非线性Schrdinger方程的高精度守恒差分格式

本文首先分析线性Schrodinger方程一种高阶差分格式的构造方法,得到方程的耗散项.在此基础上对三次非线性Schrodinger方程,提出了一种精度为O(r2 h2)的差分格式,证明了该格式保持了连续方程的两个守恒量,且是收敛的与稳定的.并通过数值例子与已有隐格式进行了比较,结果表明,本文格式在计算量类似的情况下,提高了数值精度.     

用相位调制方法测量光盘盘基应力双折射的精度分析

偏振相位调制方法是测量微小双折射的一种高精度检测方法。本文系统全面地分析了以ＰＭＣＳＡ结构形式测量光盘盘基应力双折射的相位调制方法中，由各种误差源造成的对测试结果的影响。     

Runge–Kutta interpolants for high precision computations

Runge–Kutta (RK) pairs furnish approximations of the solution of an initial value problem at discrete points in the interval of integration. Many techniques for enriching these methods with continuous approximations have been proposed. Here we construct C ¹ continuous, eighth and ninth order interpolation methods for a recently appeared RK pair of orders 9(8). These interpolants share a very small leading truncation error making them suitable for use at quadruple precision, i.e. 32–33 decimal digits of accuracy. Extended numerical results justify our effort.     

A high-current electron beam ion trap as an on-line charge breeder for the high precision mass measurement TITAN experiment

The precision of atomic mass measurements in a Penning trap is directly proportional to the charge state q of the ion and, hence, can be increased by using highly charged ions (HCI). For this reason, charge breeding with an electron beam ion trap (EBIT) is employed at TRIUMF’s Ion Trap for Atomic and Nuclear science (TITAN) on-line facility in Vancouver, Canada. By bombarding the injected and trapped singly charged ions with an intense beam of electrons, the charge state of the ions is rapidly increased inside the EBIT. To be compatible with the on-line requirements of short-lived isotopes, very high electron beam current densities are needed. The TITAN EBIT includes a 6 Tesla superconducting magnet and is designed to have electron beam currents and energies of up to 5 A and 60 keV, respectively. Once operational at full capacity, most species can be bred into a He-like configuration within tens of ms. Subsequently, the HCI are extracted, pass a Wien filter to reduce isobaric contamination, are cooled, and injected into a precision Penning trap for mass measurement. We will present the first results and current status of the TITAN EBIT, which has recently been moved to TRIUMF after assembly and commissioning at the Max-Planck-Institute (MPI) for Nuclear Physics in Heidelberg, Germany.     

An estimation of the measurement uncertainty for an optical emission spectrometric method

 A validation procedure based on the ISO/IEC 17025 standard was used to demonstrate the long-term stability of a calibration process and to assess the measurement uncertainty of a standard test method for optical emission vacuum spectrometric analysis of carbon and low-alloy steel (ASTM E 415–99a). The validation was used to provide documented evidence that the selected method fulfils the requirements and that the method is ”fit for purpose”. A test for drift was applied to determine statistically whether the analytical results vary systematically with time. The accuracy and traceability of the optimised method were tested by an analysis of closely matched matrix certified reference materials (CRMs). The measurement uncertainty estimations took account of the precision study, the bias and its uncertainty, and the qualification of uncertainties not considered in the overall performance studies. Received: 2 November 2002 Accepted: 2 January 2003 Acknowledgement The author expresses gratitude to Dr. Aleš Fajgelj for helpful discussions during the 3rd Central European Conference on Reference Materials and Measurements. Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to T. Drglin     

Measurement uncertainty of selenium determination in the reference material Seronorm Trace Elements Serum by hydride generation atomic fluorescence spectrometry

 An analytical result is not considered to be complete without a statement of the measurement uncertainty associated with it. Evaluation of measurement uncertainty is therefore an essential part of every determination. In the present study the measurement uncertainty of the result of determination of selenium in the reference material Seronorm Trace Elements Serum was studied. The combination of a digestion procedure using sulfuric acid, V₂O₅ in H₂SO₄ and hydrogen peroxide and the continuous flow approach of hydride generation atomic fluorescence spectrometry (HG-AFS) detection was used for selenium determination. The total uncertainty budget was calculated with the help of the GUM Workbench program, in which computations follow the rules of the ’ISO guide to the expression of uncertainty in measurement’. The major sources of uncertainty were found to be due to the recovery of the procedure, measurement of peak heights and the purity of Na₂SeO₃. A selenium mass fraction of 77.1±4.8 ng/g (with a coverage factor of 2.1, 95% probability) was determined, which is comparable with the recommended value of 80 ng/g. Received: 13 September 2002 Accepted: 23 December 2002 Acknowledgements We would like to thank Tinkara Buˇcar, B.Sc. for useful discussions and the IAEA Vienna, for financial support of the project 11553/RO. Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to V. Stibilj     

Response to high acidity and basicity at a platinum electrode in chronopotentiometry

A simple and rapid method is developed to determine the high acidity and the basicity of solutions by chronopotentiometry with a platinum working electrode. The acidity range from 5.0 mol/l H⁺ to 1.0 mol/l OH⁻ can be measured by the adjustment of deposition potential and time. The response mechanism to acidity and basicity has been explored. The transition potential plateau in chronopotentiograms is caused from the oxidation of hydrogen adsorbed on electrode surface.     

论测量不确定度

讨论了测量不确定度的基本概念及应用。分析了误差和不确定度两个概念的区别，探讨了不确定度及分量的评定方法。