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.     

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.     

Zero‐Hopf bifurcation in the FitzHugh–Nagumo system

We characterize the values of the parameters for which a zero‐Hopf equilibrium point takes place at the singular points, namely, O (the origin), P₊, and P_? in the FitzHugh–Nagumo system. We find two two‐parameter families of the FitzHugh–Nagumo system for which the equilibrium point at the origin is a zero‐Hopf equilibrium. For these two families, we prove the existence of a periodic orbit bifurcating from the zero‐Hopf equilibrium point O. We prove that there exist three two‐parameter families of the FitzHugh–Nagumo system for which the equilibrium point at P₊ and at P_? is a zero‐Hopf equilibrium point. For one of these families, we prove the existence of one, two, or three periodic orbits starting at P₊ and P_?. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Harnessing Electron Transfer from the Perchlorotriphenylmethide Anion to Y@C82(C2v) to Engineer an Endometallofullerene‐Based Salt

We show that electron transfer from the perchlorotriphenylmethide anion (PTM^?) to Y@C₈₂(C_2v) is an instantaneous process, suggesting potential applications for using PTM^? to perform redox titrations of numerous endohedral metallofullerenes. The first representative of a Y@C₈₂‐based salt containing the complex cation was prepared by treating Y@C₈₂(C_2v) with the [K⁺([18]crown‐6)]PTM^? salt. The synthesis developed involves the use of the [K⁺([18]crown‐6)]PTM^? salt as a provider of both a complex cation and an electron‐donating anion that is able to reduce Y@C₈₂(C_2v). For the first time, the molar absorption coefficients for neutral and anionic forms of the pure isomer of Y@C₈₂(C_2v) were determined in organic solvents with significantly different polarities.     

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.