Positive solutions and dynamics of a finite difference reaction–diffusion system

We investigate the dynamics and methods of computation for some nonlinear finite difference systems that are the discretized equations of a time-dependent and a steady-state reaction–diffusion problem. The formulation of the discrete equations for the time-dependent problem is based on the implicit method for parabolic equations, and the computational algorithm is based on the method of monotone iterations using upper and lower solutions as the initial iterations. The monotone iterative method yields improved upper and lower bounds of the solution in each iteration, and the sequence of iterations converges monotonically to a solution for both the time-dependent and the steady-state problems. An important consequence of this method is that it leads to a bifurcation point that determines the dynamic behavior of the time-dependent problem in relation to the corresponding steady-state problem. This bifurcation point also determines whether the steady-state problem has one or two non-negative solutions, and is explicitly given in terms of the physical parameters of the system and the type of boundary conditions. Numerical results are presented for both the time-dependent and the steady-state problems under various boundary conditions, including a test problem with known analytical solution. These numerical results exhibit the predicted dynamic behavior of the time-dependent solution given by the theoretical analysis. Also discussed are the numerical stability of the computational algorithm and the convergence of the finite difference solution to the corresponding continuous solution of the reaction–diffusion problem. © 1993 John Wiley & Sons, Inc.     

Synthesis and Mesogenic Properties of Liquid Crystals Containing Terminal Cyclohexylmethanol,Cyclopentylmethanol, Cyclobutylmethanol and Cyclopropylmethanol Moiety

Four series of compounds 11?50 containing terminal alicyclic rings such as cyclohexylmethyl, cyclopentylmethyl, cyclobutylmethyl, and cyclopropylmethyl rings were synthesized and their liquid crystal behavior studied. The ring size and the length of flexible alkoxy chain influence the phase formation in different ways. While the smaller ring and the shorter alkoxy chain tend to favor the formation of the N phase, the larger ring and the longer alkoxy chain tend to favor the formation of the SmC phase. All the compounds except 11 and 21 exhibit SmA phases. The widest temperature range of the N, SmA, and SmC phases are found in the compounds 41 , 46 , and 20 , respectively, which are 75 °C for 41 , 115 °C for 46 , and 100 °C for 20 .     

Synthesis and Second‐Order Nonlinearities of Chiral Prolinol‐Substituted Chromophores

A new series of thiophene‐ and furan‐containing chromophores with a chiral prolinol donor and a sulfone acceptor has been synthesized. The UV‐vis absorptions, second‐order nonlinear optical properties, and X‐ray crystal structures are described.     

Radiation patterns of electric dipole antenna in the presence of a biisotropic sphere

Analytic expressions of the dyadic Green's function of an arbitrary electric current source embedded in a general biisotropic sphere are presented at first, and the radiation characteristics of an electric dipole antenna placed on the surface of a biisotropic sphere lens are examined. The effects of the electric-and the magnetic-coefficients ( _e and _m ) of biisotropic medium on the radiation patterns of electric dipole antenna are investigated in detail.     

A comparative spectroscopic investigation of21Ne and21F by pickup reactions

The reactions²²Ne(d, t)²¹Ne and²²Ne(d, τ)²¹F have been investigated in a parallel experiment atE _d=52MeV. Energy spectra of tritons andτ particles have been measured up to excitation energies of 18MeV in both²¹Ne and²¹F nuclei. Thel values could be determined, and spectroscopic factors have been obtained by a DWBA analysis of the measured angular distributions. Together with the results from a preceding \({}^{22}Ne(\vec d, \tau ){}^{21}F\) experiment, several spins could be determined in²¹F. From a comparison of the triton andτ particle spectra,T=3/2 states in²¹Ne could be identified and on this basis the new information on spins of²¹F states could be transferred to their analog states in²¹Ne. The completeT _< andT _> parts of the (2s, 1d) strengths could be observed. The 1p strength is highly fragmented. Of theT _< part only 60% of the 1p1/2 and 40% of the lp3/2 strength could be found, but the totalT _> part of the 1p strength could be localized. The spectroscopic results for positive parity states are in qualitatively good agreement with shell model predictions.     

基于近红外光谱的维生素C片无损鉴别分析

基于近红外光谱技术与化学计量学方法,建立了一种国内外不同品牌维生素C片的无损鉴别方法。采集了国内外8个品牌的维生素C片共计40个样本的近红外光谱数据,比较了完整样品以及粉末样品的近红外光谱,采用连续小波变换技术消除背景干扰和基线漂移,基于标准偏差与相对标准偏差的变量筛选方法筛选出具有代表性的波数点,结合主成分分析方法对国内外不同品牌维生素C片进行鉴别分析。结果表明:原始光谱存在着明显的背景干扰和基线漂移现象,且粉末样品的重现性要优于完整样品;单纯使用原始光谱无法辨别来自不同品牌的维生素C片;连续小波变换可以有效消除背景干扰,提高模型鉴别能力;完整样品的鉴别准确率优于粉末样品,说明国内外不同品牌维生素C片主要成分基本一致,可能是辅剂和工艺上存在细微差异。通过结合近红外光谱分析技术与化学计量学方法,可实现对国产以及进口不同品牌维生素C片的鉴别分析。     

Rapid analysis of phthalic acid esters in environmental water using fast elution gas chromatography with mass spectrometry and adaptive library spectra

A method for the fast determination of the components in a complex sample by using gas chromatography with mass spectrometry was developed and used for the quantitative analysis of phthalic acid esters in environmental water. In the method, the adaptively corrected mass spectra were used to compensate for the differences between the library spectra and the measured ones in the experiment. The correction was obtained by the iterative transformation of the library spectra using iterative target transformation factor analysis, and the resolution was performed by non‐negative immune algorithm using the corrected spectra. Rapid analysis of 16 phthalic acid esters in water samples was achieved using fast elution gas chromatography with mass spectrometry measurements. The results show that the mass spectra and chromatographic profiles of the phthalic acid esters can be obtained from the overlapping signal of 13 min elution, and accurate quantitative analysis can be obtained. The recoveries of the phthalic acid esters obtained by standard addition are between 90.3 and 107.4%, and the relative standard deviations obtained in repeated measurements are less than 9%.