Das erste Oxoferrat(I): Zur Konstitution von K3[FeO2] und K3[NiO2]

The First Oxoferrate(I): On the Constitution of K₃[FeO₂] and K₃[NiO₂] Garnet-red single crystals of K₃[FeO₂] were obtained for the first time by heating intimate mixtures of K₆[CdO₄] and CdO (molar ratio 1:1.16) in closed Fe-cylinders at 450°C during 40 d. The same way of preparation via “reaction with the cylinder surface” was applied to prepare similarly coloured single crystals of K₃[NiO₂] (K₆CdO₄ in closed Ni-cylinders at 500°C during 49 d). The structure determination by four circle diffractometer data (MoKα , K₃[FeO₂]: 731 out of 731 I_o(hkl), R = 5.76%, R_w = 5.33%, K₃[NiO₂]: 755 out of 755 I_o(hkl), R = 8.70%, R_w = 4.25%) confirms the space groups P 4₁2₁2 and P 4₃2₁2, respectively. K₃[FeO₂]: a = 604.2(2) pm, c = 1 402.7(3) pm, Z = 4 K₃[NiO₂]: a = 603.6(1) pm, c = 1 405.2(2) pm, Z = 4. (powder data, standard deviations in parentheses) Essential feature of the structure are the dumb-bell-like anions [O? M? O]^3? (M = Fe, Ni). Their arrangement corresponds to a stuffed derivative of the KrF₂-type. Magnetic properties of K₃[FeO₂] were determined and cover the monovalence of Fe. MAPLE-calculations reveal the strong coincidence of monovalent VIIIb-cations.     

A geometric averaging procedure for constructing supertransitive approximation to binary comparison matrices

The usefulness of encoding the fuzzy evaluations of alternatives and the importance weights of criteria, in a multiple objective decision problem through binary comparison matrices (or pairwise judgment matrices) is receiving considerable attention. The methodology for identifying the best alternative in a given decision problem involves the computation of the principal eigenvectors of the binary comparison matrices. The eigenvectors transform the fuzzy evaluations of the importance of the criteria and the ratings of the alternatives into a ratio scale. A difficulty that is often experienced in using this approach in practice, is the inconsistency of the binary evaluations. This paper proposes a simple averaging procedure to construct a supertransitive approximation to a binary comparison matrix, where inconsistency is a problem. It is further suggested that such an adjustment might be necessary to more closely reflect the inherent fuzziness of the evaluations contained in a binary comparison matrix. The procedure is illustrated by means of examples.     

A new stochastic ultrametric tree unfolding methodology for assessing competitive market structure and deriving market segments

We present a new methodology for simultaneously assessing competitive market structure and deriving market segments. A hierarchical or ultrametric tree representation is estimated in a maximum likelihood framework from collected paired-comparison choice data. The derived tree portrays both brands and consumers/households/segments as terminal nodes, where the ‘closer’ a brand is to a particular consumer/household/segment in the tree, the higher the predicted probability of that consumer/household/segment choosing that particular brand. This paper initially presents an introduction to the problem of market structure assessment. We review the extensive marketing literature on market structure and survey several competing methodologies. The proposed stochastic ultrametric tree unfolding methodology is technically described and several program options are indicated. An illustration of the proposed methodology is presented with respect to paired comparison choice data collected from a convenience sample involving the over-the-counter analgesics market. Finally, several areas for future research are identified.     

Establishment of SI-traceable reference ranges for the content of various elements in the IMEP-9 water sample

 The International Measurement Evaluation Programme (IMEP) attempts to shed light on the current state of the practice in chemical measurements. The main tool, which assists this attempt and also differentiates IMEP from similar projects, is the establishment of SI-traceable reference ranges (where possible) for the elements offered for measurement to the participants for every IMEP round. The Institute for Reference Materials and Measurements (IRMM), as the founder and co-ordinator of IMEP has the responsibility of establishing the SI-traceable reference ranges. This is a large task that requires knowledge, skill and resources. IRMM collaborates with a network of reference laboratories in order to achieve the establishment of SI-traceable reference ranges in a transparent and reliable way. The IMEP reference laboratories must have demonstrated experience and have a proven and successful record in the use of primary methods of measurements (mainly isotope dilution mass spectrometry) and the application of uncertainty evaluation according to ISO/BIPM guidelines. In IMEP-9 "trace elements in water", results from 7 reference laboratories (including IRMM) were combined by IRMM to establish SI-traceable ranges for the 15 elements, which were then offered for measurement to the 200 participants worldwide. This paper does not discuss the individual contribution of the reference laboratories (this could be the subject of individual papers) but describes the procedures and criteria used in order to establish the reference ranges for the IMEP-9 samples by combining the individual contributions. All results submitted to IRMM are included, so as to make this publication as realistic as possible. Received: 31 December 1999 / Accepted: 7 March 2000     

The Factor Analytic Approach to Simultaneous Inference in the General Linear Model

Abstract

Consider the general linear model (GLM) Y = Xβ + ε. Suppose Θ₁,…, Θ_k, a subset of the β's, are of interest; Θ₁,…, Θ_k may be treatment contrasts in an ANOVA setting or regression coefficients in a response surface setting. Existing simultaneous confidence intervals for Θ₁,…, Θ_k are relatively conservative or, in the case of the MEANS option in PROC GLM of SAS, possibly misleading. The difficulty is with the multidimensionality of the integration required to compute exact coverage probability when X does not follow a nice textbook design. Noting that such exact coverage probabilities can be computed if the correlation matrix R of the estimators of Θ₁, …, Θ_k has a one-factor structure in the factor analytic sense, it is proposed that approximate simultaneous confidence intervals be computed by approximating R with the closest one-factor structure correlation matrix. Computer simulations of hundreds of randomly generated designs in the settings of regression, analysis of covariance, and unbalanced block designs show that the coverage probabilities are practically exact, more so than can be anticipated by even second-order probability bounds.     

Scaled conjugate gradient algorithms for unconstrained optimization

In this work we present and analyze a new scaled conjugate gradient algorithm and its implementation, based on an interpretation of the secant equation and on the inexact Wolfe line search conditions. The best spectral conjugate gradient algorithm SCG by Birgin and Martínez (2001), which is mainly a scaled variant of Perry’s (1977), is modified in such a manner 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 in the restart philosophy of Beale–Powell. The parameter scaling the gradient is selected as spectral gradient or in an anticipative manner 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. Preliminary computational results, for a set consisting of 500 unconstrained optimization test problems, show that this new scaled conjugate gradient algorithm substantially outperforms the spectral conjugate gradient SCG algorithm. The author was awarded the Romanian Academy Grant 168/2003.     

The nearest adjoining order method for pairwise comparisons in the form of difference of ranks

The problem of ranking of elements from some finite set on the basis of nearest adjoining order method for pairwise comparisons is investigated in this paper. It is assumed that in the set under consideration there exists a weak preference relation, which is to be identified (estimated) on the basis of pairwise comparisons in the form of difference of ranks. Moreover, the results of comparisons may be disturbed with random errors; the assumptions made about error distributions are not restrictive. The paper comprises: the problem formulation (definitions, assumptions, and optimisation problem, which provides the NAO solution) and the theoretical background – the form of distributions of random variables which make it possible to determine the properties of NAO solution, in particular, evaluation of the probability, that the NAO solution is equivalent to the errorless one. The approach presented in the paper can be extended to the case of more than one comparison for each pair of elements, i.e., completely formalised multi-experts ranking procedure. This revised version was published online in June 2006 with corrections to the Cover Date.     

A note on the quicksort asymptotics

In a recent paper, Bindjeme and Fill obtained a surprisingly easy exact formula for the L₂‐distance of the (normalized) number of comparisons of Quicksort under the uniform model to its limit. Shortly afterwards, Neininger proved a central limit theorem for the error. As a consequence, he obtained the asymptotics of the L₃‐distance. In this short note, we use the moment transfer approach to re‐prove Neininger's result. As a consequence, we obtain the asymptotics of the L_p‐distance for all Copyright © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,677–687, 2015     

External calibration in gas chromatography-combustion-isotope ratio mass spectrometry measurements of endogenous androgenic anabolic steroids in sports doping control

An alternative calibration procedure for the Gas Chromatography–Combustion–Isotope Ratio Mass Spectrometry (GC–C–IRMS) measurements of the World Antidoping Agency (WADA) Accredited Laboratories is presented. To alleviate the need for externally calibrated CO₂ gas for GC–C–IRMS analysis of urinary steroid metabolites, calibration using an external standard mixture solution of steroids with certified isotopic composition was investigated. The reference steroids of the calibration mixture and routine samples underwent identical instrumental processes. The calibration standards bracketed the entire range of the relevant δ¹³C values for the endogenous and exogenous steroids as well as their chromatographic retention times. The certified δ¹³C values of the reference calibrators were plotted in relation to measured m/z¹³CO₂/¹²CO₂ (i.e. R(45/44)) mass spectrometric signals of each calibrator. δ¹³C values of the sample steroids were calculated from the least squares fit through the calibration curve. The effect of the external calibration on δ¹³C values, using the same calibration standards and set of urine samples but different brands of GC–C–IRMS instruments, was assessed by an interlaboratory study in the WADA Accredited Laboratories of Sydney, Australia and Athens, Greece. Relative correspondence between the laboratories for determination of androsterone, etiocholanolone, 5β-androstane-3α,17β-diacetate, and pregnanediacetate means were SD(δ¹³C) = 0.12‰, 0.58‰, −0.34‰, and −0.40‰, respectively. These data demonstrate that accurate intralaboratory external calibration with certified steroids provided by United States Antidoping Agency (USADA) and without external CO₂ calibration is feasible and directly applicable to the WADA Accredited Laboratories for the harmonization of the GC–C–IRMS measurements.