Degree theory forC 1 Fredholm mappings of index 0

We develop a degree theory forC ¹ Fredholm mappings of index 0 between Banach spaces and Banach manifolds. As in earlier work devoted to theC ² case, our approach is based upon the concept of parity of a curve of linear Fredholm operators of index 0. This avoids considerations about Fredholm structures involved in other approaches and leads to a theory as complete as that of Leray-Schauder in a much broader setting. In particular, the well-known possible sign change under homotopy is fully elucidated. The technical difficulty arising withC ¹ versusC ² Fredholm mappings of index 0 is notorious: with onlyC ¹ smoothness, the Sard-Smale theorem is no longer available to handle crucial issues involving homotopy. In this work, this difficulty is overcome by using a new approximation theorem forC ¹ Fredholm mappings of arbitrary index instead of the Sard—Smale theorem when dealing with homotopies.     

Vibrational Spectra and Normal Coordinate Analysis of Diamminediiodidezinc(II) with 15N and 2H Isotopic Substitution.

The Raman and IR. spectra of solid diamminediiodidezinc (II) with ¹⁵N and ²H isotopic substitution have been measured. The spectra have been interpreted assuming C_2v symmetry for the Zn(NH₃)₂I₂ complex structure. The skeletal stretching metal-ligand modes v_s(ZnN), v_as(ZnN), v_s(ZnI), v_as(ZnI) as well as the three bending modes δ(NZnN), δ(IZnI) and δ(IZnN) were assigned by comparison with the spectra of Zn(NH₃)₂C1₂ and Zn(NH₃)₂Br₂, and by the observed isotopic shifts of the frequencies. A normal coordinate analysis for the whole complex was carried out using the Local Symmetry Force Field Model.     

Ionic imprinted polymer for nickel recognition by using the bi-functionalized 5-vinyl-8-hydroxyquinoline as a monomer: Application as a new solid phase extraction support

A new ionic imprinted polymer (IIP) for Ni(II) recognition/pre-concentration was prepared via precipitation polymerization using 2-(diethylamino) ethyl methacrylate (DEM) and divinylbenzene (DVB) as a crosslinking agent in the presence of nickel(II) and 5-vynil-8-hydroxyquinoline (5-VHQ) as a bi-functionalized ligand. An important increase on the selectivity of the synthesised IIP for nickel(II) ions was obtained when comparing to the use of 8-hydroxyquinoline (8-HQ) as a ligand. The synthesised IIP was used as a new support for solid phase extraction (SPE) of nickel(II) from seawater before inductively coupled plasma optical emission spectrometry (ICP-OES) detection. Variables affecting the SPE process, such as pH, load and elution flow rates, and concentration and volume of the eluting solution, were fully evaluated. The optimised procedure consists of a sample loading (100 mL of seawater at a pH of 9.0 ± 0.1) through IIP-SPE cartridges containing 300 mg of the synthesised IIP at a flow rate of 3.0 mL min^{− 1}. Elution was performed by passing 2.5 mL of 2.0 M nitric acid at a flow rate of 1.5 mL min^{− 1}, which gave a pre-concentration factor of 40. The limit of detection (LOD) of the method was 0.26 µg L^{− 1}, while the relative standard deviation (RSD) for eleven replicated measurements was 3%. Accuracy of the method was assessed by analyzing SLEW-3 (estuarine water) and TM-23.3 (lake water) certified reference materials. In addition to the selectivity of the synthesised material for nickel(II) ions against other transition metal ions and major alkaline and alkaline-earth metals (Na⁺, K⁺, Mg²⁺ and Ca²⁺) in seawater, it can be stated that the salt matrix is efficiently removed by using the proposed IIP-SPE procedure.     

Basin topology in dissipative chaotic scattering

Chaotic scattering in open Hamiltonian systems under weak dissipation is not only of fundamental interest but also important for problems of current concern such as the advection and transport of inertial particles in fluid flows. Previous work using discrete maps demonstrated that nonhyperbolic chaotic scattering is structurally unstable in the sense that the algebraic decay of scattering particles immediately becomes exponential in the presence of weak dissipation. Here we extend the result to continuous-time Hamiltonian systems by using the Henon-Heiles system as a prototype model. More importantly, we go beyond to investigate the basin structure of scattering dynamics. A surprising finding is that, in the common case where multiple destinations exist for scattering trajectories, Wada basin boundaries are common and they appear to be structurally stable under weak dissipation, even when other characteristics of the nonhyperbolic scattering dynamics are not. We provide numerical evidence and a geometric theory for the structural stability of the complex basin topology.     

Unified symmetric finite element and boundary integral variational coupling methods for linear fluid–structure interaction

This article concerns the development of energy-based variational formulations and their corresponding finite element–boundary element Rayleigh–Ritz approximations for solving the time-harmonic vibration and scattering problem of an inhomogeneous penetrable fluid or solid object immersed in a compressible, inviscid, homogeneous fluid. The resulting coupled finite element and boundary integral methods (FEM-BEM) have the following attractive features: (1) Separate direct and complementary variational principles lead naturally to several alternative structure variable and fluid variable methodologies. (2) The solution in the exterior region is represented by a combined single- and double-layer potential which ensures the validity of the methods for all wave numbers; even though this representation introduces hypersingular integrals, for actual computations the hypersingular operator may be rewritten in terms of single-layer potentials, which can be integrated by standard techniques. (3) Since the discretized equations for the interior region and for the boundary are derived from the first variation of bilinear functionals the resulting algebraic systems of equations are always symmetric. In addition, the transition conditions across the interface are natural. This allows one to approximate the solutions within the interior and exterior regions independently, without imposing any boundary constraints.     

A 1:2:2 complex between 1,4,10,13-tetraoxa-7,16-diazacyclooctadecane (4,13-diaza-18-crown-6), 2,6-dihydroxyanthraquinone and water

A 1:2:2 complex of diaza crown ether 1,4,10,13-tetraoxa-7,16-diazacyclooctadecane, anthraflavic acid (2,6-dihydroxyanthraquinone) and water has been synthesized. The crystal is triclinic, P1, with a = 7.705(2), b = 10.871(2), c = 11.540(2) Å, = 100.40(2), = 91.38(2), = 98.01(2)°, Z = 1, and D_calc = 1.375 mg m^–3. The main feature of the crystal structure is the formation of a supramolecular sheet by hydrogen bonding of the anthraflavic monoanions, not only head-to-tail through the hydroxyl oxygens, but sideways through the quinone oxygens. This complex represents an intermediate case between total transfer of protons of a hydroxy-guest to crown N-atoms, and no transfer.     

Chitosan magnetic microspheres for technological applications: Preparation and characterization

One of the major applications of chitosan and its many derivatives are based on its ability to bind strongly heavy and toxic metal ions. In this study chitosan magnetic microspheres have been synthesized. Acetic acid (1%w/v) solution was used as solvent for the chitosan polymer solution (2%w/v) where magnetite nanoparticles were suspended in order to obtain a stable ferrofluid. Glutaraldehyde was used as cross-linker. The magnetic characteristic of these materials allows an easy removal after use if is necessary. The morphological characterization of the microspheres shows that they can be produced in the size range 800–1100 μm.The adsorption of Cu(II) onto chitosan–magnetite nanoparticles was studied in batch system. A second-order kinetic model was used to fit the kinetic data, leading to an equilibrium adsorption capacity of 19 mg Cu/g chitosan.     

Microwave absorption behavior of a polyaniline magnetic composite in the X-band

The development of nanosized materials is a subject of considerable interest both for understanding of the fundamental properties of magnetic materials for new technological applications. Polyaniline, composites Fe₃O₄/(PANI) with conducting, magnetic and electromagnetic properties with different amounts of Fe₃O₄ were successfully prepared. The samples were structurally characterized by scanning electron microscopy (SEM), X-ray diffraction and transmission electron microscopy (TEM) and magnetically, with a superconducting quantum interference device (SQUID) magnetometer. In order to explore microwave-absorbing properties in X-band, the composite nanoparticles were mixed with an epoxy resin to be converted into a microwave-absorbing composite. Microwave behavior with different Fe₃O₄/(PANI)-epoxy resin ratio was studied using a microwave vector network analyzer (VNA) in the range 7.5 to 13 GHz. For a constant thickness of 1.5 mm, absorption increases with the magnetite contents in the composites and in the oriented samples by the application of a magnetic field.