A remark on divisibility of definable groups

We show that if G is a definably compact, definably connected definable group defined in an arbitrary o‐minimal structure, then G is divisible. Furthermore, if G is defined in an o‐minimal expansion of a field, k ∈ ? and p_k : G → G is the definable map given by p_k (x ) = x^k for all x ∈ G , then we have |(p_k )^–1(x )| ≥ k^r for all x ∈ G , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental characterization of hexatic smectic phases through electro-optic studies and dielectric relaxation spectroscopy

The electro-optic and complex dielectric behaviour of an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4'-(n-butanoyloxyprop-1-oxy)biphenyl-4-carboxylate, having chiral SmC_A* and hexatic smectic phases, have been investigated. Complex dielectric permittivities were measured as a function of frequency, d.c. bias field and temperature. Spontaneous polarization was measured by the current reversal technique; tilt angle was measured under a polarizing microscope using a low frequency electric field. The electro-optic properties and dielectric behaviour of the material are compared with results obtained by DSC and polarizing optical microscopy. Dielectric relaxation processes in SmC_A* and hexatic smectic phases were determined. The dielectric strength at the SmC_A* to hexatic smectic phase transition is discussed in terms of coupling between the long range bond orientational order and smectic C director. It seems from the results of spontaneous polarization and dielectric relaxation spectroscopy that the material might possess an additional phase between the SmC_A* and hexatic smectic I* phases.     

Effect of short glass fiber on structure and viscoelastic behavior of olefinic polymers synthesized with metallocene catalyst

Several composites were prepared on the basis of an ethylene homopolymer and different copolymers of ethylene and 1‐hexene, synthesized with a metallocene catalyst, as matrices and a content of a 5 wt % of short glass fiber. The effect of the fiber incorporation on the structure and mechanical and viscoelastic behaviors was analyzed for the different samples. The glass fibers induced a slightly higher crystallinity, and the crystallite morphology significantly changed (long spacings and crystal orientation). The incorporation of fibers did not reinforce the different matrices under study at this low content; consequently, the mechanical parameters, such as Young's modulus, yielding stress, and microhardness, were lower in the composites as compared with those values found in the neat polyolefins. The location and apparent activation energies of distinct relaxation processes are also discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1244–1255, 2003     

Ultrasonic spectroscopic evaluation of the ring‐opening metathesis polymerization of dicyclopentadiene

An in situ ultrasonic spectroscopy technique was used to study the ring‐opening metathesis polymerization of dicyclopentadiene catalyzed by bis(tricyclohexylphosphine)benzylidene ruthenium dichloride. A reaction cell employing a flexible poly(ethylene terephthalate) window for pulse echo ultrasonic spectroscopy was used to monitor the polymerization. The changes in the density, wave speed, acoustic modulus, and attenuation were all simultaneously monitored. In comparison with Fourier transform infrared (FTIR) spectroscopy data, the changes in the density, velocity, and modulus only accurately measured the rate constant for the metathesis of the cyclopentyl unsaturation. The ultrasonic values were within 6% of the values determined by FTIR. The activation energy for metathesis of the cyclopentyl unsaturation was 84 kJ mol^?1, following first‐order kinetics. Rate constants for the polymerization of the norbornyl unsaturation could not be determined by ultrasound. The gel point, vitrification, and qualitative information about the reaction rate could be determined from the change in the attenuation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1323–1333, 2003     

Mechanisms of n‐butanol formation in butyl acrylate latexes

The mechanisms involved in the formation of n‐butanol during the synthesis of butyl acrylate containing latices were investigated. The experimental results showed that neither the hydrolysis of butyl acrylate nor of the ester bond in the butyl acrylate segments of the polymer played a major role in the formation of n‐butanol, which was mainly generated from the polymer backbone, by transfer reactions to polymer chain followed by cyclization. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5838–5846, 2007     

Arsenic determination in marine sediment using ultrasound for sample preparation.

This work deals with As determination in marine sediment using ultrasound for sample preparation. It is shown that As can be quantitatively extracted from marine sediment using 20% (v/v) HCl and sonication. The slurry is centrifuged and the analyte is determined in the supernatant by hydride generation atomic absorption spectrometry (HG AAS). A flow injection (FI) system is employed for hydride generation, with 0.5% (m/v) NaBH(4) used as reducdant and a 20% (v/v) HCl used as sample carrier. The limit of quantification is 1.6 microg g(-1) of As, which is based on 800 microl of sample solution and 0.200 g of sample mass in a volume of 50 mL. Certified and non certified marine sediment samples were analyzed; the results were in accordance with the certified or reference values. Speciation analysis by HPLC-ICP-MS showed that As(V) is the only detectable As species present in the supernatant of the centrifuged sample.     

Photoluminescent properties and Raman spectra of ZnO-based scintillating glasses

Glasses in SiO₂–ZnO–BaO system with the different ZnO/BaO ratio were studied. In some cases, BaF₂ was introduced to substitute for BaO on the equal base. Photoluminescent spectra showed that ZnO in glass matrices behaved somewhat differently from ZnO crystals. Especially, the introduction of fluorine ions led to dramatic shift of UV emission band of glasses closer to that of ZnO crystals. Raman spectral analysis provided consistent results. In particular, Raman bands in the high frequency region are sensitive to effects of different ZnO/BaO or BaF₂/BaO ratio on structure of glasses.     

Parametric oscillations and stability of systems with large modulation coefficient

We study parametric oscillations of linear systems with one degree of freedom for large values of the modulation coefficient. We use the classical analytic Lyapunov-Poincaré perturbation methods and an original numerically-analytic method of accelerated convergence to construct periodic solutions and the corresponding eigenvalues. We find the boundaries of stability and instability domains. We use specific models to illustrate the main properties of parametric oscillations of systems with singular character of the perturbation dependence on the modulation coefficient. We consider periodic boundary value problems for the modified Mathieu equation and the Kochin equation modeling crankshaft torsional vibrations and show that there are significant differences between weakly and essentially perturbed periodicmotions both for the lowest and arbitrary oscillation modes. We also describe the unusual properties of the boundaries in the domain of the system determining parameters.     

Multi-mode wave propagation in ribbed plates: Part I,wavenumber-space characteristics

This paper addresses the issue of energy propagation features in ribbed panels over a wide frequency range. First, a tool for estimating the wave propagation characteristics of one- and two-dimensional structures by k-space analysis is presented. This tool uses a concept of Inhomogeneous Wave Correlation with sparse measured or extracted data, and leads to the estimation of θ-dependent wavenumbers. Here, the method is employed with the sparse simulated and measured normal velocities of a set of ribbed panels and new insights into their k-space behavior are highlighted. Behavior is essentially characterized at low frequencies by structural orthotropy. Comparisons with homogenized data show very good agreement. At higher frequencies, a new behavior pattern is observed and explained both numerically and experimentally. This is a multi-modal waveguide type of propagation in a direction parallel to the ribs.     

Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.