Convergence to strong nonlinear diffusion waves for solutions to p-system with damping

In this paper we consider the so-called p-system with linear damping, and we will prove an optimal decay estimates without any smallness conditions on the initial error. More precisely, if we restrict the initial data (V₀,U₀) in the space H³(R⁺)∩L1,γ(R⁺)×H²(R⁺)∩L1,γ(R⁺), then we can derive faster decay estimates than those given in [P. Marcati, M. Mei, B. Rubino, Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping, J. Math. Fluid Mech. 7 (2) (2005) 224-240; H. Zhao, Convergence to strong nonlinear diffusion waves for solutions of p-system with damping, J. Differential Equations 174 (1) (2001) 200-236] and [M. Jian, C. Zhu, Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant, J. Differential Equations 246 (1) (2009) 50-77].     

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.     

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.     

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.     

Platinum electrode modified with polyterthiophene doped with metallic nanoparticles,as sensitive sensor for the electroanalysis of ascorbic acid (AA)

A novel electrochemical sensor for ascorbic acid (AA) detection based on platinum electrode modified with polyterthiophene (P3T) and doped with metallic particles (Cu, Co, Ag, Au, Pd) was constructed. The electrocatalytic performances of the modified electrode with polyterthiophene-metallic particles related to the detection of AA, showed a better catalytic activity compared to the modified electrode with polyterthiophene film. The obtained results demonstrate also that the use of P3T–Ag nanocomposite allows a good sensitivity; which gives a high response in oxidation peak of AA. In order to have a good performance using this sensor, several parameters such as polymerization time of the film and immersion time of the film in AgNO₃ solution were optimized.     

The first suberate lanthanum(III) complex without uncoordinated water

catena‐Poly­[[aqua­lanthanum(III)]‐μ‐(8‐carboxy­octanoato)‐μ‐octanedioato], [La(C₈H₁₂O₄)(C₈H₁₃O₄)(H₂O)]_n, is, to our knowledge, the first reported rare‐earth complex containing a flexible long‐chain ligand that crystallizes without water of crystallization. The layered polymeric structure is built from infinite chains of one‐edge‐sharing LaO₈(H₂O) polyhedra, connected through the carbon backbone chains of the ligands. The two chemically different ligands act in the same coordination modes, exhibiting chelating bonds and μ‐1,1‐bridging monodentate linkage, and adopting the same extended conformation. In the relatively limited hydrogen‐bonding network, a very strong hydrogen bond between the deprotonated and protonated ligand ends stabilizes the framework.     

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.     

Nonlinear damped Timoshenko systems with second sound—Global existence and exponential stability

In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one‐dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle—a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established. Copyright © 2008 John Wiley & Sons, Ltd.     

Uniform decay in a Timoshenko-type system with past history

Fernández Sare and Rivera [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502] considered the following Timoshenko-type system

ρ₁φ_tt−K(φ_x+ψ)_x=0,