The converse Lyapunov’s theorem for ODEs of Carathéodory type

The converse problem of Lyapunov stability for systems of ODEs of Caratheodory type is considered. It is proved that if the right hand side of an ODE satisfies only the Osgood condition, the uniform stability of the origin is sufficient to the existence of a locally Lipschitz continuous Lyapunov function. Actually, the uniform stability is equivalent to the robust stability in this case. Moreover, as an auxiliary result, the generalization of the famous Gronwall-Bellman-Bihari inequality is also proved.     

Pupil detection and tracking for analysis of fixational eye micromovements

Even with fixed gaze, the human eye is under steady motion (tremor micosaccades and drifts). Detection of these movements requires of invasive techniques or expensive devices with sophisticated detection methods. In this paper we present a technique for pupil segmentation and contour analysis which will provide valuable information about fixational eye movements. The method is based on fitting an ellipse to the pupil contour. Pupillary hippus, microsaccades and drifts are obtained as well as cyclotorsional movements. The method is simple and the experimental requirements are easily available since just a biomicroscope and a digital videocamera are required.     

Femtosecond pulsed laser deposition of nanostructured TiO2 films

Nanostructured deposits of TiO₂ were grown on Si (1 0 0) substrates by laser ablating a TiO₂ sintered target in vacuum or in oxygen using a Ti:sapphire laser delivering 80 fs pulses. The effect of the laser irradiation wavelength on the obtained nanostructures, was investigated using 800, 400 and 266 nm at different substrate temperatures and pressures of oxygen. The composition of the deposits was characterized using X-ray photoelectron spectroscopy (XPS) and the surface morphology was studied by environmental scanning electron microscopy (ESEM) and atomic force microscopy (AFM). Deposits are absent of microscopic droplets in all conditions explored. The best deposits, constituted by nanoparticles of an average diameter of 30 nm with a narrow size distribution, were obtained at the shorter laser wavelength of 266 nm under vacuum at substrate room temperature.     

Looking for the optimal DTI acquisition scheme given a maximum scan time: are more b-values a waste of time?

In this study we used simulated data to investigate how valuable the use of multiple b-values is, in terms of improving the accuracy and reproducibility of Diffusion Tensor Imaging (DTI) results. Our results show that the systematic bias of the estimated scalar diffusion parameters [apparent diffusion coefficient and fractional anisotropy (FA)] - due to the Rician distribution of magnetic resonance noise - can be minimized by increasing the number of b-values and not by increasing the number of sampling directions. In addition, the use of more than one b-value accounts better for the wide range of diffusivities found in the human brain by bringing closer together the FA estimates for fibres with different mean diffusivities. It is also shown that while for tractography studies we should use as many sampling directions as allowed by scan time limitations, for follow-up, intersubject or multicenter studies, the use of more than one b-value will improve the accuracy of the scalar diffusion parameters, as long as the minimum number of directions required for robust estimation of each parameter is still used.     

On the Existence of Traveling Waves in the 3D Boussinesq System

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.     

Cu(II)-imprinted styrene-divinylbenzene beads as a new sorbent for flow injection-flame atomic absorption determination of copper

The paper reports preparation and analytical features of a new Cu(II)-imprinted polymer, based on salen-OMe ligand 2,2′-[ethane-1,2-diylbis(nitrilo(E)methylylidene)]bis(6-allyl-4-methoxyphenol) and styrene-divinylbenzene matrix, as well as its application to on-line preconcentration and flame atomic absorption determination of copper. Sorbent beads (average diameter of 60-80 µm) were obtained using suspension polymerization technique and employed as a column filling. Copper sorption was the most effective at pH 6.8, whereas the highest elution effectiveness was observed when 0.5% HNO₃ was applied. The sorbent exhibited good long-term stability and acid resistance. Enrichment factor (EF) of 12 was found for 60 s loading time and loading flow rate of 4 mL min^− 1. EF value may be further increased by expanding the loading time and/or flow rate. Batch sorbent capacity in optimal pH conditions was found to be 0.16 mmol g^− 1 (9.55 mg g^− 1) of a dry polymer. Calcium(II) turned out to be the only significant interferent. Cadmium(II), silver(I), nickel(II), zinc(II) in concentrations lower than about 1 mg L^− 1 did not disturb copper(II) preconcentration. Different calibration methods such as: set of standards method (SSM), standard addition method (SAM) and combinatory calibration method (CCM) were employed for copper(II) determination in tap water, spring mineral water and certified reference material. Analysis of EU-H-3 reference material confirmed good accuracy of the proposed method. Relative standard deviation (RSD) was 3.2 for standard addition method and 2.8% for set of standard calibration method. Detection limit for sample consumption 16 mL was 1.03 and 1.07 µgL^-1 respectively.     

New polyacrylate-based lead(II) ion-selective electrodes

A novel polyacrylate-based matrix for potentiometric ion-selective electrodes has been developed. Isododecyl acrylate, acrylonitrile and hexanedioldiacrylate co-monomers along with the thermo-initiator 2,2-dimethoxy-2-phenylacetophenone were used as polymeric matrix components. A lead(II)-selective electrode (Pb-ISE) was constructed using the above matrix. The electrode showed comparable analytical performance in the micromolar range to Pb-ISEs with conventional poly(vinyl chloride)-based membranes containing neutral ionophore and with solid-state membranes containing a mixture of lead sulphide and silver sulphide. Electrochemical impedance spectroscopy studies revealed much lower ion mobility in the polyacrylate membrane than in plasticized poly(vinyl chloride) membranes. This result additionally indicates the possibility of obtaining a lower detection limit for ISEs using the new acrylate matrix.     

Lewis Base Behavior of Bridging Nitrido Ligands of Titanium Polynuclear Complexes

The Lewis base behavior of μ₃‐nitrido ligands of the polynuclear titanium complexes [{Ti(η⁵‐C₅Me₅)(μ‐NH)}₃(μ₃‐N)] ( 1 ) and [{Ti(η⁵‐C₅Me₅)}₄(μ₃‐N)₄] ( 2 ) to MX Lewis acids has been observed for the first time. Complex 1 entraps one equivalent of copper(I ) halide or copper(I ) trifluoromethanesulfonate through the basal NH imido groups to give cube‐type adducts [XCu{(μ₃‐NH)₃Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}] (X=Cl ( 3 ), Br ( 4 ), I ( 5 ), OSO₂CF₃ ( 6 )). However, the treatment of 1 with an excess (≥2 equiv) of copper reagents afforded complexes [XCu{(μ₃‐NH)₃Ti₃(η⁵‐C₅Me₅)₃(μ₄‐N)(CuX)}] (X=Cl ( 7 ), Br ( 8 ), I ( 9 ), OSO₂CF₃ ( 10 )) by incorporation of an additional CuX fragment at the μ₃‐N nitrido apical group. Similarly, the tetranuclear cube‐type nitrido derivative 2 is capable of incorporating one, two, or up to three CuX units at the μ₃‐N ligands to give complexes [{Ti(η⁵‐C₅Me₅)}₄(μ₃‐N)_4?n{(μ₄‐N)CuX}_n] (X=Br ( 11 ), n=1; X=Cl ( 12 ), n=2; X=OSO₂CF₃ ( 13 ), n=3). Compound 2 also reacts with silver(I ) trifluoromethanesulfonate (≥1 equiv) to give the adduct [{Ti(η⁵‐C₅Me₅)}₄(μ₃‐N)₃{(μ₄‐N)AgOSO₂CF₃}] ( 14 ). X‐ray crystal structure determinations have been performed for complexes 8 – 13 . Density functional theory calculations have been carried out to understand the nature and strength of the interactions of [{Ti(η⁵‐C₅H₅)(μ‐NH)}₃(μ₃‐N)] ( 1′ ) and [{Ti(η⁵‐C₅H₅)}₄(μ₃‐N)₄] ( 2′ ) model complexes with copper and silver MX fragments. Although coordination through the three basal NH imido groups is thermodynamically preferred in the case of 1′ , in both complexes the μ₃‐nitrido groups act as two‐electron donor Lewis bases to the appropriate Lewis acids.     

Unprecedented Solvent‐Assisted Reactivity of Hydrido W3CuS4 Cubane Clusters: The Non‐Innocent Behaviour of the Cluster‐Core Unit

Opening the cluster core : Substitution of the chloride ligand in the novel cationic cluster [W₃CuS₄H₃Cl(dmpe)₃]⁺ (see figure; dmpe=1,2‐bis(dimethylphosphino)ethane) by acetonitrile is promoted by water addition. Kinetic and density functional theory studies lead to a mechanistic proposal in which acetonitrile or water attack causes the opening of the cluster core with dissociation of one of the Cu? S bonds to accommodate the entering ligand.