Rational approximation to trigonometric operators

We consider the approximation of trigonometric operator functions that arise in the numerical solution of wave equations by trigonometric integrators. It is well known that Krylov subspace methods for matrix functions without exponential decay show superlinear convergence behavior if the number of steps is larger than the norm of the operator. Thus, Krylov approximations may fail to converge for unbounded operators. In this paper, we propose and analyze a rational Krylov subspace method which converges not only for finite element or finite difference approximations to differential operators but even for abstract, unbounded operators. In contrast to standard Krylov methods, the convergence will be independent of the norm of the operator and thus of its spatial discretization. We will discuss efficient implementations for finite element discretizations and illustrate our analysis with numerical experiments. AMS subject classification (2000)  65F10, 65L60, 65M60, 65N22     

A new rational auxiliary equation method and exact solutions of a generalized Zakharov system

A new rational auxiliary equation method for obtaining exact traveling wave solutions of constant coefficient nonlinear partial differential equations of evolution is proposed. Its effectiveness is evinced by obtaining exact solutions of a generalized Zakharov system, some of which are new. It is shown that the G^′/G and the generalized projective Ricatti expansion methods are special cases of the auxiliary equation method. Further, due the solutions obtained, four other new and practicable rational methods are deduced.     

A New Indirect Electroanalytical Method to Monitor the Contamination of Natural Waters with 4‐Nitrophenol Using Multiwall Carbon Nanotubes

The electrochemical detection of the hazardous pollutant 4‐nitrophenol (4‐NP) at low potentials, in order to avoid matrix interferences, is an important research challenge. This study describes the development, electrochemical characterization and utilization of a multiwall carbon nanotube (MWCNT) film electrode for the quantitative determination of 4‐NP in natural water. Electrochemical impedance spectroscopy measurements showed that the modified surface exhibits a decrease of ca. 13 times in the charge transfer resistance when compared with a bare glassy carbon (GC) surface. Voltammetric experiments showed the possibility to oxidize a hydroxylamine layer (produced by the electrochemical reduction of 4‐NP on the GC/MWNCT surface) in a potential region which is approximately 700 mV less positive than that needed to oxidize 4‐NP, thus minimizing the interference of matrix components. The limit of detection for 4‐NP obtained using square‐wave voltammetry (0.12 μmol L^?1) was lower than the value advised by EPA. A natural water sample from a dam located in São Carlos (Brazil) was spiked with 4‐NP and analyzed by the standard addition method using the GC/MWCNT electrode, without any further purification step. The recovery procedure yielded a value of 96.5% for such sample, thus confirming the suitability of the developed method to determine 4‐NP in natural water samples. The electrochemical determination was compared with that obtained by HPLC with UV‐vis detection.     

模型外载与自重并存变动外载的光弹性分析法

提出一个变动模型外载，分析大模型在外载与自重共同作用时的尤弹性法。它与用离心力模拟自重试验的传统方法完全不同，只要在大模型上变动外载，就可以获得上述两种载荷共同作用下的应力分析结果。此法避免了用离心模型自重受模型尺寸限制等诸多因素影响的缺点，为自重不可的大型复杂空间工程结构模型试验应力分析提出了一条新的途径。文中给出了本方法的基本原理及其简要的实验验证和工程应用结果。     

力调制显微术在台阶边缘附近的边界效应

力调制显微术被用于观测铜基碳化硅样品，实验中发现在样品表面台阶边缘处出现一些异常信息。为此，文章作者通过测试一种表面同样有台阶但却是由同一种材料组成的样品来通信验证这些异常主要是由台阶的边界引起的，并对引起的异常作了半定量的估算。     

Anharmonic effects on lattice resonant modes of impure metallic crystals

The effect of lattice anharmonicity on the resonant modes of dilute impurities for Au-Cu, Au-Ag and W-Cr metallic systems are studied from the poles of the double time temperature dependent impure Green’s function of these crystals. The third order force constants used in the present work are derived assuming the systems to obey the Lennard-Jones potential. The inclusion of lattice anharmonicity has been found to increase the resonant frequency which depends upon the mass defect, force constant change parameter and the impurity concentration terms. Some interesting features about the phase shift and the change in width of the vibrational spectrum are reported at room temperature for the isotopic defects and the defects interacting with host atoms. The results are found to be in qualitative agreement with the experiments on the systems considered.     

Traveling wave fronts of delayed non-local diffusion systems without quasimonotonicity

This paper is concerned with the existence of traveling wave fronts for delayed non-local diffusion systems without quasimonotonicity, which can not be answered by the known results. By using exponential order, upper-lower solutions and Schauder's fixed point theorem, we reduce the existence of monotone traveling wave fronts to the existence of upper-lower solutions without the requirement of monotonicity. To illustrate our results, we establish the existence of traveling wave fronts for two examples which are the delayed non-local diffusion version of the Nicholson's blowflies equation and the Belousov-Zhabotinskii model. These results imply that the traveling wave fronts of the delayed non-local diffusion systems without quasimonotonicity are persistent if the delay is small.     

On the solutions of the time-delayed Burgers equation

The time-delayed Burgers equation is introduced and the improved tanh-function method is used to construct exact multiple-soliton and triangular periodic solutions. For an understanding of the nature of the exact solutions that contained the time-delay parameter, we calculated the numerical solutions of this equation by using the Adomian decomposition method and the variational iteration method (IVM) to the boundary value problem.     

电子束辐照硬铝产生热击波及层裂的估算

 本文对LY-12铝受到强流低能相对论电子束辐照时产生的热击波及层裂效应进行了估算。在预估中等能量沉淀产生材料的动态响应时必须适当地考虑熔化过程。我们所用的状态方程是GRAY三相状态方程，它对熔化区域中的金属作了详细且在热力学上更为完善的描述。将计算值同实验结果进行比较表明，二者基本上是一致的。     

多光束全息互连元件效率的理论分析

多光束全息互连元件往往需要大量的耦合波方程才能描述。本文通过分析记录时生成的互调制光栅的性质及其对衍射的影响,对问题进行适当的简化。通过解不同条件下的耦合波方程、分别给出了多光束全息图在各种不同情况下的衍射效率的近似解析表达式,展示了衍射效率与各实验参量之间的关系。为进一步研究多光束全息互连元件的性质、比较各种条件下的效率以及各参量对总体效率的影响,提供了方便。