Resonance and non-resonance in a problem of boundedness

This paper studies the existence of bounded solutions of a forced non-linear differential equation of arbitrary order. Necessary and sufficient conditions for the existence of such solutions are obtained. These results are inspired by classical results on the periodic problem, both in the resonant and non-resonant cases.

     

Experimental Study of a Ka-Band Cylindrical Open Resonator

A study of the electrodynamical properties of a Ka-band gyrotron open resonator was experimentally conducted. Experiments were accomplished to measure resonant frequencies and their respective loaded quality factors for TE modes in the frequency range from 26 to 40 GHz. In particular, a perturbation technique was used to determine the axial, radial and azimuthal electric field profiles, as an identification method of the TE₀₂₁ mode operating around 35 GHz. In any experimental event, good agreement with the values predicted by theory was found.     

Characterization of Al(III) complexes with hematein in artistic alum logwood inks

The complexes between Al(III) and hematein, the main coloring matter in alum logwood inks, were characterized by Raman and ²⁷Al NMR (nuclear magnetic resonance) spectroscopies. Raman spectra of the crystallized complexes and of the compounds applied on a paper substrate are presented and assigned based on published data for the parent compounds. These Raman spectra show that the coordination of the hematein to the Al(III) ions takes place in both cases through the carbonyl and hydroxyl groups in the molecule, and that the aromatic rings are also involved in the interaction. The Raman spectra of the pure hematein–Al(III) complexes were found to be consistent with those recorded for a logwood ink prepared following a late 19th century recipe, using logwood chips instead of pure hematein, and applied on a paper substrate. These spectra can be used as references for the noninvasive identification of the compounds in works of art. ²⁷Al solid‐state NMR showed that the coordination of the Al(III) atoms in the crystallized powder is predominantly octahedral, while when applied on a paper substrate the colorant is present mainly as a tetrahedral complex, with an octahedral coordination also present in a smaller proportion. The fact that the predominant coordinations for the complexes in the crystallized material and for the ones present on the paper substrate are different is relevant for the study of the lightfastness and thermal stability of works of art bearing these media. Copyright © 2009 John Wiley & Sons, Ltd.     

Direct measurement of the single-metal-cluster optical absorption

The absorption of a single isolated metal cluster is directly measured using a novel far-field optical technique based on modulation of its position. Single gold nanoparticles with average diameters down to 5 nm, dispersed on a transparent substrate, are optically detected and their absolute absorption cross section determined.     

Observation of B Meson decays to b1pi and b1K

We present the results of searches for decays of B mesons to final states with a b1 meson and a charged pion or kaon. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 382x10(6) BB[over ] pairs produced in e+e- annihilation. The results for the branching fractions are, in units of 10(-6), B(B+-->b1(0)pi+)=6.7+/-1.7+/-1.0, B(B+-->b1(0)K+)=9.1+/-1.7+/-1.0, B(B0-->b1(-/+)pi(+/-))=10.9+/-1.2+/-0.9, and B(B0-->b1(-)K+)=7.4+/-1.0+/-1.0, with the assumption that B(b1-->omega pi)=1. We also measure charge and flavor asymmetries A(ch)(B+-->b1(0)pi+)=0.05+/-0.16+/-0.02, Ach(B+-->b1(0)K+)=-0.46+/-0.20+/-0.02, A(ch)(B0-->b1(-/+)pi(+/-))=-0.05+/-0.10+/-0.02, C(B0-->b1(-/+)pi(+/-))=-0.22+/-0.23+/-0.05, DeltaC(B0-->b1(-/+)pi(+/-))=-1.04+/-0.23+/-0.08, and A(ch)(B0-->b1(-)K+)=-0.07+/-0.12+/-0.02. The first error quoted is statistical, and the second systematic.     

Production and characterization of refractive index gratings in high-birefringence fibre optics

In this work, we report production and modelling of both Bragg gratings and rocking filters in high birefringence fibre optics. Bragg gratings are produced by UV (257.0 nm) external interferometric exposition of a frequency-doubled Ar⁺ ion laser, whereas for rocking filters formation the visible Ar⁺ ion laser lines in 488.0 and 514.5 nm are used in an internal method. The spectral characteristics due to the birefringence properties are studied through numerical methods and experimental techniques. The spectral responsivity of the structures under temperature changes and stress application is presented.     

Development of an optical refractometer by analysis of one-dimensional photonic bandgap structures with defects

A theoretical analysis of an optical fiber photonic-bandgap-based refractometer is presented. The design is based on a quarter-wave reflector with one defect. By modifying both the real and the imaginary parts of the index of refraction of the defects we begin to change either the frequency or the amplitude of the localized optical mode. So we could fabricate a specific optical fiber refractometer by combining all the variables: index of refractive index of the defects and the rest of layers, thickness of the defect, number of layers, etc. to yield a large set of design possibilities, for example, detecting wider or thinner ranges of refractive indices, or controlling the detection accuracy. Some rules for the practical implementation of the refractometer are given.     

Determination of Pb,Zr, Ti,Sr, Cr,Nb and La in lead zirconate titanate ceramics by particle‐induced X‐ray emission

A particle‐induced X‐ray emission (PIXE) technique has been used in the determination of the principal components Pb, Zr and Ti and the substituting elements Sr, Cr, Nb and La in lead zirconate titanate ceramics. In general, precision of analysis was concentration dependent from each element under study. For Pb, precision varied between 0.13% and 0.16%, at higher concentration of 59.32–64.5%. It was around 6–9% for Sr, Cr and Nb at concentrations of 1% or lower. Particular attention was devoted to the estimation of the analysis trueness. With this purpose, three methods were applied: (1) comparison of PIXE and inductively coupled plasma optical emission spectrometry concentrations, (2) recovery study and (3) comparison with a laboratory standard. Trueness of analysis was around 100 ± 10% for the evaluated elements Pb, Zr, Ti, Sr and Cr. The expected stoichiometry and elemental composition homogeneity of a wide group of produced ceramics were confirmed by the PIXE technique. Copyright © 2012 John Wiley & Sons, Ltd.     

Unusual thermal diffusion in polymer solutions

Thermal diffusion forced Rayleigh scattering results on thermal diffusion of poly(ethylene oxide) (PEO) in ethanol/water mixtures are presented. In water-rich solvent mixtures, PEO is found to migrate towards regions of lower temperature. This is typical for polymer solutions and corresponds to a positive Soret coefficient of PEO. In solvent mixtures with low water content, however, the polymer is found to migrate towards higher temperatures, corresponding to a negative Soret coefficient of PEO in ethanol-rich solutions. To our knowledge, this is the first observed sign change of the Soret coefficient of a polymer in solution. We also present a simple lattice model for the polymer solvent system and calculate Soret coefficients with statistical mechanics methods. The calculated values agree qualitatively with the experimental results.