数学实验课程的教学与数学素质的培养

分析了现行工科数学教学中存在的主要问题 ,认为数学实验课程的教学是培养数学素质不可缺少的环节 ,并就如何更好地发挥数学实验课程教学的作用提出了一些具体的建议 .     

An improved class of generalized Runge–Kutta methods for stiff problems. Part I: The scalar case

A new family of p-stage methods for the numerical integration of some scalar equations and systems of ODEs is proposed. These methods can be seen as a generalization of the explicit p-stage Runge–Kutta ones, while providing better order and stability results. We will show in this first part that, at the cost of losing linearity in the formulas, it is possible to obtain explicit A-stable and L-stable methods for the numerical integration of scalar autonomous ODEs. Scalar autonomous ODEs are of very little interest in current applications. However, be begin studying this kind of problems because most of the work can be easily extended to a more general situation. In fact, we will show in a second part (entitled ‘The separated system case'), that it is possible to generalize our methods so that they can be applied to some non-autonomous scalar ODEs and systems. We will obtain linearly implicit L-stable methods which do not require Jacobian evaluations. In both parts, some numerical examples are discussed in order to show the good performance of the new schemes.     

用EWB进行自动控制原理实验的探索

将虚拟电子平台软件EWB用于自动控制原理实验，补充了其它几种实验方法的不足，既实用、灵活又简单直观，使自控原理实验的质和量都得到了很大提高，用EWB模拟的自动控制实验系统、所用的信号源以及各种测试仪器都与现场实物相仿，但功能更强，使用更方便。     

Design of Computer Experiments for Metamodel Generation

We review the use of statistical design and analysis of computer experiments (DACE) for the generation of parsimonious, surrogate models, also known as metamodels. Such metamodels are used to replace cpu- or memory-intensive, discretized approximations that often arise in MEMS and MOEMS. Emphasis is placed on optimal designs.     

Composition of vanadium carbides formed by solidification in ternary Fe-V-C alloys

The solidification behaviour of Fe-V-C alloys, was studied by differential thermal analysis. The composition and the nature of the phases were analysed by quantitative electron probe microanalysis and X-ray diffraction. Accurate microanalysis of carbon in vanadium carbides (VC_x and V₂C) were performed. A liquidus projection of the system Fe-V-C in the Fe-V rich region was proposed.     

Pseudo-spectral Approximations for a Class of the Kdv-Burgers Type Equation

In this paper, the pseudo-spectral approximations for a class of the Kdv-Burgers type equation is presented. Convergence and stability of the approximation have been proved by Sobolev‘s inequalities and the bounded extensive method of the nonlinear function. Finally, the numerical examples are proposed.     

Factorization in retrocausality: a response to O. Costa de Beauregard

Costa de Beauregard's reformulation of joint probability, in connection with retrocausality, reveals a mathematical paradox independent of time-reversal. That paradox is intrinsic to Bell's theorem and has a physical manifestation in the Orsay experiments.     

Simulation methodology — An introduction for queueing theorists

Simulation is a widely used methodology for queueing systems. Its superficial simplicity hides a number of pitfalls which are not all as well known as they should be. In particular simulation experiments need careful design and analysis as well as good presentations of the results. Even the elements of simulation such as the generation of arrival and service times have a chequered history with major problems lying undiscovered for 20 years. On the other hand, good simulation practice can offer much more than is commonly realized.     

Orthogonal arrays: An introduction and their application in optimizing underrelaxation factors in ‘simple’-based algorithm

The primary aim of this paper is to demonstrate how the ‘design-of-experiments’ techniques which are successful in physical experiments could also be adapted to a numerical simulation code. As an example this technique is applied to a general finite difference code used for predicting three-dimensional turbulent recirculating flows. Here the equations for velocities and continuity are solved using the algorithm called SIMPLE, which stands for semi-implicit method for pressure-linked equations. Physical modelling of turbulence is taken care of by means of kinetic energy and turbulence dissipation rate equations. The objective is to optimize the underrelaxation factors of primary and secondary flow variables so that the number of iterations required for convergence is minimum. This is done by the orthogonal array technique (a particular type of design-of-experiment technique). The geometry considered for this purpose is that of a simple gas turbine can combustor and the study is restricted to the isothermal non-reacting condition. Tests are carried out on three different grid configurations. In each case the underrelaxation factor for velocities contributed most to speed up the rate of convergence. Also, for each grid configuration the underrelaxation factor settings for minimum iterations for convergence was found to be same. Hence it is proposed that when doing grid independence tests for any similar flow situation, all the underrelaxation factors could be optimized on coarse grids.     

High Power THz Undulator Radiation from Linear Accelerator

A 30-MeV femto-second electron linac is built at the Shanghai Institute of Applied Physics, which can produce high power, coherent THz undulator radiation. We report the experimental facility and measurement of the power, frequency spectrum. First experiments show the averaged power at THz to be about 20mW.