Heteroscedastic controlled calibration model applied to analytical chemistry

In chemical analyses performed by laboratories, one faces the problem of determining the concentration of a chemical element in a sample. In practice, one deals with the problem using the so‐called linear calibration model, which considers that the errors associated with the independent variables are negligible compared with the former variable. In this work, a new linear calibration model is proposed assuming that the independent variables are subject to heteroscedastic measurement errors. A simulation study is carried out in order to verify some properties of the estimators derived for the new model and it is also considered the usual calibration model to compare it with the new approach. Three applications are considered to verify the performance of the new approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Assessment uncertainty associated to the analysis of organic compounds linked to particulate matter of atmospheric aerosols

Current work has evaluated uncertainty associated to quantification of several organic compounds present in particulate matter of atmospheric aerosols, setting out the stages of analytical procedure that contribute most to the global uncertainty. Several sources of uncertainty have been identified, which were clustered into five main contributions: sampling, extraction, clean-up, derivatization and analysis. A discussion of the main contributions to the overall uncertainty is reported, allowing authors to locate the largest ones and plan future improvements. Combined uncertainties ranged between 10-18% (alkanes), 12-16% (PAHs), 10-18% (alcohols) and 9-21% (acids). The analytical procedure was validated by analysing a standard reference material (SRM1649a, urban dust). Also, the proposed method was applied to the analysis of four samples of particulate matter.     

气相色谱-质谱联用法测定化妆品中邻苯二甲酸酯类化合物的不确定度评定

气相色谱-质谱联用法测定化妆品中邻苯二甲酸酯类化合物不确定度的主要来源有标准溶液引入的不确定度、样品引入的不确定度、样品处理过程中引入的不确定度。以邻苯二甲酸二丁酯(DBP)为例,对各不确定度分量进行了评定,计算了合成不确定度和扩展不确定度。当化妆品中DBP测量结果为10.39 mg/L时,其扩展不确定度为0.50 mg/L(k=2)。     

扭摆法测物体转动惯量的不确定度分析

扭摆法是测量物体转动惯量的有效方法,其不确定度分析是关键.本文推导了扭摆法测物体转动惯量准确的不确定度传递公式,得到各直接测量量及其不确定度对转动惯量不确定度的影响.并进行了算例分析.结果表明,扭摆法比三线摆测得物体的转动惯量的误差以及不确定度要小很多.这对实验方法的选择和仪器的研制具有重要的实际意义.     

关于不确定度的教学探讨

文章澄清了大学物理实验中关于不确定度内容的教学中遇到的一些困惑,给出了相应的解决办法.     

高功率激光装置打靶精度测试技术

 多路激光打靶精度在惯性约束聚变实验中起着至关重要的作用,提出了基于X光针孔相机的激光打靶精度测试方法。根据显微镜读取的靶平面坐标系的靶孔中心坐标及打多孔靶后X光针孔相机所记录的靶孔中心坐标,建立靶平面坐标系和X光针孔相机坐标系之间的转换关系;通过打焦斑靶,建立焦斑模板,采用套模板的方法,读取X光针孔相机坐标系中焦斑中心坐标;由靶平面坐标系和X光针孔相机坐标系之间的转换关系,求出靶平面坐标系中焦斑中心坐标,计算得到激光打靶精度,分析打靶精度测试结果的不确定度,从而给出多路激光打靶精度测量技术和方法。     

光斑环围参量阵列测试法的测量不确定度

 为评定光斑环围参量（包括环围功率和环围尺寸）阵列测试法的测量不确定度,给出了环围参量一般形式的定义和连续形式的计算表达式,归纳并比较了阵列测试法下光斑环围参量的3种常用计算方法,即近似环围功率法、准确环围功率法和等效环围尺寸法,给出了零阶近似下环围参量离散形式的计算表达式。根据不确定度传递律,推导了基于等效环围尺寸法的环围参量测量不确定度的一般表达式,讨论了常见简化条件下的环围参量测量不确定度表达式。建立了光斑环围参量计算及其不确定度评定的一套较完整的方法。以强度为高斯分布的光斑为例,得到了简化条件下的环围参量测量不确定度的解析表达式,并用数值模拟法验证了其正确性。     

浅析量子力学中的不确定性原理

德国物理学家海森伯在1927年提出的不确定性原理,包括两力学量间的不确定性原理和能量与时间的不确定性原理,它的提出意味着量子力学不仅有了完整的数学形式,而且有了合理的理论解释.本文尝试通过对不确定性原理的创立背景、过程、应用等来对这一原理做简要介绍,特别强调了科学讨论在科学发展中的作用.     

Risk models for the Prize Collecting Steiner Tree problems with interval data

Given a connected graph G=(V,E)with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V′V,the Prize Collecting Steiner Tree(PCST)problem is to find a tree T in G interconnecting all vertices of V′such that the total cost on edges in T minus the total prize at vertices in T is minimized.The PCST problem appears frequently in practice of operations research.While the problem is NP-hard in general,it is polynomial-time solvable when graphs G are restricted to series-parallel graphs.In this paper,we study the PCST problem with interval costs and prizes,where edge e could be included in T by paying cost xe∈[c e,c+e]while taking risk(c+e xe)/(c+e c e)of malfunction at e,and vertex v could be asked for giving a prize yv∈[p v,p+v]for its inclusion in T while taking risk(yv p v)/(p+v p v)of refusal by v.We establish two risk models for the PCST problem with interval data.Under given budget upper bound on constructing tree T,one model aims at minimizing the maximum risk over edges and vertices in T and the other aims at minimizing the sum of risks over edges and vertices in T.We propose strongly polynomial-time algorithms solving these problems on series-parallel graphs to optimality.Our study shows that the risk models proposed have advantages over the existing robust optimization model,which often yields NP-hard problems even if the original optimization problems are polynomial-time solvable.     

Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.