Interlaboratory study of a liquid chromatography method for erythromycin: determination of uncertainty

Erythromycin is a mixture of macrolide antibiotics produced by Saccharopolyspora erythreas during fermentation. A new method for the analysis of erythromycin by liquid chromatography has previously been developed. It makes use of an Astec C18 polymeric column. After validation in one laboratory, the method was now validated in an interlaboratory study. Validation studies are commonly used to test the fitness of the analytical method prior to its use for routine quality testing. The data derived in the interlaboratory study can be used to make an uncertainty statement as well. The relationship between validation and uncertainty statement is not clear for many analysts and there is a need to show how the existing data, derived during validation, can be used in practice. Eight laboratories participated in this interlaboratory study. The set-up allowed the determination of the repeatability variance, s(2)r and the between-laboratory variance, s(2)L. Combination of s(2)r and s(2)L results in the reproducibility variance s(2)R. It has been shown how these data can be used in future by a single laboratory that wants to make an uncertainty statement concerning the same analysis.     

Spectroscopic detection of COClF in the tropical and mid-latitude lower stratosphere

We report retrievals of COClF (carbonyl chlorofluoride) based on atmospheric chemistry experiment (ACE) solar occultation spectra recorded at tropical and mid-latitudes during 2004-2005. The COClF molecule is a temporary reservoir of both chlorine and fluorine and has not been measured previously by remote sensing. A maximum COClF mixing ratio of (10^-12 per unit volume, 1 sigma) is measured at 28 km for tropical and subtropical occultations (latitudes below 20^° in both hemispheres) with lower mixing ratios at both higher and lower altitudes. Northern hemisphere mid-latitude mixing ratios (30-50°N) resulted in an average profile with a peak mixing ratio of , 1 sigma, at 27 km, also decreasing above and below that altitude. We compare the measured average profiles with the one reported set of in situ lower stratospheric mid-latitude measurements from 1986 and 1987, a previous two-dimensional (2-D) model calculation for 1987 and 1993, and a 2-D-model prediction for 2004. The measured average tropical profile is in close agreement with the model prediction; the northern mid-latitude profile is also consistent, although the peak in the measured profile occurs at a higher altitude (2.5-4.5 km offset) than in the model prediction. Seasonal average 2-D-model predictions of the COClF stratospheric distribution for 2004 are also reported.     

铝合金中Si、Fe含量测定的实验室间比对结果分析

为了解河南省内实验室在铝合金化学成分检测领域的整体水平,国家建材质检中心组织实施了铝合金化学成分中Si、Fe含量测定的实验室间比对。本次实验室比对共有20个实验室参加,推荐检测方法为：GB/T 7999-2007《铝及铝合金光电直读发射光谱分析方法》,也可采用其他国家标准方法。结果表明：实验室满意结果率为80%,不满意结果率为15%,可疑结果率为5%。参加比对的绝大多数实验室能够准确检测铝合金化学成分含量。     

Analysis of reliability systems via Gini-type index

Different strategies of reliability theory for the analysis of coherent systems have been studied by various researchers. Here, the Gini-type index is utilized as an applicable tool for the study and comparison of the ageing properties of complex systems. A new stochastic order in terms of Gini-type index is introduced to compare the speed of ageing of components and systems. The parallel-series and series-parallel systems with shared components are studied by their corresponding Gini-type indexes. Also, the generalization of Gini-type index for the multidimensional case is discussed, and is used to compare components lifetimes properties in the presence of other dependent components. It is shown that the ageing properties of a component lifetime can differ when the other components are working or have already failed. Numerous illustrative examples are given for better intuition of Gini-type and generalized Gini-type indexes throughout the paper.     

A scaled nonlinear conjugate gradient algorithm for unconstrained optimization

The best spectral conjugate gradient algorithm by (Birgin, E. and Martínez, J.M., 2001, A spectral conjugate gradient method for unconstrained optimization. Applied Mathematics and Optimization, 43, 117–128). which is mainly a scaled variant of (Perry, J.M., 1977, A class of Conjugate gradient algorithms with a two step varaiable metric memory, Discussion Paper 269, Center for Mathematical Studies in Economics and Management Science, Northwestern University), is modified in such a way as to overcome the lack of positive definiteness of the matrix defining the search direction. This modification is based on the quasi-Newton BFGS updating formula. The computational scheme is embedded into the restart philosophy of Beale–Powell. The parameter scaling the gradient is selected as spectral gradient or in an anticipative way by means of a formula using the function values in two successive points. In very mild conditions it is shown that, for strongly convex functions, the algorithm is global convergent. Computational results and performance profiles for a set consisting of 700 unconstrained optimization problems show that this new scaled nonlinear conjugate gradient algorithm substantially outperforms known conjugate gradient methods including: the spectral conjugate gradient SCG by Birgin and Martínez, the scaled Fletcher and Reeves, the Polak and Ribière algorithms and the CONMIN by (Shanno, D.F. and Phua, K.H., 1976, Algorithm 500, Minimization of unconstrained multivariate functions. ACM Transactions on Mathematical Software, 2, 87–94).     

A modified Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization

A modified Polak–Ribière–Polyak conjugate gradient algorithm which satisfies both the sufficient descent condition and the conjugacy condition is presented. These properties are independent of the line search. The algorithms use the standard Wolfe line search. Under standard assumptions, we show the global convergence of the algorithm. Numerical comparisons with conjugate gradient algorithms using a set of 750 unconstrained optimization problems, some of them from the CUTE library, show that this computational scheme outperforms the known Polak–Ribière–Polyak algorithm, as well as some other unconstrained optimization algorithms.     

A heuristic method to rectify intransitive judgments in pairwise comparison matrices

This paper investigates the effects of intransitive judgments on the consistency of pairwise comparison matrices. Statistical evidence regarding the occurrence of intransitive judgements in pairwise matrices of acceptable consistency is gathered by using a Monte-Carlo simulation, which confirms that relatively high percentage of comparison matrices, satisfying Saaty’s CR criterion are ordinally inconsistent. It is also shown that ordinal inconsistency does not necessarily decrease in the group aggregation process, in contrast with cardinal inconsistency. A heuristic algorithm is proposed to improve ordinal consistency by identifying and eliminating intransitivities in pairwise comparison matrices. The proposed algorithm generates near-optimal solutions and outperforms other tested approaches with respect to computation time.     

Resistance and conductance in structured Zermelo tournaments

The mathematical model that Zermelo developed for ranking by paired comparisons and that was later popularized by Bradley and Terry has several attractive theoretical properties, but computation of the associated ratings may involve solution of a system of several high-degree polynomial equations in several variables. This paper describes how to define quantities analogous to electrical resistance and conductance for certain generalized tournaments in such a way that these quantities are well-behaved with respect to certain types of decomposition of tournaments and permit comparison of the ratings of pairs of nodes. Application of this theory is illustrated through consideration of specific examples.     

A comparative study of two fast nonlinear free‐surface water wave models

This paper presents a comparison in terms of accuracy and efficiency between two fully nonlinear potential flow solvers for the solution of gravity wave propagation. One model is based on the high‐order spectral (HOS) method, whereas the second model is the high‐order finite difference model OceanWave3D. Although both models solve the nonlinear potential flow problem, they make use of two different approaches. The HOS model uses a modal expansion in the vertical direction to collapse the numerical solution to the two‐dimensional horizontal plane. On the other hand, the finite difference model simply directly solves the three‐dimensional problem. Both models have been well validated on standard test cases and shown to exhibit attractive convergence properties and an optimal scaling of the computational effort with increasing problem size. These two models are compared for solution of a typical problem: propagation of highly nonlinear periodic waves on a finite constant‐depth domain. The HOS model is found to be more efficient than OceanWave3D with a difference dependent on the level of accuracy needed as well as the wave steepness. Also, the higher the order of the finite difference schemes used in OceanWave3D, the closer the results come to the HOS model. Copyright © 2011 John Wiley & Sons, Ltd.