Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type

We consider the Laplace equation in ? ^d?1 × ?⁺ × (0,+∞) with a dynamical nonlinear boundary condition of order between 1 and 2. Namely, the boundary condition is a fractional differential inequality involving derivatives of noninteger order as well as a nonlinear source. Nonexistence results and necessary conditions are established for local and global existence. In particular, we show that the critical exponent depends only on the fractional derivative of the least order.     

Exponential decay for a quasilinear viscoelastic equation

We consider the following nonlinear viscoelastic equation together with Dirichlet-boundary conditions, in a bounded domain Ω and ρ > 0. We prove an exponential decay result for a class of relaxation functions. Our result is established without imposing the usual relation between g and its derivative (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exponential decay for a viscoelastic problem with a singular kernel

In this paper we consider a problem which arises in viscoelasticity. We prove exponential decay of solutions for the problem with a memory term involving a kernel which is singular at zero. This is established by introducing an appropriate Lyapunov type functional and using the energy method. This work extends earlier results.      

Highly sensitive determination and validation of gabapentin in pharmaceutical preparations by HPLC with 4-fluoro-7-nitrobenzofurazan derivatization and fluorescence detection

A sensitive HPLC method with pre-column fluorescence derivatization using 4-Fluoro-7-Nitrobenzofurazan (NBD-F) has been developed for the determination of gabapentin in pharmaceutical preparations. The method is based on the derivatization of gabapentin with (NBD-F) in borate buffer of pH 9.5 to yield a yellow, fluorescent product. The HPLC separation was achieved on a Inertsil C(18) column (250 mm × 4.6 mm) using a mobile phase of methanol water (80:20, v/v) solvent system at 1.2 mL/min flow rate. Mexiletine was used as the internal standard. The fluorometric detector was operated at 458 nm (excitation) and 521 nm (emission). The assay was linear over the concentration range of 5 50 ng/mL. The method was validated for specificity, linearity, limit of detection, limit of quantification, precision, accuracy, robustness. Moreover, the method was found to be sensitive with a low limit of detection (0.85 ng/mL) and limit of quantitation (2.55 ng/mL). The results of the developed procedure for gabapentin content in capsules were compared with those by the official method (USP 32). Statistical analysis by t- and F-tests, showed no significant difference at 95 confidence level between the two proposed methods.     

The investigation of some physical properties and microstructure of Zn-doped hydroxyapatite bioceramics prepared by sol–gel method

In this study, the effect of Zn-dopant on the physical properties and microstructure of hydroxyapatite (HAP) bioceramics was investigated. The average crystallite size, phase composition and degree of crystallization of the pure hydroxyapatite and Zn-doped hydroxyapatite bioceramic samples prepared by sol–gel method were determined by X-ray diffraction method. It was seen that all the bioceramic samples were composed of the nanoparticles (29–46 nm). Fourier transform infrared spectroscopy was used to determine the functional groups in the samples. The dielectric properties of the bioceramics were investigated by dielectric impedance spectroscopy method, and the surface morphologies of them were analyzed using scanning electron microscopy technique. When the densities of the samples were measured by Archimedes method, it was seen that the densities of the samples increased with the increase of the molar ratio of Zn. The crystallization degree for all the samples dramatically decreased with the increasing content of the Zn dopant. With the increase of Zn to HAP, a change was observed in the degree of the crystallization, phase compositions, dielectric properties and microstructures of the samples.     

Bromophilic substitution/carbophilic substitution cascade reactions of α,α-dibromo-2-methoxyacetophenone with C-, N- and O-nucleophiles

α,α-Dibromo-2-methoxyacetophenone reacts, under mild reaction conditions, with C-, N- and O-nucleophiles via a bromophilic substitution/protonation/carbophilic substitution cascade process to afford α-monosubstituted-2-methoxyacetophenones in moderate to good yield. The only exception from this reaction pathway is the reaction with the anion derived from malononitrile in which 2-aroyl-1,1,3,3-tetracyanopropene is obtained.     

Existence and uniqueness for a nonlinear inverse reaction‐diffusion problem with a nonlinear source in higher dimensions

This paper analyzes the existence and the uniqueness problem for an n‐dimensional nonlinear inverse reaction‐diffusion problem with a nonlinear source. A transformation is used to obtain a new inverse coefficient problem. Then, a parabolic differential operator L_λ is defined to establish the relation between the solution of L_λ = 0 and the new inverse problem. Following this, it is shown that the inverse problem has at least one solution in the class of admissible coefficients. Furthermore, it is proved that this solution is the unique solution of the undertaken inverse problem. A numerical example is given to illustrate ill‐posedness of the inverse problem. Copyright © 2013 John Wiley & Sons, Ltd.     

Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball

We establish new results for the radial nonlinear wave and Schrödinger equations on the ball in ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$, for random initial data. More precisely, a well-defined and unique dynamics is obtained on the support of the corresponding Gibbs measure. This complements results from Burq and Tzvetkov (2008) [8], [9] and Tzvetkov (2006, 2008) [10], [11].