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.     

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.     

Competitive ion complexation to polyelectrolytes: determination of the stepwise stability constants. The Ca2+/H+/polyacrylate system

This work presents a new methodology aimed at obtaining the stepwise stability constants corresponding to the binding of ions (or other small molecules) to macromolecular ligands having a large number of sites. For complexing agents with a large number of sites, very simple expressions for the stepwise stability constants arise. Such expressions are model-independent; that is, they allow the determination of the stepwise stability constants without making any previous assumption of the detailed complexation mechanism. The formalism is first presented for a single complexing ion and further extended to competitive systems where the competing ions can display, in general, different stoichiometric relationships. These ideas are applied to the analysis of experimental titrations corresponding to competitive binding of calcium ions to poly(acrylic acid) for different pH values and ionic strengths. Intrinsic stability constants were estimated from the stepwise stability constants (by removing the corresponding statistical factor), and split into specific and electrostatic contributions (by means of the Poisson-Boltzmann equation). After this treatment, the specific proton binding energies showed almost no dependence on the coverage and ionic strength. Likewise, for the range of concentrations studied, the specific component of the intrinsic stability constants of the calcium ions, calculated assuming bidentate binding of Ca to neighboring groups of a linear chain, is almost independent of the calcium and proton coverage and ionic strength.     

Qualitative analysis of phenolic compounds in apple pomace using liquid chromatography coupled to mass spectrometry in tandem mode

The occurrence of phenolic compounds in apple residues resulting from the juice industry was investigated to provide an alternative use for this raw material. For the identification of these compounds, liquid chromatography coupled to ionspray mass spectrometry in tandem mode (LC/MS/MS) with negative ion detection was used. The residues were first extracted and then chromatographed on Sephadex LH-20 to yield 13 fractions. Positive identification of the compounds was based on their retention times and mass spectra in full scan mode (MS), and in different MS/MS modes (product ion scan, precursor ion scan and neutral loss scan). In this way, 60 compounds, including cinnamic and benzoic acid derivatives and flavonoids, were identified, some of them not previously reported in apple waste.