Local and global existence of solutions for a class of integro-differential equations with delay

In this article we consider a class of first order nonlinear integro-differential equations with delay. We propose new approach for investigating local and global existence of the solutions of its Cauchy problem. This approach gives new results.     

A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems

We study the backward problem for non-linear (semilinear) parabolic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new Fourier truncated regularization method for stabilising the ill-posed problem. In comparison with previous studies on solving the nonlinear backward problem, our method shows a significant improvement.     

Effect of the preparation route on the structure and microstructure of LaCoO3

Lanthanum cobaltite oxide, LaCoO₃, was prepared by the evaporation technique and the amorphous metal complex method. Powders were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy, and surface area measurements. The effect of the synthesis route on the phase purity, particle size, surface area, and morphology of the powders was studied. A single perovskite phase was synthesized at 700°C using the amorphous metal complex route. However, the evaporation technique required higher temperature for LaCoO₃ crystallization. Based on the characterization results, low temperature formation of LaCoO₃ was attributed to the homogeneity of the precursors. Such behavior also results in different microstructures. Powder synthesized by the amorphous metal complex method exhibited the highest surface area and the lowest particle size.     

Approximate analytical solution for MHD stagnation-point flow in porous media

In this paper, the steady two-dimensional laminar forced MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium which was solved numerically using the implicit finite-difference of Keller-box method [Yih KA. The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media. Acta Mech 1998;130:147–58] is revisited. A simple analytic approach of the Adomian decomposition method (ADM) is employed to obtain an approximate analytical solution of the problem. The skin friction coefficient and the rate of heat transfer given by the ADM are in good agreement with the numerical solutions of the Keller-box method.     

The profile of blowing-up solutions to a nonlinear system of fractional differential equations

We investigate the profile of the blowing-up solutions to the nonlinear nonlocal system (FDS):

     

Analysis of thermally induced solid-solid interactions in vanadia-alumina system

V₂O₅/Al₂O₃ solids of varying compositions were prepared, dried at 100°C and calcined in air at 400–1000°C. The solid-solid interactions between the mixed oxides were investigated by means of DTA, TG and XRD techniques.The results revealed that ammonium metavanadate and aluminium hydroxide decomposed at 260 and 290°C, respectively, to yield an ammonium vanadium intermediate compound and Al₂O₃ as solids. The intermediate compound readily decomposed at 360°C to give V₂O₅.Solid V₂O₅ generally catalyses the crystallization of Al₂O₃ to an extent proportional to its amount present. The solid-solid interactions between Al₂O₃ and V₂O₃ to produce AlV₂O₄ and AlVO₄ took place at 750 and 900°C. These solids decomposed entirely at 1000°C, producing V₂O₅ and alpha-corundum. The pure Al₂O₃ samples employed existed as amorphous solids even when heated in air at 750°C, but in the presence of V₂O₅ (7–18 wt.%) they crystallized to thetaalumina at 600°C. The pure solid alumina crystallized at 1000°C to a mixture of theta and kappa-alumina. In the presence of V₂O₅, alpha-corundum together with kappa and theta phases was obtained on heating at 900°C.     

Application of rhodanine,fluorene and semicarbazide hydrochloride as new spectrophotometric reagents for quinones

New selective and sensitive Spectrophotometric methods for quinone determination are described. Quinone samples are treated with either methanolic solution of rhodanine, fluorene in ammoniacal media or aqueous semicarbazide hydrochloride solution. Semicarbazide is the most sensitive reagent for the determination of 1,4-benzoquinone, 1,4-naphthoquinone and 2-methyl-1,4-naphthoquinone. Quinones substituted with electron withdrawing groups are better determined using rhodanine. The average recovery is 99.1%, 98.7% and 99.2% using rhodanine, fluorene and semicarbazide as reagents, respectively.     

A comparative study on p-doping behavior of polythiophenes with CH_3SO_3H

Four kinds of polythiophenes have been doped with CH3SO3H in CHCl3 under air,oxygen,and nitrogen. In the doping of two types of poly(3-hexylthiophene)s,P3HexTh(Zn/Ni)and P3HexTh(Fe)with different contents of a head-to-tail unit,the p-doping occurs at a similar rate.The reaction between poly(3-dodecylthiophene),P3DodTh,and the acid takes place more rapidly.P3OBuTh with a butoxy substituent undergoes more facile p-doping and receives photochemical reaction with CHCl3,and this reaction obeys a pseudo-first-order rate law with a rate constant kobs of 1.42×10-5s-1at room tempera- ture.     

Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate

The third-order nonlinear partial differential equation modelling the unsteady boundary-layer flows caused by an impulsively stretching fiat plate is solved by using the Adomian decomposition method （ADM）. The ADM yields analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The series solution using the ADM for the unsteady flows is presented for the first time.