Mortar element methods for parabolic problems

In this article a standard mortar finite element method and a mortar element method with Lagrange multiplier are used for spatial discretization of a class of parabolic initial‐boundary value problems. Optimal error estimates in L^∞(L²) and L^∞(H¹)‐norms for semidiscrete methods for both the cases are established. The key feature that we have adopted here is to introduce a modified elliptic projection. In the standard mortar element method, a completely discrete scheme using backward Euler scheme is discussed and optimal error estimates are derived. The results of numerical experiments support the theoretical results obtained in this article. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

High‐order 𝒞1 finite‐element interpolating schemes—Part I: Semi‐Lagrangian linear advection

This paper is devoted to the development of accurate high‐order interpolating schemes for semi‐Lagrangian advection. The characteristic‐Galerkin formulation is obtained by using a semi‐Lagrangian temporal discretization of the total derivative. The semi‐Lagrangian method requires high‐order interpolators for accuracy. A class of ??¹ finite‐element interpolating schemes is developed and two semi‐Lagrangian methods are considered by tracking the feet of the characteristic lines either from the interpolation or from the integration nodes. Numerical stability and analytical results quantifying the amount of artificial viscosity induced by the two methods are presented in the case of the one‐dimensional linear advection equation, based on the modified equation approach. Results of test problems to simulate the linear advection of a cosine hill illustrate the performance of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Hyperbolic positive mass theorem under modified energy condition

We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang’s previous result for modified asymptotically ?at initial data sets.     

Synthesis and properties of fluorescent cotton cellulose labeled with norfloxacin

To expand the application of cellulose in the field of fluorescence techniques, the cotton cellulose was labeled with norfloxacin (Cell-NF) via a three-step reaction, involving alkali treatment, epoxy activation, and opening of the epoxy rings with norfloxacin molecules. And the coordination complexes of Cell-NF with rare earth ions terbium (Cell-NF-Tb) and europium (Cell-NF-Eu) were obtained. The products were detected by IR, TG, XPS, UV and fluorescence spectra. Results showed that the norfloxacin content of the labeled cellulose was about 6.73 w% and the start temperature of decomposition of the Cell-NF was raised by 40°C compared with the stock cotton cellulose. When excited at 340 nm, the Cell-NF, Cell-NF-Tb, and Cell-NF-Eu in the solid state could emit violet (430 nm), green (549 nm) and red (620 nm) light, respectively.     

以离子水合能解释离子选择电极响应机理

用相继切换不同浓度I^-试液的活度阶梯法研究了碘化银基离子选择电极（I^--ISE）的瞬时响应。随电位变化的离子水合自由能△Gh(I^-）显示出|△Gh（I^-）|越小，正活度阶民位跃迁越快而负活度阶梯电位变化越慢。将－△Gh(I^-）看作I（H2O）n^-与I^--ISE表面反应的活化能解释了这个现象。比起传统电位法，活度阶梯法的主要优点是ISEs响应非常快并且更灵敏，有可能实现小体积试液的快速分析。     

Application of a coated-wire electrode to an acetylcholine sensor

An acetylcholine sensor was constructed with acetylcholinesterase which was immobilized on a hydrogen ion-selective coated-wire electrode and fundamental properties of this sensor were investigated. Acetylcholine could be determined in the range 0.1–10 rum with response times of 3–10 min. The effects of pH and concentration of buffer solution on the determination and fluctuations in the data obtained with this sensor were also investigated. Possibilities for the practical use of this acetylcholine micro-sensor are suggested.     

Effect of random density irregularities on nonlinear evolution of Langmuir waves in interplanetary medium

The evolution of nonlinear Langmuir waves in the interplanetary medium is investigated by appropriately accounting for the random density irregularities of the medium. A pair of modified Zakharov equations, which describe these waves, is solved numerically as an initial value problem for large scale (≫ 10² km) initial pertubations. For an ion acoustic-Langmuir solitary wave, the random irregularities damp the Langmuir wave by way of scattering and let the ion density perturbation radiate away in a few days. However an initial solitary or shock-like Langmuir wave excites the ion density perturbations within a fraction of a second, and then itself gets damped. These effects will strongly decelerate the collapse of large scale Langmuir waves. The possibility of detecting these processes, by means of interplanetary scintillation, is discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Electrochemical Detection of Anions on an Electrophoresis Microchip with Integrated Silver Electrode

A poly(dimethylsiloxane)/glass hybrid microfluidic chip with integrated silver electrode is described for electrochemical detection of anions. The working electrode was directly fabricated on a glass slide and the chip formed by reversibly sealing of a PDMS slab with microchannels to the slide. Under an alkaline phosphate condition, thiocyanide and three halides were sensitively detected. Factors influencing the separation and detection procedure were discussed and optimized. Linear responses over two magnitudes were obtained with limit of detection at the micromolar level.     

Electrochemical properties of niosomes‐modified Au electrode and its interaction with 1‐anilino‐8‐naphthalene‐sulfonate

The gold electrode was modified by noisomes, prepared by sonicating the mixed solution of PEG 6000/Tween 80/Span 80/H₂O. Electrochemical cyclic voltammetry (CV) and impedance spectroscopy (EIS) were performed for characterizing the modification. The construction of multilayer films of octadecanethiol (ODT)‐niosomes had almost no pinholes, which elicited that niosomes‐coated electrode through ODT assembly was more effective immobilization compared to direct modification method. A large semicircle formation in the entire range of frequency indicated the complete electron‐transfer control for the redox reaction, implying a perfect blocking behavior. The Nyquist plot was consisting of two depressed semicircles after storage for 36 h in air, which implied a progressive and uniform construction manner, as expected for porous coatings. The modified electrode was used to investigate the interaction between 1‐anilino‐8‐naphthalene‐sulfonate (ANS) and noisomes. It was found that the low‐frequency semicircular arcs increase in diameter, indicating that the increase in the resistance R_p attributed mainly to the niosomes/solution interface. It was due to the binding of ANS to the niosomes‐modified electrode surface, exhibited against diffusing species through the pores. Copyright © 2009 John Wiley & Sons, Ltd.     

Determination of the Robin coefficient in a nonlinear boundary condition for a steady‐state problem

In this paper, a constant heat transfer coefficient present in a nonlinear Robin‐type boundary condition associated with an elliptic equation is reconstructed uniquely from a single boundary energy measurement. Two types of such boundary energy measurement are considered, and solvability theorems for the solution of the resulting nonlinear inverse problems are provided. Further, one‐dimensional numerical results are presented and discussed. Copyright © 2008 John Wiley & Sons, Ltd.