Nonlocal boundary value problems for discrete systems

Our goal in this paper is to provide sufficient conditions for the existence of solutions to discrete, nonlinear systems subject to multipoint boundary conditions. The criteria we present depends on the size of the nonlinearity and the set of solutions to the corresponding linear, homogeneous boundary value problems. Our analysis is based on the Lyapunov–Schmidt Procedure and Brouwer?s Fixed Point Theorem. The results presented extend the previous work of D. Etheridge and J. Rodríguez (1996, 1998) [5], [6] and J. Rodríguez and P. Taylor (2007) [18], [19].     

Thermal degradation of copolymers from vinyl acetate and vinyl alcohol

The thermal degradation of poly(vinyl acetate) (PVA), poly(vinyl alcohol) (PVAL), vinyl acetate-vinyl alcohol (VAVAL), vinyl acetate-vinyl-3,5-dinitrobenzoate (VAVDNB) and vinyl alcohol-3,5-dinitrobenzoate (VALVDNB) copolymers have been studied using differential thermal analysis (DTA) and thermogravimetry (TG) under isothermal and dynamic conditions in nitrogen. Thermal analysis indicates that PVA and PVAL are thermally more stable than VAVAL copolymers, being PVAL the most stable polymer. The presence of small amounts of vinyl-3,5-dinitrobenzoate (VDNB) in PVA or PVAL produces a marked decrease in the thermal stability of both homopolymers, being VALVDNB copolymers the less stable materials. The apparent activation energy of the degradative process was determined by the Kissinger and Flynn-Wall methods which agree well.     

Rapid capillary zone electrophoresis method for the determination of metal cations in beverages

A rapid and reliable capillary zone electrophoresis method for the determination of inorganic cations was developed. The complete separation of K⁺, Ba²⁺, Ca²⁺, Na⁺, Mg²⁺, Mn²⁺, Ni²⁺, Cd²⁺, Li⁺ and Cu²⁺ can be achieved in 4 min with a simple electrolyte composed by 10 mM imidazole as the carrier buffer and background absorbance provider and acetic acid as the complexing agent (pH 3.60). Injection was performed hydrostatically by elevating the sample at 10 cm for 30 s. The running voltage was +25 kV at room temperature. Indirect UV-absorption detection was achieved at 185 nm. The detection limit was in the range between 0.06 mg/l (Mg²⁺) and 0.57 mg/l (K⁺) and the quantification limits ranged from 0.10 mg/l (Ni²⁺) to 0.80 mg/l (Cu²⁺). The calibration graphs were linear in the concentration range from the quantification limit till at least 1 g/l in K⁺, 10 mg/l in Ba²⁺, Ca²⁺, Mg²⁺, Mn²⁺, Ni²⁺ and Cd²⁺, 40 mg/l in Na⁺ and 12 mg/l in Li⁺ and Cu²⁺. The repeatability, intraday and interday analysis were ≤1.55% and ≤3.64% for migration time and ≤3.38% and ≤3.63% for peak area. The method developed has been applied to several beverage samples with only a simple dilution and filtration treatment of the sample. The proposed method is simple, fast, cheap and it is achieved with common products in either laboratory. For these reasons, it is a very useful method for routine analysis.     

Determination of selected non-authorized insecticides in peppers by liquid chromatography time-of-flight mass spectrometry and tandem mass spectrometry

In this work, two analytical methods based on liquid chromatography coupled to electrospray time-of-flight mass spectrometry (LC/ESI-TOFMS) and tandem mass spectrometry (LC/ESI-MS/MS) are described for the identification, confirmation and quantitation of three insecticides non-authorized in the European Union (nitenpyram, isocarbophos and isofenphos-methyl) but detected in recent monitoring programmes in pepper samples. The proposed methodologies involved a sample extraction procedure using liquid-liquid partition with acetonitrile followed by a cleanup step based on dispersive solid-phase extraction. Recovery studies performed on peppers spiked at different fortification levels (10 and 50 microg kg(-1)) yielded average recoveries in the range 76-100% with relative standard deviation (RSD) (%) values below 10%. Identification, confirmation and quantitation were carried out by LC/TOFMS and LC/MS/MS using a hybrid triple quadrupole linear ion trap (QqLIT) instrument in multiple-reaction monitoring (MRM) mode. The obtained limits of quantitation (LOQs) were in the range 0.1-5 microg kg(-1), depending on each individual technique. Finally, the proposed methods were successfully applied to the analysis of suspected pepper samples.     

Structure and vibrational spectra of Ti(IV) hydroxides and their clusters with expanded titanium coordination. DFT study

Equilibrium structures of H(4-n)Ti(OH)n (n = 2-4) molecules and the Ti(OH)4 dimer and trimers were optimized at the B3LYP level of theory. Theoretical vibrational frequencies of TiO stretching modes obtained with several basis sets were compared with the existing experimental frequencies of these vibrations, and the 6-31+G(d) set was chosen for cluster calculations. Only one energy minimum was found for the [Ti(OH)4](2) dimer, but two isomers without symmetry elements stabilized by internal hydrogen bonds and two isomers, belonging to C(s) and C(i) point groups, with free OH groups were found as minima at the [Ti(OH)4](3) potential energy surface. The structure with the linear arrangement of hexacoordinated titanium atoms in the Ti3O12 skeleton may be proposed for trimeric species observed in liquid titanium alkoxides as the only structure satisfying experimental spectroscopic evidence about the presence of center of inversion in these species. Frequency changes of TiO4 modes which accompany the oligomer formation are predicted and discussed.     

Unexpected ferromagnetic interaction in a new tetranuclear copper(II) complex: synthesis, crystal structure, magnetic properties, and theoretical studies

The new tetranuclear carbonate complex [Cu2L)2(CO3)] x 8H2O (1 x 8H2O) (H3L = (2-(2-hydroxyphenyl)-1,3-bis[4-(2-hydroxyphenyl)-3-azabut-3-enyl]-1,3-imidazolidine) has been obtained by two different synthetic routes and fully characterized. Recrystallization of 1 x 8H2O in methanol yields single crystals of {[(Cu2L)2(CO3)]}2 x 12H2O (1 x 6H2O), suitable for X-ray diffraction studies. The crystal structure of 1 x 6H2O shows two crystallographically different tetranuclear molecules in the asymmetric unit, 1a and 1b. Both molecules can be understood as self-assembled from two dinuclear [Cu2L]+ cations, joined by a mu4-eta(2):eta(1):eta(1) carbonate ligand. The copper atoms of each crystallographically different [(Cu2L)2(CO3)] molecule present miscellaneous coordination polyhedra: in both 1a and 1b, two metal centers are in square pyramidal environments, one displays a square planar chromophore and the other one has a geometry that can be considered as an intermediate between square pyramid and trigonal bipyramid. Magnetic studies reveal net intramolecular ferromagnetic coupling between the metal atoms. Density functional calculations allow the assignment of the different magnetic coupling constants and explain the unexpected ferromagnetic behavior, because of the presence of an unusual NCN bridging moiety and countercomplementarity of the phenoxo (or carbonate) and NCN bridges.     

H-abstraction is more efficient than cis-trans isomerization in (4-methylcyclohexylidene) fluoromethane. An ab initio molecular dynamics study

Non-adiabatic molecular dynamics simulations have been performed in the fluoro-olefin (4-methylcyclohexylidene) fluoromethane (4MCF) using multiconfigurational CASSCF (complete active space self-consistent field) on-the-fly calculations. As an olefin containing a C[double bond, length as m-dash]C double bond, 4MCF is expected to undergo cis-trans isomerization after light irradiation. However, ab initio molecular dynamics shows that a preferential dissociation of atomic hydrogen is taking place after population transfer to the bright ππ* state. This state is strongly mixed with πσ* states allowing dissociation in the electronic excited state before deactivation to the ground state occurs. A minor amount of trajectories experiences F-dissociation, followed by pyramidalization at the sp(2) carbons and CHF dissociation. In contrast, the amount of trajectories undergoing torsion around the double bond, and therefore cis-trans isomerization, is marginal. The H-abstraction reaction is ultrafast, taking place in less than 60 fs.     

Transformations of diphenylphosphinothioic acid tertiary amides mediated by directed ortho metallation

ortho-Lithiation of N,N-diisopropyl-P,P-diphenylphosphinothioic amide using n-BuLi in the presence of TMEDA in diethyl ether followed by electrophilic trapping is described as an efficient method for the synthesis of ortho-functionalised derivatives in high yields. The structural modification of the phosphinothioic amide includes C-X (X = P, S, Si, Sn, I) and C-C bond forming reactions with a large variety of electrophiles. Additional applications based on functional group transformations are also reported. They include imine formation, desulfurization and Suzuki cross-coupling reactions on selected compounds.     

A non-adiabatic quantum-classical dynamics study of the intramolecular excited state hydrogen transfer in ortho-nitrobenzaldehyde

Ab initio surface-hopping dynamics calculations have been performed to simulate the intramolecular excited state hydrogen transfer dynamics of ortho-nitrobenzaldehyde (o-NBA) in the gas phase from the electronic S(1) excited state. Upon UV excitation, the hydrogen is transferred from the aldehyde substituent to the nitro group, generating o-nitrosobenzoic acid through a ketene intermediate. The semiclassical propagations show that the deactivation from the S(1) is ultrafast, in agreement with the experimental measurements, which detect the ketene in less than 400 fs. The trajectories show that the deactivation mechanism involves two different conical intersections. The first one, a planar configuration with the hydrogen partially transferred, is responsible for the branching between the formation of a biradical intermediate and the regeneration of the starting material. The conversion of the biradical to the ketene corresponds to the passage through a second intersection region in which the ketene group is formed.     

Conformational flexibility of a synthetic glycosylaminoglycan bound to a fibroblast growth factor. FGF-1 recognizes both the (1)C(4) and (2)S(O) conformations of a bioactive heparin-like hexasaccharide

The first direct NMR determination of the conformation of a conformationally flexible heparin-like hexasaccharide bound to a key receptor, FGF-1, is described. The determination has been based on the use of a 13C-labeled protein and a regular 12C sugar. FGF-1 recognizes several conformations of the iduronic moieties of the hexasaccharide. Therefore, this case is different than that described for the controversial recognition of heparin-like saccharides by AT-III, which seems to recognize just one conformation of the iduronic acid residues.