Pointwise Improvement of Multivariate Kernel Density Estimates

Multivariate kernel density estimators are known to systematically deviate from the true value near critical points of the density surface. To overcome this difficulty a method based on Rao–Blackwell's theorem is proposed. Local corrections of kernel density estimators are achieved by conditioning these estimators with respect to locally sufficient statistics. The asymptotic as well as the small sample size behavior of the improved estimators are studied. Asymptotic bias and variance are investigated and weak and complete consistency are derived under mild hypothesis.     

General decay of solutions of a nonlinear system of viscoelastic wave equations

This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and Liu (Nonlinear Anal. 71:2257–2267, 2009) in which only the exponential and polynomial decay rates are considered.     

Thermomechanical behaviors and dielectric properties of polyaniline‐doped para‐toluene sulfonic acid/epoxy resin composites

Composites based on conductive organic/inorganic fillers dispersed in insulating matrix have been widely investigated because of their widespread applications such as electromagnetic shielding, electrostatic discharge, and sensors. In this context, novel composite materials based on epoxy resin matrix charged with polyaniline (PANI)‐doped para‐toluene sulfonic acid were elaborated. Fourier transform infrared spectroscopy, X‐ray diffraction and scanning electron microscopy were used to check the structure and the morphology of the samples. Viscoelastic behavior and thermal stability of the composites were explored by dynamic mechanical thermal analysis and thermogravimetric analysis. It was shown that the PANI particles exhibited a partial crystalline structure and were homogeneously dispersed in epoxy matrix. Consequently, this structure affected the thermal stability and viscoelastic properties of the composites. Furthermore, the dielectric and electrical properties were investigated up to 1 MHz. Measurements of dielectric properties revealed that with loading fillers in matrix, the dielectric parameters increased to high values at low frequency then decreased at values around 40 and 32 of real and imaginary parts, respectively, at 1 MHz with 15% of PANI content. Copyright © 2011 John Wiley & Sons, Ltd.     

Cloud-point measurement for (sulphate salts + polyethylene glycol 15000 + water) systems by the particle counting method

The phase separation of (water + salt + polyethylene glycol 15000) systems was studied by cloud-point measurements using the particle counting method. The effect of three kinds of sulphate salt (Na₂SO₄, K₂SO₄, (NH₄)₂SO₄) concentration, polyethylene glycol 15000 concentration, mass ratio of polymer to salt on the cloud-point temperature of these systems have been investigated. The results obtained indicate that the cloud-point temperatures decrease linearly with increase in polyethylene glycol concentrations for different salts. Also, the cloud points decrease with an increase in mass ratio of salt to polymer.     

Polymeric tetra­aqua­tris­(malonato)­dilanthanum(III) monohydrate

The title compound, [La₂(C₃H₂O₄)₃(H₂O)₄]·H₂O, forms a layer‐type polymeric structure. The layers, which contain infinite puckered four‐membered La—O—La—O rings in a pseudo‐ternary symmetry, are formed by the lanthanum and one independent malonate group. They are interconnected by the second independent malonate group, giving a three‐dimensional framework in which wide channels accommodate one disordered water mol­ecule of crystallization. The La atom lies on a twofold axis and is ten‐coordinated by eight O atoms from carboxyl­ate groups and two water mol­ecules. One malonate group is monodentate and triply bridging chelating, whilst the other is doubly monodentate. The extensive network of hydrogen bonds and bridge bonds observed in this structure enhances the structural stability. Despite some identical subfeatures, this structure is quite different from that observed in [La₂(C₃H₂O₄)₃(H₂O)₃]·2H₂O.     

Hydrogen bonding interactions between α-, β-glucose,and methacrylic acid

Intermolecular interactions between α-, β-glucose, and methacrylic acid (MAA) have been investigated. Twenty-two possible conformations have been optimized at the DFT(B3LYP) level of theory with the 6-31G(d) basis set. The geometrical parameters for the most stable configurations of hydrogen bonding sites in the optimized systems have been determined. The binding energies ΔE _bind have been calculated at the MP2/6-311++G(d,p) level of approximation taking into account the basis set superposition error (BSSE) and the zero-point vibrational energies corrections. Results indicate that the most stabilized complexes form hydrogen bonds either through carboxylic and hemiacetal oxygen atoms acting as proton acceptors. Both, α- and β-anomers are studied in the pyranose six-membered ring. In all complexes, the nuclear quadrupole coupling constants (χ) for ¹⁷O nuclei were obtained about 10.0 MHz, while for the ²H atoms they vary from ≈200.0 to ≈350.0 kHz.     

Femtosecond spectroscopy with vacuum ultraviolet pulse pairs

We combine different wavelengths from an intense high-order harmonics source with variable delay at the focus of a split-mirror interferometer to conduct pump-probe experiments on gas-phase molecules. We report measurements of the time resolution (<44 fs) and spatial profiles (4 μm × 12 μm) at the focus of the apparatus. We demonstrate the utility of this two-color, high-order-harmonic technique by time resolving molecular hydrogen elimination from C(2)H(4) excited into its absorption band at 161 nm.     

Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier's law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U ₀?∈?H ^s (?)?∩?L ¹(?). In addition, by restricting the initial data to U ₀?∈?H ^s (?)?∩?L ^1,γ(?) and γ?∈?[0,?1], we can derive faster decay estimates with the decay rate improvement by a factor of t ^?γ/2.