A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle

In this paper, a generalized anti–maximum principle for the second order differential operator with potentials is proved. As an application, we will give a monotone iterative scheme for periodic solutions of nonlinear second order equations. Such a scheme involves the L^p norms of the growth, 1 ≤ p ≤ ∞, while the usual one is just the case p = ∞.     

Synthesis of N-Vinyloxyalkyl Imines

Russian Journal of Organic Chemistry -     

Spectra Analysis of a Novel Ti-Doped LiAlO2 Single Crystal

LiAlO2 single crvstals doped with Ti at concentration 0.2at.% are grown by the Czochralskl technique with dimensions φ42×55mm. Ti ions in the crystal are quadrivalence proven by comparing the absorption and fluorescence spectra of pure LiAlO2 and Ti： LiAlO2. After air and Li-rich atmosphere annealing, the absorption peaks in the range of 600-800nm disappear. We conclude that 682 and 756nm absorption peaks are attributed to the VLi and Vo absorptions, respectively： The peaks at 716nm and 798nm may stem from the VLi^＋ and absorptions. The colour-centre model can be applied to explain the experimental phenomena. Ti^4＋-doping produces more lithium vacancies in the LiAlO2 crystal. The intensities of [LiO4] and the associated bonds remain unchanged, which improves the anti-hydrolyzation and thermal stability of LiAlO2 crystals.     

On a Generalized Cochrane Sum and Its Hybrid Mean Value Formula

The main purpose of this paper is to use a mean value theorem of Dirichlet L-functions to study the asymptotic property of a hybrid mean value of a generalized Cochrane sum, and give an interesting mean value formula.2000 Mathematics Subject Classification: Primary—11F20; Secondary—11F99     

The Convergence and Stability of Splitting Finite-Difference Schemes for Nonlinear Evolutionary Equations

We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. We prove the convergence and stability of the scheme in L ₂ and C norms. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005.     

Optical corrosion meter

In a previous study, a mathematical model relating surface and bulk behaviours of metals in aqueous solution has been developed. The model was established based on principles of holographic interferometry for measuring microsurface dissolution, i.e. mass loss, and on those of electrochemistry for measuring the bulk electronic current, i.e. corrosion current. In the present work, an optical corrosion meter was built based on the above model. The corrosion meter consists of an electrochemical cell in which the sample is immersed in aqueous solution. Furthermore, the corrosion meter has a holographic camera with a thermoplastic film for in situ processing of holograms in order to obtain real-time holographic interferoms of the sample in the electrochemical cell. Results of the present work indicate that optical holography is a very useful technique for measuring the corrosion current density of different alloys in aqueous solutions. As a result, the corrosion current density of aluminium, stainless steel, and low-carbon steel in 1 M KCl, 1 M NaCl, and 1 M NaOH solutions were obtained. A comparison between the corrosion data of samples showed that the corrosion current density of the stainless steel in 1 M NaCl is nearly three-folds higher than that of the aluminium in 1 M KCl and the low-carbon steel in 1 M NaOH.     

The accurate dimensional measurements within small internal structures

This paper shows that the dimension of internal structure of a component can be measured remotely to a resolution better than 5 μm by use of the combination of high resolution optical microscopy and image processing.A specialised high resolution, long working distance and diffraction limited lens was used to image within the component. A series of digital images were made to map spatially the interior of the component. An edge detector was then used to localise the specific location of features in order that an accurate internal measurement could be made. A visualisation of the internal surface finish was also achieved.