A new Taylor collocation method for nonlinear Fredholm‐Volterra integro‐differential equations

The aim of this article is to present an efficient numerical procedure for solving nonlinear integro‐differential equations. Our method depends mainly on a Taylor expansion approach. This method transforms the integro‐differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unkown Taylor coefficients. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer program written in Maple10. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Unexpected formation of higher polythionates in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium

It has been clearly shown that not only tetrathionate but also pentathionate or even higher polythionates is formed in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium. In thiosulfate excess, the absorbance-time curves registered at 250 nm may go through a maximum followed by a minimum, suggesting the presence of a short-lived absorbing intermediate proposed to be S(2)O(3)OCl(3-). Matrix rank analysis (MRA) studies have revealed that altogether five independent absorbing species are present in the wavelength range 240-400 nm. A kinetic model is suggested to take all of the experimental observations into account.     

Nonlinear Eigenvalues for a Quasilinear Elliptic System in Orlicz–Sobolev Spaces

Using an Orlicz–Sobolev Space setting, we consider an eigenvalue problem for a system of the form

Dynamic instability of thin viscoelastic films under lateral stress

We study the influence of lateral stress on the stability of thin viscoelastic films. The free surface of a deposited film under stress is shown to undergo an instability initiated by an anisotropic diffusion of the polymer molecules. This instability ultimately results in the formation of holes provided that the initial surface fluctuations are larger than a critical value. The latter is found to decrease when increasing the stress. An increase of the holes number density with the stress is therefore predicted. Most interestingly, the holes number density is also predicted to increase when increasing the molecular weight of the polymers. Additionally, we demonstrate that the friction of the substrate suppresses any spatial coherence between holes on large length scales. These predictions explain recent experimental observations made on thin spin-coated polystyrene films [G. Reiter, Nat. Mater. 4, 754 (2005)10.1038/nmat1484].     

Direct experimental evidence for atomic tunneling of europium in crystalline Eu8Ga16Ge30

M?ssbauer-effect and microwave absorption experimental evidence unambiguously demonstrates the presence of slow, approximately 450 MHz, tunneling of magnetic europium between four equivalent sites in Eu8Ga16Ge30, a stoichiometric clathrate. Remarkably, six of the eight europium atoms, or 11% of the constituents in this solid, tunnel between these four sites separated by 0.55 A. The off centering of the atoms or ions in crystalline clathrates appears to be a promising route for producing Rabi oscillators in solid-state materials.     

Comparison of the band alignment of strained and strain-compensated GaInNAs QWs on GaAs and InP substrates

We present a comparison of the band alignment of the Ga_1−xIn_xN_yAs_1−y active layers on GaAs and InP substrates in the case of conventionally strained and strain-compensated quantum wells. Our calculated results present that the band alignment of the tensile-strained Ga_1−xIn_xN_yAs_1−y quantum wells on InP substrates is better than than that of the compressively strained Ga_1−xIn_xN_yAs_1−y quantum wells on GaAs substrates and both substrates provide deeper conduction wells. Therefore, tensile-strained Ga_1−xIn_xN_yAs_1−y quantum wells with In concentrations of x0.53 on InP substrates can be used safely from the band alignment point of view when TM polarisation is required. Our calculated results also confirm that strain compensation can be used to balance the strain in the well material and it improves especially the band alignment of dilute nitride Ga_1−xIn_xN_yAs_1−y active layers on GaAs substrates. Our calculations enlighten the intrinsic superiority of N-based lasers and offer the conventionally strained and strain-compensated Ga_1−xIn_xN_yAs_1−y laser system on GaAs and InP substrates as ideal candidates for high temperature operation.     

Normal Subgroups of Hecke Groups <Emphasis Type="Italic">H</Emphasis>(<Emphasis Type="Italic">λ</Emphasis>)

Let λ ≥ 2 and let H(λ) be the Hecke group associated to λ. Also let H(λ)\U be the Riemann surface associated to the Hecke group H(λ). In this article, we study the even subgroup H _e (λ) and the power subgroups H ^m (λ) of the Hecke groups H(λ). We also study some genus 0 normal subgroups of finite index of H(λ). Finally, we discuss free normal subgroups of H(λ).     

Multiple Unbounded Positive Solutions for Three-Point BVPs with Sign-Changing Nonlinearities on the Positive Half-Line

This work is concerned with the existence of unbounded positive solutions for a second-order nonlinear three-point boundary value problem on the positive half-line. The interesting points of the results are that the nonlinearity depends on the solution and its derivative and may change sign. Moreover, it satisfies general polynomial growth conditions. New existence results of nontrivial single and multiple positive solutions are proved using recent fixed point theorems on cones in a special Banach space.     

Swelling Kinetics of PAAm–κ-Carrageenan Composites: A Fluorescence Technique

The steady-state fluorescence (SSF) technique was introduced for studying swelling of disc-shaped polyacrylamide (PAAm) gels containing various amount of κ?carrageenan (κC). They were prepared by free-radical cross-linking copolymerization. N,N^′-methylenebisacrylamide (BIS) and ammonium persulfate (APS) were added as a cross-linker and an initiator, respectively. Composite gels were prepared at 80°C with pyranine as a fluorescence probe. After drying of these gels, swelling kinetics were performed in water at 60°C by real-time monitoring of the pyranine fluorescence intensity, I, which decreased as swelling proceeded. The Li–Tanaka equation was used to determine the swelling time constants, τ ₁, and cooperative diffusion coefficients, D ₀, from fluorescence intensity, weight, and volume variations of the gels during the swelling processes in all cases. It was observed that τ ₁ decreased and D ₀ increased as the κC concentrations in the composites were increased indicating that high κC gels swell faster than low κC gels.