An error-free algorithm to solve a linear system of polynomial equations

The paper presents an error-free algorithm to solve a system of linear equations with polynomial coefficients. Modular arithmetic in residual polynomial class and in residual numeric class is employed. The algorithm is iterative and well suited for implementation for computers with vector operations and fast and error-free convolutors.     

A new tuning procedure for the DTL RF field pattern

The DTL tank is a multi-cell cavity.In a fabricated tank,the measured average axial field E0 for each cell may obviously deviate from the designed value.It is generally thought the deviation is due to the errors in fabrication and assembly.But it is not always true.In this paper,it is shown that the deviation may already exist before fabrication in some cases.It is partly due to the imperfection of the current design procedures.A new design method is introduced to reduce the deviation in the design stage.     

Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.     

数值积分公式中间点的渐近性质及其应用

主要研究了三类数值积分公式的中间点的渐近性质,得到了更一般性的结果.基于中间点的渐近性质,获得了数值积分的校正公式及其条件误差估计.数值例子显示了校正公式的精度明显高于对应的计算公式.     

拉脱法测液体表面张力系数的误差分析

对拉脱法测量液体表面张力系数实验的原理和仪器做了简要的介绍,并着重对该实验误差的来源进行了分析探讨。     

Asymptotic properties of local polynomial regression with missing data and correlated errors

The main objective of this work is the nonparametric estimation of the regression function with correlated errors when observations are missing in the response variable. Two nonparametric estimators of the regression function are proposed. The asymptotic properties of these estimators are studied; expresions for the bias and the variance are obtained and the joint asymptotic normality is established. A simulation study is also included.     

Potential energy curves for the X~1Σ_g~ , B~1△_g and B′~1Σ_g~ states of C_2 using MRCI and approximate CI methods

The potential energy curves for the X1Σ g , B1△g and B′1Σ g states of C2 have been studied by using MRC and approximate CI methods, and are benchmarked against the calculations of full configuration in teraction (FCI). The results obtained by MRCI method agree with the FCI very well, and even are accu rate enough to compare other approximate methods as benchmark, when the calculations of FCI ar not feasible. The approximate CI methods mentioned in this paper are reliable for treating chemica problems.     

The assessment of compliance with legal limits. Part 2. How to consider both type I and type II errors when working in the concentration domain

Considering the uncertainty of measurement when assessing compliance with reference values given in compositional specifications and statutory limits is still a controversial matter. In theory, assessing compliance requires considering both type I (false positive) and type II (false negative) errors. The more the concentration of the analyte in the sample under investigation is close to the allowed concentration limit, the more critical it is to consider both types of errors. This paper describes how this could be done. The matter is discussed in the light of the most recent literature information.     

The effect of capillary column diameter on the performance of thermal conductivity detectors

The concentration sensitivity of a thermal conductivity detector (TCD) depends, among other factors, on the amount of sample mixture in the detector's sensing cell. Since the cell volume has to be appropriately matched with column diameter, it makes the concentration sensitivity of a TCD dependent on column diameter and, therefore, on the speed of gas chromatography. Through reduction of column diameter, higher speed tends to lead to a reduction in the concentration sensitivity of the cell. The factor which the most directly affects the concentration sensitivity of a TCD cell is the heat power conducted through the cell. The higher the power, the greater the sensitivity. The limit of detection of a TCD depends on the concentration-sensitivity of its cell and on the level of statistical errors in the measurement. The errors increase with increasing analysis speed. As the column diameter is reduced, the errors cause additional worsening (on top of the decrease in concentration sensitivity) of the detection limit, dynamic range, and other performance characteristics of the TCD.