A blow up result for a fractionally damped wave equation

In this paper we prove a blow up result for solutions of the wave equation with damping of fractional order and in presence of a polynomial source. This result improves a previous result in [5]. There we showed that the classical energy is unbounded provided that the initial data are large enough.     

An inversion method for identification of elastoplastic properties of a beam from torsional experiment

A new method of determining elastoplastic properties of a beam from an experimentally given value T?T(φ) of torque (or torsional rigidity), during the quasistatic process of torsion, given by the angle of twist φ∈[φ_*,φ^*], is proposed. The mathematical model leads to the inverse problem of determining the unknown coefficient g=g(ξ²), ξ?|∇u|, of the non-linear differential equation −∇(g(|∇u|²)∇u)=2φ, x∈Ω⊂R². The inversion method is based on the parametrization of the unknown coefficient, according to the discrete values of the gradient ξ?|∇u|. Within the range of J₂-deformation theory, it is shown that the considered inverse coefficient problem is an ill-conditioned one. A numerical reconstruction algorithm based on parametrization of the unknown coefficient g=g(ξ²), with optimal selection of the experimentally given data T_m?T(φ_m), is proposed as a new regularization scheme for the considered inverse problem. Numerical results with noise free and noisy data illustrate applicability and high accuracy of the proposed method.     

Synthesis,crystal structure and spectral analysis of diaquatetrakis(N‐methylimidazole)Ni(II)(2,4,6‐tribromophenol)

Diaquatetrakis(N‐methylimidazole)Ni(II)(2,4,6‐tribromophenol), Ni(H₂O)₂(C₃N₂(CH₃))₄^.2(C₆H₃Br₃O), was synthesized via reaction of nickel sulphate and 2,4,6‐tribromophenolate in aqueous media in the presence of N‐methyl imidazole and sodium hydroxide. The complex crystalizes in the triclinic space group P1 with one formula unit of Ni(C₃H₃N₂(CH₃))₄(H₂O)₂.2(C₆H₃Br₃O) in the cell. The coordination around the Ni(II) ion is a slightly distorted octahedron, involving four N atoms from four different di(N‐methyl imidazole) ligand in the basal plane. The two oxygen atoms of the water molecules located at the apical positions result in an octahedral coordination. The two tribomophenol groups in the unit cell are connected via hydrogen‐bonds to the atoms of the coordination sphere, to build one dimensional chains along the a‐axis. For characterization of complex FTIR, UV spectroscopy, DSC and TGA thermal analysis were performed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

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.     

Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball

We establish new global well-posedness results along Gibbs measure evolution for the nonlinear wave equation posed on the unit ball in R³${\mathbb{R}}^3$ via two distinct approaches. The first approach invokes the method established in the works Bourgain (1994, 1996) ,  and  based on a contraction-mapping principle and applies to a certain range of nonlinearities. The second approach allows to cover the full range of nonlinearities admissible to treatment by Gibbs measure, working instead with a delicate analysis of convergence properties of solutions. The method of the second approach is quite general, and we shall give applications to the nonlinear Schrödinger equation on the unit ball in subsequent works Bourgain and Bulut (2013)  and .     

Determination of bupropion using liquid chromatography with fluorescence detection in pharmaceutical preparations, human plasma and human urine

A novel pre-column derivatization reversed-phase high-performance liquid chromatography with fluorescence detection is described for the determination of bupropion in pharmaceutical preparation, human plasma and human urine using mexiletine as internal standard. The proposed method is based on the reaction of 4-chloro-7-nitrobenzofurazan (NBD-Cl) with bupropion to produce a fluorescent derivative. The derivative formed is monitored on a C18 (150 mm × 4.6 mm i.d., 5 μm) column using a mobile phase consisting of methanol-water 75:25 (v/v), at a flow-rate of 1.2 mL/min and detected fluorimetrically at λ(ex) = 458 and λ(em) = 533 nm. The assay was linear over the concentration ranges of 5-500 and 10-500 ng/mL for plasma and urine, respectively. The limits of detection and quantification were calculated to be 0.24 and 0.72 ng/mL for plasma and urine, respectively (inter-day results). The recoveries obtained for plasma and urine were 97.12% ± 0.45 and 96.00% ± 0.45, respectively. The method presents good performance in terms of precision, accuracy, specificity, linearity, detection and quantification limits and robustness. The proposed method is applied to determine bupropion in commercially available tablets. The results were compared with an ultraviolet spectrophotometry method using t- and F-tests.     

Determination and validation of duloxetine hydrochloride in capsules by HPLC with pre-column derivatization and fluorescence detection

A high-performance liquid chromatographic (HPLC) method is described for the determination of duloxetine hydrochloride in capsules. The method was based on pre-column derivatization with 4-chloro-7-nitrobenzo-2-oxa-1,3-diazole using the fluorimetric detection technique. Duloxetine hydrochloride was analyzed by HPLC using an Inertsil C18 column (5 μm, 150 × 4.6 mm) and mobile phase consisted of methanol and water (65:35, v/v). The fluorescence detector was adjusted at excitation and emission wavelengths of 461 and 521 nm, respectively. The linearity of the method was in the range of 10-600 ng/mL. Limits of detection and quantification were 0.51 and 1.53 ng/mL, respectively. The proposed method was successfully applied for determination of duloxetine hydrochloride in its pharmaceutical preparation. The results were in good agreement with those obtained using a reference method.     

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.