Bifurcation of critical points for continuous families of C 2 functionals of Fredholm type

Given a continuous family of C ² functionals of Fredholm type, we show that the nonvanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of bifurcation points along the branch. We use this result for several parameter bifurcation, estimating the number of connected components of the complement of the set of bifurcation points in the parameter space and apply our results to bifurcation of periodic orbits of Hamiltonian systems. By means of a comparison principle for the spectral flow, we obtain lower bounds for the number of bifurcation points of periodic orbits on a given interval in terms of the coefficients of the linearization.     

On-line ionic imprinted polymer selective solid-phase extraction of nickel and lead from seawater and their determination by inductively coupled plasma-optical emission spectrometry

Nickel(II) and lead(II) ionic imprinted 8-hydroxyquinoline polymers were synthesized by a precipitation polymerization technique and were used as selective solid phase extraction supports for the determination of nickel and lead in seawater by flow injection solid phase extraction on-line inductively coupled plasma-optical emission spectrometry. An optimum loading flow rate of 2.25 mL min⁻¹ for 2 min and an elution flow rate of 2.25 mL min⁻¹ for 1 min gave an enrichment factor of 15 for nickel. However, a low dynamic capacity and/or rate for adsorption and desorption was found for lead ionic imprinted polymer and a flow rate of 3.00 mL min⁻¹ for 4-min loading and a flow rate of 2.25 mL min⁻¹ for 1-min elution gave a enrichment factor of 5. The limit of detection was 0.33 μg L⁻¹ for nickel and 1.88 μg L⁻¹ for lead, with a precision (n = 11) of 8% (2.37 μg Ni L⁻¹) for nickel and 11% (8.38 μg Pb L⁻¹) for lead. Accuracy was also assessed by analyzing SLEW-3 (estuarine water) and TM-24 (lake water) certified reference materials, and the values determined were in good agreement with the certified concentrations.     

Formation of a magnetic composite by reduction of Co-Nd doped strontium hexaferrite in a hydrogen gas flow

Co-Nd strontium hexaferrite nanoparticles synthesized by the self-combustion method were treated in a hydrogen flow at different temperatures and times. The samples were characterized structurally by scanning electron microscopy and X-ray diffraction and magnetically with a vibrating sample magnetometer. Phase identification showed decomposition of the hexaferrite structure into Fe₃O₄ and different strontium mixed oxides. The sample treated at 500 °C for 30 minutes shows good magnetic properties due to the formation of a magnetite/hexaferrite composite. In this case magnetization is very close to the original sample while the coercivity slightly diminishes. The hexagonal phase is almost completely transformed into different oxides at a reducing temperature of 500 °C for 120 minutes. The obtained results are analyzed in terms of the phase composition and of the magnetic susceptibility of the studied samples.     

Empirical likelihood for conditional quantile with left-truncated and dependent data

In this paper, we employ the method of empirical likelihood to construct confidence intervals for a conditional quantile in the presence and absence of auxiliary information, respectively, for the left-truncation model. It is proved that the empirical likelihood ratio admits a limiting chi-square distribution with one degree of freedom when the lifetime observations with multivariate covariates form a stationary α-mixing sequence. For the problem of testing a hypothesis on the conditional quantile, it is shown that the asymptotic power of the test statistic based on the empirical likelihood ratio with the auxiliary information is larger than that of the one based on the standard empirical likelihood ratio. The finite sample performance of the empirical likelihood confidence intervals in the presence and absence of auxiliary information is investigated through simulations.     

Electromagnetic properties of manganese-zinc ferrite with lithium substitution

Polycrystalline manganese-zinc ferrite with lithium substitution of composition Li_0.5xMn_0.4Zn_0.6−xFe_2+0.5xO₄ (0.0≤x≤0.4) was prepared by the usual ceramic method. X-ray diffraction analysis confirmed that the samples have a spinel structure and are of single phase for some values of Li content. Lithium doping considerably modifies saturation magnetization since its value increases from 57.5 emu/g for x=0.0 to 82.9 emu/g for x=0.4. Lithium inclusion increases the real permeability (over 1 MHz) while the natural resonance frequency shifts to lower values as the fraction of Li increases. These ferrites show good electromagnetic properties as absorbers in the microwave range of 1 MHz - 1 GHz.     

A substitute for the Sard-Smale theorem in theC 1 case

IfF is a Fredholm mapping of indexΝ ∃ ℤ and classC ^max(Ν,0)+1 between separable Banach spaces, the Sard—Smale theorem yields the existence of arbitrarily small perturbations ofF having 0 as a regular value. The smoothness requirement cannot be weakened in the Sard—Smale theorem itself, at least whenΝ ≥ 0, but we prove that the approximation result remains valid irrespective of the indexΝ whenF is only of classC ¹ and satisfies appropriate properness-like conditions. The separability of the spaces is not needed either. Everything carries over to the setting of Banach manifolds modeled on spaces with a norm of classC ¹ away from the origin. We also show that in Banach spaces, theC ¹ norm assumption can be dropped without major prejudice. The application to degree theory forC ¹ Fredholm mappings of index 0 is developed in a separate paper.     

A Bridged High-Spin Complex Bis-[Ni(II)( rac-5,5,7,12,12,14-hexamethyl- 1,4,8,11-tetraazacyclotetradecane)]-2,5-pyridinedicarboxylate Diperchlorate Monohydrate

A bridged high-spin complex,bis-[Ni(II)(rac-5,5,7,l2,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane)]-2,5-pyridinedicarboxylate diperchlorate monohydrate has been obtained by reaction of [Ni(II)(rac-5,5,7, 12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane)](ClO₄)₂ and 2,5-pyridinedicarboxylic acid in aqueousalkaline (NH₄OH) medium. C₃₉H₇₇Cl₂N₉Ni₂O₁₃, chemical formula weight 1068.42, orthorhombic, P2₁2₁2₁, a = 11 .423(3) Å,b = 14.770(6) Å, c = 31.608(7) Å, = = =90.00°, V = 5333(3) ų, Z = 4, D_calc = 1.331 g cm^-3, _calc = 0.869 mm^-1, F(000) = 2272, T = 293(2), R = 0.0870 for 2686 observed reflections [I > 2(I)]. The complexincludes two folded [Ni(rac- Me₆[14]aneN₄)]²⁺ units havingopposite diastereomeric configuration. They are bridged through a dianion of2,5-pyridinedicarboxylic acid, with one Ni-atom coordinated to the O-atom ofthe 2-carboxylic group and the pyridine N-atom (forming a 5-membered chelatering), and with the second Ni-atom coordinated to both O-atoms of the 5-carboxylic group (forming a 4-membered chelate ring). Hydrogen bonding involving macrocyclic NH groups, both 2- and 5-carboxylic groups, perchlorate anions and water molecules gives rise to the formation of an infinite supramolecular network in the title compound's crystals.     

Preparation of a biocompatible magnetic film from an aqueous ferrofluid

Very promising nanoparticles for biomedical applications or in medical drug targeting are superparamagnetic nanoparticles based on a core consisting of iron oxides (SPION) that can be targeted through external magnets. Polyvinyl alcohol (PVA) is a unique synthetic biocompatible polymer that can be chemically cross-linked to form a gel. Biotechnology applications of magnetic gels include biosensors, targeted drug delivery, artificial muscles and magnetic buckles. These gels are produced by incorporating magnetic materials in the polymer composites. In this paper we report the synthesis of an aqueous ferrofluid and the preparation of a biocompatible magnetic gel with polyvinyl alcohol and glutharaldehyde (GTA). HClO₄ was used to induce the peptization since this kind of ferrofluid does not have surfactant. The magnetic gel was dried to generate a biocompatible film.