalkenes are obtained stereospecifically without byproducts, provided that the reactions are carried out in CF(3)CHOHCF(3) and, in general, with 30 mol % of Ag(2)CO(3) (or AgOAc/2,6-lutidine) as an additive. Fragment C10-C18 of cytotoxic amphidinolides B1-B3 and D has been synthesized using this improved procedure.     

Planar Vector Fields with a Given Set of Orbits

We determine all the \({\mathcal{C}^1}\) planar vector fields with a given set of orbits of the form y ? y(x) = 0 satisfying convenient assumptions. The case when these orbits are branches of an algebraic curve is also study. We show that if a quadratic vector field admits a unique irreducible invariant algebraic curve \({g(x, y) = \sum_{j=0}^S a_j(x) y^{S-j}= 0}\) with S branches with respect to the variable y, then the degree of the polynomial g is at most 4S.     

Negative differential resistance (NDR) in similar molecules with distinct redox behaviour

The transport characterization of self-assembled monolayers (SAMs) based on the closed and open-shell forms of a fully conjugated polychlorotrimethylphenyl (PTM) derivative hybridized with the gold substrate reveals that both systems exhibit negative differential resistance (NDR) in their I-V curves which was attributed to similar resonant tunnelling with unoccupied molecular orbitals. This work demonstrates that distinct transport mechanisms can dominate depending on the bias-voltage applied and shows that NDR processes are not influenced here by the redox character of the molecules.     

Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields

We provide normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian nilpotent centers of linear plus cubic homogeneous planar polynomial vector fields.     

Increasing the isomerisation kinetics of azo dyes by chemical bonding to liquid-crystalline polymers

It is well known that the proper substitution of the azobenzene core allows tuning the thermal cis-to-trans isomerisation kinetics of azo dyes. The thermal isomerisation process of nitro-substituted azobenzenes is accelerated up to 13 times with respect to that in the common isotropic solvents when they are doped in nematic low molar mass liquid crystals. This kinetic acceleration is even stronger when these azo dyes are covalently linked to a nematic siloxane polymer. In this environment, the isomerisation process is accelerated more than 10(3) times. This effect is presented herein for the first time. The possible application of the networks obtained as possible photo-actuators has been also considered.     

Structural and EPR studies on single-crystal and polycrystalline samples of copper(II) and cobalt(II) complexes with N2S2-based macrocyclic ligands

The properties of Cu(II) and Co(II) complexes with oxygen- or nitrogen-containing macrocycles have been extensively studied; however, less attention has been paid to the study of complexes containing sulfur atoms in the first coordination sphere. Herein we present the interaction between these two metal ions and two macrocyclic ligands with N2S2 donor sets. Cu(II) and Co(II) complexes with the pyridine-containing 14-membered macrocycles 3,11-dithia-7,17-diazabicyclo[11.3.1]heptadeca-1(17),13,15-triene (L) and 7-(9-anthracenylmethyl)-3,11-dithia-7,17-diazabicyclo[11.3.1]heptadeca-1(17),13,15-triene (L1) have been synthesized. The X-ray structural analysis of {[Co(ClO4)(H2O)(L)][Co(H2O)2(L)]}(ClO4)3 shows two different metal sites in octahedral coordination. The EPR spectra of powdered samples of this compound are typical of distorted six-coordinated Co(II) ions in a high-spin (S=3/2) configuration, with the ground state being S=1/2 (g1=5.20, g2=3.20, g3=1.95). The EPR spectrum of [Cu(ClO4)(L)](ClO4) was simulated assuming an axial g tensor (g1=g2=2.043, g3=2.145), while that of [Cu(ClO4)(L1)](ClO4) slightly differs from an axial symmetry (g1=2.025, g2=2.060, g3=2.155). These results are compatible with a Cu(II) ion in square-pyramidal coordination with N2S2 as basal ligands. Single-crystal EPR experiment performed on [Cu(ClO4)(L1)](ClO4) allowed determining the eigenvalues of the molecular g tensor associated with the copper site, as well as the two possible orientations for the tensor. On the basis of symmetry arguments, an assignment in which the eigenvectors are nearly along the Cu(II)-ligand bonds is chosen.     

Polynomial, rational and analytic first integrals for a family of 3-dimensional Lotka-Volterra systems

We extend the study of the integrability done by Leach and Miritzis (J Nonlinear Math Phys 13:535–548, 2006) on the classical model of competition between three species studied by May and Leonard (SIAM J Appl Math 29:243–256, 1975), to all real values of the parameters. Additionally, our results provide all polynomial, rational and analytic first integrals of this extended model. We also classify all the invariant algebraic surfaces of these models.     

A synthetic approach to palmerolides via Negishi cross coupling. The challenge of the C15–C16 bond formation

The esterification of fragment C1–C8 (2) with fragment C16–C23 (3) to give iodo derivative 4, followed by a Pd-catalysed coupling with a C9–C15 fragment (7 or 8), may provide a common precursor of most palmerolides. Ligands and reaction conditions were exhaustively examined to perform the C15–C16 bond formation via Negishi reaction. With simple models, pre-activated Pd–Xantphos and Pd–DPEphos complexes were the most efficient catalysts at RT. Zincation of the C9–C15 fragment (8) and cross coupling with 4 required 3 equiv of t-BuLi, 10 mol % of Pd–Xantphos and 60 °C.     

Tetrathiafulvalene‐Based Mixed‐Valence Acceptor–Donor–Acceptor Triads: A Joint Theoretical and Experimental Approach

This work presents a joint theoretical and experimental characterisation of the structural and electronic properties of two tetrathiafulvalene (TTF)‐based acceptor–donor–acceptor triads (BQ–TTF–BQ and BTCNQ–TTF—BTCNQ; BQ is naphthoquinone and BTCNQ is benzotetracyano‐p‐quinodimethane) in their neutral and reduced states. The study is performed with the use of electrochemical, electron paramagnetic resonance (EPR), and UV/Vis/NIR spectroelectrochemical techniques guided by quantum‐chemical calculations. Emphasis is placed on the mixed‐valence properties of both triads in their radical anion states. The electrochemical and EPR results reveal that both BQ–TTF–BQ and BTCNQ–TTF–BTCNQ triads in their radical anion states behave as class‐II mixed‐valence compounds with significant electronic communication between the acceptor moieties. Density functional theory calculations (BLYP35/cc‐pVTZ), taking into account the solvent effects, predict charge‐localised species (BQ ^{. ?}–TTF–BQ and BTCNQ ^{. ?}–TTF–BTCNQ) as the most stable structures for the radical anion states of both triads. A stronger localisation is found both experimentally and theoretically for the BTCNQ–TTF–BTCNQ anion, in accordance with the more electron‐withdrawing character of the BTCNQ acceptor. CASSCF/CASPT2 calculations suggest that the low‐energy, broad absorption bands observed experimentally for the BQ–TTF–BQ and BTCNQ–TTF–BTCNQ radical anions are associated with the intervalence charge transfer (IV‐CT) electronic transition and two nearby donor‐to‐acceptor CT excitations. The study highlights the molecular efficiency of the electron‐donor TTF unit as a molecular wire connecting two acceptor redox centres.