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  • Analytical Chemistry and Spectroscopy  (1,518)
  • LUNAR AND PLANETARY EXPLORATION  (928)
  • Inorganic Chemistry  (727)
  • 2015-2019
  • 1990-1994  (3,173)
  • 1993  (3,173)
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  • 2015-2019
  • 1990-1994  (3,173)
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  • 1
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    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 7 (1993), S. 153-163 
    ISSN: 0886-9383
    Keywords: Generalized inverse ; K-matrix analysis ; P-matrix analysis ; Least squares ; Principal component regression ; Partial least squares ; Continuum regression ; Beer's law ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper consists of two distinct but related parts. In the first part a geometric theory of generalized inverses is presented and a methodology based on this theory is developed and applied to solve the K-matrix and P-matrix forms of Beer's law. It is shown that most currently accepted and practiced methods for solving these forms of Beer's law are just special cases of this geometric theory of generalized inverses. In addition, this geometric theory is used to explain why the current methods work and why they fail.In the second part a general methodology that includes as special cases least squares, principal component regression, partial least squares 1 and 2, continuum regression plus a variety of other described and undescribed methodologies is presented and then applied to solve the P-matrix formulation of Beer's law. This general methodology, like the first, is also geometric in nature and relies on an understanding of projections.The main emphasis of this paper is one of perspective, which, if understood, provides the proper foundation for answering the general but extremely hard and possibly unanswerable question “what is the best method?”.
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  • 2
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    Journal of Chemometrics 7 (1993), S. 99-115 
    ISSN: 0886-9383
    Keywords: Classification ; Appreciation function ; Regularized discriminant analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Regularized discriminant analysis has proven to be a most effective classifier for problems where traditional classifiers fail because of a lack of sufficient training samples, as is often the case in highdimensional settings. However, it has been shown that the model selection procedure of regularized discriminant analysis, determining the degree of regularization, has some deficiencies associated with it. We propose a modified model selection procedure base on a new appreciation function. By means of an extensive simulation it was shown that the new model selection procedure performs better than the original one. We also propose that one of the control parameters of regularized discriminant analysis be allowed to take on negative values. This extension leads to an improved performance in certain situations. The results are confirmed using two chemical data sets.
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  • 3
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    Journal of Chemometrics 7 (1993), S. 527-541 
    ISSN: 0886-9383
    Keywords: Principal component analysis ; Projection pursuit ; Simulated annealing algorithm ; Robust statistics ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Principal component analysis (PCA) is a widely used technique in chemometrics. The classical PCA method is, unfortunately, non-robust, since the variance is adopted as the objective function. In this paper, projection pursuit (PP) is used to carry out PCA with a criterion which is more robust than the variance. In addition, the generalized simulated annealing (GSA) algorithm is introduced as an optimization procedure in the process of PP calculation to guarantee the global optimum. The results for simulated data sets show that PCA via PP is resistant to the deviation of the error distribution from the normal one. The method is especially recommended for use in cases with possible outlier(s) existing in the data.
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  • 4
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    Journal of Chemometrics 7 (1993), S. 165-176 
    ISSN: 0886-9383
    Keywords: Measurement error ; Outliers ; Environmental ; Quality control ; Multivariate kurtosis ; Generalized distance ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Environmental data are usually multivariate, with the variables conforming to some correlation structure. Occasionally, measurements which do not conform in structure or magnitude may occur in one or more variables. It is important (1) to characterize these discordancies in terms of the disturbed variables and the direction and magnitude of the anomalous error and (2) to associate each discordant observation with a specific cause of measurement error in order to prevent further mismeasurement. We describe a procedure for identifying suspected causes of discordant observations in otherwise multinormal data sets. Variables are assigned to groups, each of which is associated with a specific cause of measurement error. Discordant observations are identified with the generalized distance test or the multivariate kurtosis test. Suspected causes of measurement error are identified by repeating the tests with one of the groups of variables omitted in each analysis. The procedures are evaluated with simulated data sets having a correlation structure similar to that of a large environmental data set.
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  • 5
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    Journal of Chemometrics 7 (1993), S. 195-212 
    ISSN: 0886-9383
    Keywords: Calibration ; Non-linearity ; Principal components ; Stein estimate ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new regression method for non-linear near-infrared spectroscopic data is proposed. The technique is based on a model which is linear in the principal components and simple functions (squares and products) of them. Added variable plots are used to determine which squares and products to incorporate into the model. The regression coefficients are estimated by a Stein estimate which shrinks towards the estimate determined by the first several principal components and the selected non-linear terms. The technique is not computationally intensive and is appropriate for routine predictions of chemical concentrations. The method is tested on three data sets and in all cases gives more accurate predictions than does linear principal components regression.
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  • 6
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    Journal of Chemometrics 7 (1993), S. 213-222 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 7
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 8
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 9
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    Journal of Chemometrics 7 (1993) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 10
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    Journal of Chemometrics 7 (1993), S. 393-425 
    ISSN: 0886-9383
    Keywords: Preprocessing ; Closure ; Normalization ; Ratioing ; Constant sum transformation ; Constant length transformation ; Maximum value transformation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The geometric properties of three common object-preprocessing transformations (constant sum, or closure; constant length, or normalization; and maximum value, or ratioing) are investigated. An argument is made for using absolute values in the constant sum and maximum value transformations. In general, each transformation distorts the shape and dimensionality of patterns in the data: transformed data lie on (C-1)-dimensional surfaces in the original C-dimensional space. A data set that has been closed by one of these transformations can be reopened if a vector containing the constant sums, constant lengths or maximum values of the original objects was retained. Transformed data sets may be freely interconverted among these three transformations without the loss of information.
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  • 11
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    Journal of Chemometrics 7 (1993), S. 447-452 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 12
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    Journal of Chemometrics 7 (1993), S. 143-148 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 13
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    Journal of Chemometrics 7 (1993), S. 131-142 
    ISSN: 0886-9383
    Keywords: Classification ; Discriminant analysis ; Class modeling ; Specification limits ; Cross-validation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: There are many chemical products where product conformity is decided upon by qualitative human judgements of overall product quality. Nowadays, quantitative instrumentally determined quality parameters become available which are intended to replace such qualitative judgements by means of automatic decision rules using multivariate specification limits. Six classification methods to derive such limits are compared in terms of their power to predict corresponding human judgemets on overall color conformity of 17 dyestuffs based on historical quality data. Standard statistical classification methods turned out to be unacceptable for the routine generation of decision rules because of the frequent distinct suboptimality of their predictive power. Instead, a simple non-statistical classification method utilizing a priori knowledge about the underlying data structure yielded uniformly satisfactory decision rules.
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  • 14
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    Journal of Chemometrics 7 (1993), S. 149-150 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 15
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    Journal of Chemometrics 7 (1993) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 16
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    Journal of Chemometrics 7 (1993), S. 151-151 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 17
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    Journal of Chemometrics 7 (1993), S. 477-494 
    ISSN: 0886-9383
    Keywords: Three-way principal components analysis ; Core matrix ; Body diagonalization ; Lower and upper bounds ; Simulation ; Soil contamination ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In contrast with conventional PCA, a direct superposition and joint interpretation of loading plots is not possible in three-way PCA, since there may be data variance which is described by unequal components of different modes. The contributions to variance of all possible combinations of components are described in the core matrix. Body diagonalization, which is achieved by appropriate rotation of component matrices, is an essential tool for simplifying the core matrix structure. The maximum degree of body diagonality which may be obtained from such transformations is analysed from both the mathematical and simulation viewpoints. It is shown that, at least in the average case, high degrees can be expected, which makes the procedure reasonable for many practical applications. Furthermore, simulation as well as theoretical derivation show that the success of body diagonality depends on the so-called polarity of the core array. The methodology is illustrated by a three-way data example from environmental chemistry.
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  • 18
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    Journal of Chemometrics 7 (1993), S. 495-526 
    ISSN: 0886-9383
    Keywords: Standard errors ; Eigenvalues ; PCA ; MLR ; GRAM ; Rank estimation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: New expressions are derived for the standard errors in the eigenvalues of a cross-product matrix by the method of error propagation. Cross-product matrices frequently arise in multivariate data analysis, especially in principal component analysis (PCA). The derived standard errors account for the variability in the data as a result of measurement noise and are therefore essentially different from the standard errors developed in multivariate statistics. Those standard errors were derived in order to account for the finite number of observations on a fixed number of variables, the so-called sampling error. They can be used for making inferences about the population eigenvalues. Making inferences about the population eigenvalues is often not the purposes of PCA in physical sciences. This is particularly true if the measurements are performed on an analytical instrument that produces two-dimensional arrays for one chemical sample: the rows and columns of such a data matrix cannot be identified with observations on variables at all. However, PCA can still be used as a general data reduction technique, but now the effect of measurement noise on the standard errors in the eigenvalues has to be considered. The consequences for significance testing of the eigenvalues as well as the usefulness for error estimates for scores and loadings of PCA, multiple linear regression (MLR) and the generalized rank annihilation method (GRAM) are discussed. The adequacy of the derived expressions is tested by Monte Carlo simulations.
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  • 19
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    Journal of Chemometrics 7 (1993), S. 551-557 
    ISSN: 0886-9383
    Keywords: Krylov sequence ; Partial least squares ; Polynomial regression ; Principal component regression ; R2 ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: PLS1 regression is generally viewed as lying in between PCR and OLS regression. Proof is given that the coefficient of determination, R2, for a PLS multivariate calibration model is at least as high as that for a PCR model with the same number of components. It appears that PLS can be linked to a correlation-weighted polynomial regression of a constant response on the eigenvalues of the covariance matrix of the predictor variables.
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  • 20
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    Journal of Chemometrics 7 (1993), S. 543-550 
    ISSN: 0886-9383
    Keywords: Fragment occurrence data ; Molecular similarity ; Similarity searching ; Standardization ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Substructural fragment occurrence data are widely used as the basis for measures of inter-molecular structural similarity. This paper investigates the effect of standardization on the effectiveness of such measures using eight data sets for which both structural and biological activity data are available. Eight different standardization methods are studied and it is shown that there is no significant difference in the effectivenesses of the various methods; accordingly, any of them can be used for the calculation of intermolecular structural similarity.
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  • 21
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    Journal of Chemometrics 7 (1993), S. 77-88 
    ISSN: 0886-9383
    Keywords: Direct trilinear decomposition method ; Curve resolution ; Trilinear data ; Similarity transformation ; Generalized rank annihilation method ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The direct trilinear decomposition method (DTDM) is an algorithm for performing quantitative curve resolution of three-dimensional data that follow the so-called trilinear model, e.g. chromatography-spectroscopy or emission-excitation fluorescence. Under certain coditions complex eigenvalues and eigenvectors emerge when the generalized eigenproblem is solved in DTDM. Previous publications never treated those cases. In this paper we show how similarity transformations can be used to eliminate the imaginary part of the complex eigenvalues and eigenvectors, thereby increasing the usefulness of DTDM in practical applications. The similarity transformation technique was first used by our laboratory to solve the similar problem in the generalized rank annihilation method (GRAM). Because unique elution profiles and spectra can be derived by using data matrices from three or more samples simultaneously, DTDM with similarity transformations is more efficient than GRAM in the case where there are many samples to be investigated.
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  • 22
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    Journal of Chemometrics 7 (1993), S. 227-242 
    ISSN: 0886-9383
    Keywords: Non-linear mapping ; Graphical methods ; SAR ; SPR ; Quality of representation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: From a review of the theoretical aspects of non-linear mapping and the different algorithms available in the literature, the methodological and practical problems linked to the use of this multivariate method in structure-activity and structure-property relationship studies are underlined. Useful tools for the graphical display of the outputs and the interpretation of the obtained clusters are presented. Statistical parameters estimating the quality of the graphical representation of each individual are also introduced. An example of application on a data matrix of 37 acaricides described by four physicochemical descriptors (π, F, R, MR) is presented.
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  • 23
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    Journal of Chemometrics 7 (1993), S. 243-253 
    ISSN: 0886-9383
    Keywords: Orthogonal expansion ; Mapping ; Modelling ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper we discuss the orthogonal expansion of data matrices and its application to mapping and modelling. Two new methods, modified optimal discriminant plane (MODP) for mapping and order Gram-Schmidt orthogonalization (OGSO) for modelling, are proposed and examples are given.
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  • 24
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    Journal of Chemometrics 7 (1993), S. 255-265 
    ISSN: 0886-9383
    Keywords: Multicomponent calibration ; Non-linearity ; Selectivity ; Wavelength selection ; Graphical diagnostics ; Outliers ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Modern scanning infrared reflectance/absorption spectroscopes measure absorptions or reflectance at a sequence of around 1000 wavelengths. Training data may consist of 10-100 carefully designed sample mixtures whose true compositions are either known by formulation or accurately determined by wet chemistry. In future, one wishes to predict the true composition of a newly presented sample from its spectrum. Varying compositions of a mixture of three sugars in water are used for illustration of several different graphical techniques; the spectral measurements here are near-infrared (NIR) absorbances, but there is nothing exclusively infrared about the methodology. Graphs display the adequacy of a linear explanation of absorbance variability at each wavelength by wavelength linearity plots. These highlight regions of the spectrum where non-linearities and interaction effects are substantial. By selecting out these substantially non-linear regions, one can concentrate on linear formulae for prediction with resultant robust linear modelling. Such selections are further aided by plots which identify the component sugar for which each wavelength is most selective. Such plots offer rather natural pre-screening as an alternative or supplement to the wavelength selection method of Brown.We also display prediction diagnostics (R, Rx) which on a sample-by-sample basis may diagnose a particularly unusual presented spectrum. These diagnostics are shown to have predictive import for a validation data set.
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  • 25
    ISSN: 0886-9383
    Keywords: Kalman filter ; Multivariate calibration ; Condition number ; Prediction error ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The usefulness of the Kalman filter as an algorithm for calibration in a real system is shown. Results are compared with classical least squares and pure component calibration. The prediction of four priority pollutant chlorophenols in binary, ternary and quaternary mixtures was also carried out by Kalman filtering. The condition number, standard deviation and prediction error have been employed to choose the most suitable wavelength range. Comparison of the standard error of prediction in the validation set shows significant differences between the evaluated chlorophenols, the best results being obtained with Kalman multivariate calibration.
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  • 26
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    Journal of Chemometrics 7 (1993), S. 455-475 
    ISSN: 0886-9383
    Keywords: Biological activity ; Cross-validation ; Exchangeability ; Molecular descriptors ; Prediction ; Relationship ; Structure ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The two parts of this paper form a critique of a variety of statistical techniques of actual or potential use in quantitative structure-activity relationship (QSAR) studies and related fields. Part I explores the statistical thinking that is needed to underpin those techniques. Emphasis as placed on (a) the role of ‘exchangeability’ as an alternative to unrealistic statistical modelling and (b) the use of cross-validation to limit self-deception in the use of any particular technique. The problem of the almost unlimited range of molecular descriptors is seriously addressed. (Part II provides a concise critical review of methods-some well-established and some new.)
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  • 27
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    Journal of Chemometrics 7 (1993) 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Chemistry and Pharmacology
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  • 28
    ISSN: 0886-9383
    Keywords: Multicomponent analysis ; Factor analysis ; Detection limit ; Local rank ; Zero-component region ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper we redefine the term detection limit to embrace the inherent multivariate nature of samples, instrumental measurements and chemometrics resolution procedures. The so-called zero-component regions, i.e. parts with no chemical components eluting, are used as repeated analytical blanks to estimate a statistical multivariate detection limit for determining the number of chemical species in local regions of a single two-way chromatogram or a collection of synchronized one-way chromatograms. For two-way chromatography the detection limit is determined from the distribution of the first eigenvalues obtained from all possible combinations of spectra in the zero-component regions. The number of spectra in each calculation should correspond to the number included in the later examination of the local retention time regions. For one-way chromatography on a collection of samples with similar chemical components at varying concentrations the same procedure is used, with the samples taking the role of the spectra in two-way chromatography. The detection limit can be chosen at various confidence levels depending on whether false positive or negative detection of minor components is most critical. The results obtained from the zero-eigenvalue distribution are more robust than those obtained by a previously developed F-test.
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  • 29
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    Journal of Chemometrics 7 (1993), S. 305-340 
    ISSN: 0886-9383
    Keywords: Stem & leaf display ; Histogram ; Boxplot ; Quantile plot ; Scatterplot ; Regression ; Smoothing ; 3D rotation ; Scatterplot matrix ; OMEGA strategy ; Dimension reduction ; Stability of structure ; Resampling ; Interpretation of structure ; Prediction models ; Variables selection ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Exploratory data analysis (EDA) is a toolbox of data manipulation methods for looking at data to see what they seem to say, i.e. one tries to let the data speak for themselves. In this way there is hope that the data will lead to indications about ‘models’ of relationships not expected a priori. In this respect EDA is a pre-step to confirmatory data analysis which delivers measures of how adequate a model is. In this tutorial the focus is on multivariate exploratory data analysis for quantitative data using linear methods for dimension reduction and prediction. Purely graphical multivariate tools such as 3D rotation and scatterplot matrices are discussed after having introduced the univariate and bivariate tools on which they are based. The main tasks of multivariate exploratory data analysis are identified as ‘search for structure’ by dimension reduction and ‘model selection’ by comparing predictive power. Resampling is used to support validity, and variables selection to improve interpretability.
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  • 30
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    Journal of Chemometrics 7 (1993), S. 369-379 
    ISSN: 0886-9383
    Keywords: Simulated annealing ; Constrained background bilinearization ; Calibration ; Two-way bilinear data ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Generalized simulated annealing (GSA) is an optimization technique for locating the global optimum. In this paper GSA was used as the optimization procedure in the constrained background bilinearization (CBBL) of two-way bilinear data in order to reduce the possibility of sinking into local optima. The behaviour of the algorithm and its comparison with the modified Powell algorithm were studied by simulations and real fluorescence excitation-emission data for organic dye mixtures.
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  • 31
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    Journal of Chemometrics 7 (1993) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 32
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    Journal of Chemometrics 7 (1993), S. 1-14 
    ISSN: 0886-9383
    Keywords: Continuum regression ; Dynamic model identification ; Principal component regression ; Partial least squares regression ; Finite impulse response ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The use of continuum regression (CR) for the identification of finite impulse response (FIR) dynamic models is investigated. CR encompasses the methods of principal component regression (PCR), partial least squares (PLS) and multiple linear regression (MLR). PCR and MLR are at the two extremes of the continuum. In PCR and PLS, cross-validation is used to determine the optimum number of factors or ‘latent variables’ to retain in the regression model. CR allows one to vary the method in addition. Cross-validation then determines both the optimum method and the number of latent variables. The CR ‘prediction error surface’ - a function of the method and number of latent variables - is elucidated. The optimal model is defined as the minimum of this surface. Among the cases studied, the optimal model usually comes from the region of the continuum between PCR and PLS. Few derive from the region between PLS and MLR. It is also demonstrated that FIR models identified by CR have frequency domain properties similar to those identified by PCR.
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  • 33
    ISSN: 0886-9383
    Keywords: Curve resolution ; Multicomponent analysis ; Latent projections ; Local factor analysis ; Chlorophyll degradation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: High-performance liquid chromatography with diode array detection (HPLC--DAD) is used to characterize mixtures from chlorophyll a degradation experiments. Overlapping chromatographic peaks are resolved by means of the heuristic evolving latent projections (HELP) method. The HELP method is a self-modelling curve resolution method. No assumptions are made about spectral and/or chromatographic peak shape. In the first step the method establishes the real noise level in the data by use of the so-called zero-component regions. This information is used to reveal selective chromatographic information and the number of chemical species at every retention time in unresolved chromatographic peaks. Utilising the selective chromatographic regions in combination with the zero-concentration windows, unique resolution into concentration profiles and spectra of the pure chemical species is accomplished. HPLC-DAD data from six chlorophyll a degradation experiments were analysed. Consistent results were obtained even with very similar spectra for six or seven overlapping chemical components.
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  • 34
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    Journal of Chemometrics 7 (1993), S. 45-59 
    ISSN: 0886-9383
    Keywords: Partial least squares ; PLS algorithm ; Kernel ; Multivariate image analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A fast and memory-saving PLS regression algorithm for matrices with large numbers of objects is presented. It is called the kernel algorithm for PLS. Long (meaning having many objects, N) matrices X (N × K) and Y (N × M) are condensed into a small (K × K) square ‘kernel’ matrix XTYYTX of size equal to the number of X-variables. Using this kernel matrix XTYYTX together with the small covariance matrices XTX (K × K), XTY (K × M) and YTY (M × M), it is possible to estimate all necessary parameters for a complete PLS regression solution with some statistical diagnostics. The new developments are presented in equation form. A comparison of consumed floating point operations is given for the kernel and the classical PLS algorithm. As appendices, a condensed matrix algebra version of the kernel algorithm is given together with the MATLAB code.
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  • 35
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    Journal of Chemometrics 7 (1993), S. 61-73 
    ISSN: 0886-9383
    Keywords: Compression ; Multivariate analysis ; B-splines ; Maximum entropy ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For efficient handling of very large data arrays, pretreatment by compression is mandatory. In the present paper B-spline methods are described as good candidates for such data array compression. The mathematical relation between the maximum entropy method for compression of data tables and the B-spline of zeroth degree is described together with the generalization of B-spline compression to nth-order data array tables in matrix and tensor algebra.
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  • 36
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    Journal of Chemometrics 7 (1993) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 37
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    Journal of Chemometrics 7 (1993), S. 75-76 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 38
    ISSN: 0886-9383
    Keywords: Factor analysis ; Window factor analysis ; Multicomponent analysis ; Ultraviolet spectroscopy ; Cu(II) complexes ; Ethylenediaminetetraacetic acid ; EDTA ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Window factor analysis (WFA) is a self-modeling chemometric technique for obtaining the concentration profiles of components from evolutionary processes such as chromotography, titration and reaction kinetics. By specifying the ‘window’, i.e. the region along the evolutionary axis indigenous to a component, the concentration profile of the component can be obtained without recourse to any information concerning the other components. Mathematical expressions required to perform such computations are derived. The method is applied to the investigation of copper(II) complexation with ethylenediaminetetraacetate (EDTA) by recording and factor analyzing the ultraviolet spectra of aqueous solutions containing a fixed amount of the disodium salt of EDTA and varying amounts of CuCl2. Evidence for four different species of EDTA is obtained. Clues concerning the stoichiometry of the species are garnered from the concentration profiles.
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  • 39
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    Journal of Chemometrics 7 (1993), S. 117-130 
    ISSN: 0886-9383
    Keywords: Calibration ; Rank annihilation ; Three-way ; Trilinear ; Bilinear ; Non-bilinear ; Net analyte signal ; MS/MS ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Several multivariate methods are now available for the calibration of second-order or hyphenated instruments (e.g. GC/MS). When applied to bilinear data, it has been shown that calibration can be performed in the presence of unknown interferences - a significant advantage over first-order calibration. In this paper, non-bilinear rank annihilation (NBRA), a method which has the potential of handling, second-order non-bi-linear data, is studied through theoretical analysis and computer simulation. It is found that the second-order advantage can be carried over to non-bilinear data if a property defined as net analyte rank (NAR) holds for the analyte of interest. The net analyte signal (NAS) is defined accordingly for second-order calibration and the analogy to and difference from lower-order calibration are discussed. With NAS, some analytical figures of merit such as signal-to noise ratio, selectivity, sensitivity and limit of determination can be calculated for second order calibration. An application to MS/MS data is also given.
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  • 40
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    Journal of Chemometrics 7 (1993), S. 439-445 
    ISSN: 0886-9383
    Keywords: Calibration ; Rank annihilation ; Residual bilinearization ; Three-way ; Trilinear ; Net analyte rank ; Second-order ; Generalized rank annihilation method (GRAM) ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Through theoretical analysis and computer simulation, this short communication comments on the residual bilinearization (RBL) method and compares it with non-bilinear rank annihilation (NBRA) for the treatment of second-order calibration with non-bilinear data. It is found that these two methods are mathematically equivalent but have different noise propagation properties. The second-order advantage, namely quantitation in the presence of unknown interferences, can be carried over to non-bilinear data only if there exists a net analyte rank (NAR) for the analyte of interest.
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  • 41
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    Journal of Chemometrics 7 (1993) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 42
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    Journal of Chemometrics 7 (1993), S. 453-454 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 43
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    Journal of Chemometrics 7 (1993), S. 291-304 
    ISSN: 0886-9383
    Keywords: Partial least squares ; Monte Carlo methods ; Cross validation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Partial least squares (PLS) regression is a commonly used statistical technique for performing multivariate calibration, especially in situations where there are more variables than samples. Choosing the number of factors to include in a model is a decision that all users of PLS must make, but is complicated by the large number of empirical tests available. In most instances predictive ability is the most desired property of a PLS model and so interest has centred on making this choice based on an internal validation process. A popular approach is the calculation of a cross-validated r2 to gauge how much variance in the dependent variable can be explained from leave-one-out predictions. Using Monte Carlo simulations for different sizes of data set, the influence of chance effects on the cross-validation process is investigated. The results are presented as tables of critical values which are compared against the values of cross-validated r2 obtained from the user's own data set. This gives a formal test for predictive ability of a PLS model with a given number of dimensions.
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    Journal of Chemometrics 7 (1993), S. 177-193 
    ISSN: 0886-9383
    Keywords: Multivariate analysis ; Function space ; Coefficient space ; B-splines ; Compression ; PCA ; PLS ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general framework for manipulating spectra as functions in traditional multivariate methods such as PCA and PLS is described. The functional representation is very convenient for compression, ensuring smoothness and continuity. There are two fundamentally different types of representations: (a) by functions and (b) by function coefficients. The use of coefficients is the most practical way of analysis.
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    Journal of Chemometrics 7 (1993), S. 559-566 
    ISSN: 0886-9383
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 46
    ISSN: 0886-9383
    Keywords: Reaction kinetics ; Initial rate ; Kinetic order ; Response surface modelling ; Canonical analysis ; Organic synthesis ; Optimization ; Reaction mechanisms ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method is presented by which it is possible to estimate the initial rate of chemical reactions when the experimental conditions are varied according to a response surface design. The method is intended as a complementary method for analysing data obtained from experiments in synthetic chemistry when the objective is to optimize the yield of the reaction.Data obtained by simulations have been used to develop the method. From the simulated reactions it is shown that sequential analysis of the chemical yield of the reaction makes it possible to estimate models which describe how the parameters of the response surface of the yield vary over time. The derivatives of these time functions of the response surface parameters can be used to define a rate function which describes how the variations in the experimental conditions influence the rate of the reaction.It is shown how such rate functions can be used to afford reasonable estimates of the initial rates of the reaction. The initial reaction rates thus estimated can be used to determine the kinetic order of the reactants and also to provide estimates of the activation energy of the reaction.A thorough discussion of how canonical analysis of the rate function may assist in the elucidation of reaction mechanisms is given.
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  • 47
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    Journal of Chemometrics 7 (1993), S. 381-392 
    ISSN: 0886-9383
    Keywords: Factor analysis ; Kolmogorov-Smirnov test ; Non-parametric tests in factor analysis ; Non-parametric test for principal components ; Principal component analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Each eigenvector of the dispersion matrix [X]T [X] was shown to be a partial predictor of the original data matrix [X], the sum of the predictions from the individual principal components being equal to the expectance of [X]. By comparing the distributions of the members of two neighbouring predicted matrices, [X̃]1…i and [X̃]1…i+1 (i.e. the sums of the first i and i + 1 individual predictions respectively), it was shown that they should be indistinguishable provided that i is equal to or greater than the effective rank of [X], and significantly different otherwise. This was confirmed by analysing the visible absorption spectra of methyl orange and methyl red solutions as well as the Raman spectra of Na2SO4 and MgSO4 solutions. On the grounds of these findings, a non-parametric goodness-of-fit test for assessing the effective rank of [X] was proposed which proved to be comparatively conservative and more robust than most currently used tests.
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    Journal of Chemometrics 7 (1993), S. 427-438 
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    Keywords: Quality control ; Kerosene ; Variable reduction ; Cross-validation ; Variable selection ; Procrustes rotation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper deals with a typical question encountered in all industrial analytical laboratories: are all the tests performed in the laboratory to characterize the final product really necessary? In this work the cross-validation technique, Procrustes rotation techniques and statistical variable selection have been used to reduce the 26 initial British Petroleum and ASTM kerosene specification test to ten ‘essential’ ones. Statistical as well as chemical considerations were used to select the optimum subset of original variables to be retained from all the possible ones.
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    Rapid Communications in Mass Spectrometry 7 (1993) 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Physics
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  • 50
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Physics
    Notes: Improvements in methodology for liquid chromatography/continuous flow secondary-ion mass spectrometry (LC/CFSIMS) are described. Practical procedures have been developed for the preperation of packed fusedsilica capillary liquid chromatography columns and the coupling of these columns to the CFSIMS probe. A modified probe tip is described that significantly reduced ion beam instability arising from acceleration voltage discharge, changes in mobile phase composition during gradient elution, and uneven tip wettability. Interfering matrix background ions in LC/CFSIMS experiments are eliminated by reaction monitoring: the detection limit of the plant hormone metabolite, abscisic acid glucose ester, ABAGE is below 100 pg (235 fmol) with this technique. Reproducibility for quantitation is achieved by parallel reaction monitoring of the analyte and an added internal standard, ABAGE-d6. The d6/d0 ABAGE response ratio for the monitored transitions is linear over the range 100 pg to 10 ng of injected ABAGE.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 20-26 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The use of ultraviolet matrix-assisted laser desorption (MALD) to ionize peptides for analysis in a quadrupole ion trap is described. An ion source was modified to accommodate a fiber optic to transmit laser radiation from a notrogen laser (337 nm) to the tip of the sample probe containing peptide of protein samples in a matrix of 2,5-dihydroxybenzoic acid (DHB) or 3,4-dimethoxy-4-hydrexy-cinnamic acid. Detection limits are demonstrated with 10 fmol of sperm-whale-myoglobin. The dimer of sperm-whale myoglobin was also observed at m/z 34, 430. A. comparison is made of the tandem mass spectrum of (MS/MS) of human angiotensin I desorbed by MALD to that of the peptide desorbed by liquid secondary-ion mass spectrometry. Both spectra were found to contain abundant structural information.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 37-40 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Physics
    Notes: The applicability of thermal surface ionization in liquid chromatography/particle-beam mass spectrometry is investigated for the analysis of quaternary ammonium compounds. The compounds are mass anlyzed in a filament-off mode of operation with a particle-beam interface. An intense signal of the molecular cations is observed, while fragmentation can be induced by gas collisions and characterized using tandem mass spectrometry. A significant gain in signal-to-noise ratio in thermal surface ionization relative to electron ionization is observed.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 43-45 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Physics
    Notes: The versatility of the quadrupole ion trap as a mass spectrometer in which the mass resolution may be varied over a wide range has been demonstrated. Mass resolution of 0.8 × 107 and 1.2 × 107 have been obtained for ions of m/z 414 and m/z 614, respectively, well in excess of the normal value of 3m, where m is the mass of ion. At the highest mass resolution, peak-widths at half-maximum are but 52 × 10-6 u. While it has been shown previously that enhanced mass reslution in the quadrupole ion trap can be achieved by reduction of the mass scanning rate, the range of mass resolutions reported here were achieved by reducing the mass scanning rate, in stages, by an overall factor of ca 5.5 × 104.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 53-57 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Physics
    Notes: Cu+, Ag+ and Au+ gas-phase ions have been found, in laser desorption time-of flight experiments, to attach efficiently to polybutadiene, a polymer containing no polar groups. The desorption and cation attachment were accomplished using the fundamental frequency of Nd:YAG laser, at a wavelength of 1064 nm, and supporting the samples on probe tips made of the appropriate metal. laser powers were in the range of 1.0-2.0 × 108 W/cm2. Time delays between the application of the laser pulse and the sampling of the resultant ion population were in the range 30-80 μs. The Au+ attachment is contrary to the reported findings from a laser desorption charge-exchange spectrum obtained from a gold surface by Kahr and Wilkins. The differences in the spectra are discussed in terms of the differences in the two experimental methods. Attachment by these ions could be useful in the laser desorption analysis of other polymer molecules, particularly those containing no polar groups.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 71-84 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Physics
    Notes: A three-dimensional surface of signal vs molecular weight and adduct ion mass (H+, Na+, NH+ 3, etc) is introduced as an analysis tool for determining the mass of higher-molecular-weight compounds from their representations as a series of multiply charged peaks in a mass spectrum produced by electrospray ionization. This three-dimensional approach has distinct advantages over conventional two-dimensional analysis techniques with regard to detecting errors in the mass scale calibration, assessing the confidence level of a deconvoluted molecular-weight assignment and in analyzing complex multiply charged spectra of mixtures. Special techniques are introduced which allow analysis of multiply charged spectra; containing adduct ion mixtures. solvent molecules absorbed on the parent molecule and ‘peaks’ resulting from partial dissociation of the parent molecule.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 112-126 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: A directory of companies which supply mass spectrometers and mass spectrometry components and services. This directory updates an earlier version.
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Notes: A new approach has been applied to study processes which take place during the thermochemical action of air (or other) plasma on heat protection materials. Vaporization processes of the borosilicate coating of ‘Buran's’ heatprotective tiles, both the initial state and after rf-entry simulation testing (up to 100 landings), were investigated by the Knudsen mass spectrometric effusion method. Modelling of the thermochemical action of the shock-layer plasma onto the front surfaces of real-scale tiles was carried out by using an induction plasma genetor of 500kW power. It was established that the thermochemical action of the plasma causes, essentially, a decrease of vapour pressure over the coating. However, despite this decrease, the pressures observed are significantly higher than those over the SiO2-B2O3 system at the same temperature, due to gas-phase SiO production by reaction between boron and silicon oxides and SiB4, which are contanied in the coating. The data available aiiow one to postulate the presence of the SiBO molecule in the gas phase. Data on mass-loss rates obtained by direct measurments after re-entry simulation compared nwell with the values calcuted from mass spectrometric data. It is suggested that the difference observed is caused by thermochemical action of atomic oxygen on the coating.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 315-317 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Rapid Communications in Mass Spectrometry 7 (1993), S. ii 
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    Rapid Communications in Mass Spectrometry 7 (1993) 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Notes: The reactions of the metal dicarbonyl anion Fe(CO)2- with methanol and five of its isotopomers, namely CD3OH, CH3OD, CD3OH and CH318OH have been studied by the use of Fourier-transform ion cyclotron resonance mass spectrometry. Three competitive reaction channels have been identified in these trapped-ion/molecule studies which, for methanol, lead to the formation of three primary reaction products, namely [HFe(CO)(OCH)3]- formed in a decarbonylation channel; Fe(CO)3- in a channel involving C—H and O—H bond activations and bis-dehydrogenation of a collision complex; and also [(CH2O)Fe(CO)2]- in a separate channel involving the elimination of a single H2 molecule. The primary product ion [HFe(CO)(OCH)3]- further reacts with methanol to give a bis-alkoxy substituted metal carbonyl ion [(CH3O)2Fe(CO)]- at trapping times of several seconds. Complex deuterium isotope effects of an interactive nature with respect to the three reaction channels also have been observed.
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Notes: Some synthetically obtained linear and cyclic phosphopeptides of low molecular weight have been studied by fast-atom bombardment and tandem mass spectrometry to verify the position of the phosphate group in these compounds. Based upon the occurrence/non-occurrence of loss of phosphoric acid from low abundance fragment ions induced by low- and high-energy collisions with target gases, it is shown that the position of the phosphate group in the phosphopeptides studied can be determined unequivocally.
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    Rapid Communications in Mass Spectrometry 7 (1993) 
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 789-794 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Physics
    Notes: The 70 eV electron ionization mass spectrometric behaviour of some C6F13-compounds has been studied in detail by means of mass-analyzed ion kinetic energy spectroscopy and compared with that of the C6H13-analogs. As a general trend, the incorporation of fluorine leads to a strengthening of the alkyl chain; in fact the extensive primary fragmentation processes related to the chain cleavages observed for hydrocarbon derivatives are strongly suppressed in the case of the corresponding fluorocarbons. Moreover, the interaction of fluorine with functional groups leads to unexpected decomposition processes. The —CH2—CF2— bond, often considered in condensed-phase chemistry as a weak point in the molecule, never undergoes fragmentation.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 819-821 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Physics
    Notes: Multiple excitation collisional activation (MECA) has been examined using Fourier-transform mass spectrometry. In analogy to recently reported multiple excitation detection schemes, MECA is a process in which ions are translationally excited to larger orbits by applying an RF signal over the desired mass range. Next, collisional cooling of the ions collapses them, spatially, back to the center of the cell, where the process can be repeated. Two examples of the utility of MECA are given. The first involves a novel way of growing cluster ions by sequential ion/molecule reactions followed by MECA. The second uses MECA to increase the energy deposition in a stable and difficult-to-fragment ion, thereby inducing fragmentation.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 822-827 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: A novel method for trapping ions produced by matrix-assisted laser desorption ionization (MALDI) using controlled gating of the trapping field is suggested. Because it does not use collisions with helium atoms for reducing ion kinetic energy, trapping can be accomplished at low pressures of the buffet gas. The method has been implemented on an ion-trap detector, modified for MALDI experiments inside an ion trap with axial introduction of the sample probe. High mass resolution (1 part in 12 000) is reported.
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  • 67
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 837-843 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: A quadrupole ion-trap storage/reflectron time-of-flight mass spectrometer (IT/RETOFMS) has been used to enhance resolution in the ultraviolet matrix-assisted laser desorption/ionization (MALDI) of peptides. The MALDI of peptides is performed directly inside an ion-trap storage device using 266 nm laser radiation from a 2,5-dihydroxybenzoic acid matrix. Helium buffer gas is used to collisionally cool the hot desorbed ions and to rapidly relax the ions to the center of the ion trap. The result is that upon ejection into the TOF device, a resolution of nearly 6200 is obtained-for Substance P using a 90 ms storage time. A resolution of 3000-6000 is consistently obtained for peptides up to 2100 u used in this study. The individual ion peaks from the isotopic distribution are easily resolved under these conditions. In addition, the ion trap is found to be useful as an ion-storage device for enhancing the signal where multiple laser desorption pulses can be stored per cycle in the trap before ejection into the RETOF. Also, using the relatively high resolving power of the IT/RETOF instrument, excellent mass accuracy can be obtained using the matrix background and bradykinin as internal standards.
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  • 68
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 848-852 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Solvation of the gas-phase transition-metal d0 complexes ScO+, YO+, YCHCN+ and NbO2+ with some protic and aprotic solvents has been studied using Fourier-transform ion cyclotron resonance mass spectrometry. The relative rate constants for formation of the solvated oxides show strong non-monotonic fluctuations with increasing extent of solvation. For ScO+ and YO+ the third solvent molecule attaches more rapidly than the second, while for NbO2+ the second attaches more rapidly than the first. This behavior suggests that in spite of the formal d0 character of the metal centers in these systems, simple electrostatic binding is not occurring. In contrast, YCHCN+ shows a continuous decrease in the rate for solvation with up to three molecules of CH3CN. The effects of solvation on the subsequent reactions of the metal oxides has been studied. YO+ solvation (with up to three H2O or two NH3 molecules) does not affect its arene C—H bond activation reactions. However, solvation of ScO+ and NbO2+ with one or two NH3 or H2O molecules shuts off benzene dehydrogenation.
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  • 69
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 857-860 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: We present a new multiply pulsed collision-gas technique forion axialization for Fourier-transform ion cyclotron resonace (FTICR) high-resolution mass analysis. Ions are axialized in the source trap of a dural-trap FTICR spectrometer y aimuthal quadrupolar irradiation for several tens of seconds at a steady-state pressure maintained y repeated pulses of coolision gas (argon), folowed by removal of the collision gas and detection at a much lower pressure after transfer to the analyzer trap. Magnitufe-mode FTICR mass resolving power, m/Δm≍1770000, for [M + K]+ ions from laser-desorbed/ionized leucne enkephalin at m/z 594 is demonstrated. This resolving power is the highest yet reported for a peptide with any type of laser desorption/ionization mass analyzer.
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  • 70
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 861-864 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Accurate mass determination on the 13+ ion of myoglobin, MW 16951, has been performed with a magnetic sector mass spectrometer equipped with a newly designed electrospray ion source. At a mass resolution of 20000 a mass deviation of 1 ppm from the expected value has been achieved.
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  • 71
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 865-865 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
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  • 72
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    Notes: The spontaneous unimolecular dissociative reactions of dimethylsilyl cations (CH3)2Si+H (1+; m/z 59) have been investigated by mass-analyzed ion kinetic energy (MIKE) spectrometry and deuterium-labelling studies. Excepting the losses of H and H2, the ions 1+ mainly eliminate C2H4 and CH4 to produce product ions at m/z 31 and 43, respectively. Almost complete hydrogen scrambling occurs prior to the C2H4 loss, but only a small degree of scrambling occurs in the CH4 loss. Predominantly, the hydrogen atom bound to Si participates in the latter reaction, contrary to the previously reported mechanism.
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  • 73
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 416-420 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The vaporization of Ba2CaWO6 and Ba2SrWO6 was investigated by Knudsen-cell mass spectrometry. According to the results obtained with a Knudsen cell made of tungsten, the reduction of barium-calcium tungstates is a non-equilibrium process whereas the sublimation of BaWO4 and its decomposition in the gas phase to BaO(g) and WO3(g) are equilibrium reactions. From the temperature dependence of the partial pressure BaWO4(g) the enthalpy of sublimation is obtained as ΔHToII = 469 ± 4kJ/mol, which is in excellent agreement with the value obtained by third-law calculations. The origin of the most abundant ions in the gas phase, i.e., BaWO4+, BaWO3+, BaO+ Ba+ etc, has been explained from measurements of the corresponding ionization energy (IE) and appearance energy (AE) values.The difference between the AE values for Ba2CaWO6 and Ba2SrWO6 is negligible. The presence of BaWO4 in the condensed phase was confirmed by X-ray diffraction measurements. Neither X-ray analysis nor the mass spectra show the presence of CaWO4 or SrWO4 in the solid phase or in the gas phase.
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  • 74
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    Notes: Analysis of urine from cancer patients by capillary gas chromatography/mass spectrometry positively identified 14 urinary nucleosides including several modified nucleosides. Levels of the modified nucleosides 1-methyl-adenosine, 2-methylguanosine, N2,N2-dimethylguanosine and 1-methylinosine as well as the total nucleoside level were elevated in the urine when a malignant tumour was present; the levels of N2,N2-dimethylguanosine were found to correlate with the stage of the cancer.
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  • 75
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 440-445 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The effects of performing ion resonance collisional activation in two steps separated by an intermediate phase were studied. The results show that the time duration and the tickle frequency setting used in this intermediate stage determine the phase of the tickle output in the second activation stage which it is essential to control, to ensure the efficiency of the activation process. The following interpretation is offered: the activation process can be efficiently resumed after a period of interruption, provided the tickle voltage in the second activation step is in-phase with the axial motion of the ions induced by the tickle field during the first activation stage.
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  • 76
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    Topics: Physics
    Notes: In a previous paper, the presence in human kidney vein tissue of a novel blood group A heptaglycosylceramide based on the type-3 carbohydrate chain GalNAcαl-3(Fucαl-2)Galα1-3GalNAcαl-3(Fucα1-2)Galβl-4Glcβl-1 Ceramide, was suggested based on thin-layer immunostaining and electron ionization mass Spectrometry. Ions corresponding lo a structure containing two deoxyhexoses, two hexosamines and three hexoses were identified, but no information was obtained from mass spectrometry concerning the carbohydrate sequence5. In the present paper, we report the identification of carbohydrate sequence ions corresponding to a type-3 chain A heptaglyco-sylceramide by electron ionization-tandem mass spectrometry of a permethylated-reduced glycosphingolipid mixture isolated from human kidney vein tissue. The use of a microchannel-plate-array detector increased the sensitivity for collision-induced dissociation spectra by a factor of at least ten over a conventional electron multiplier.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 454-459 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Large-ring ionized cycloalkylamines of low internal energy lose ammonia and homologous alkyl radicals competitively. It is shown by deuterium-labelling experiments, that ammonia is lost mainly after ring-contraction of the original parent ion to an alkyl-monosubstituted cyclohexylamine isomer. This fragmentation is preceded by abundant hydrogen exchanges occurring mainly in this rearranged structure, but also, for the largest ring compounds, to some extent in the original structure.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 449-453 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The mass spectrometric behaviour of some 2-[3-hydroxy-pyridyl]-2-(3H)-thiazolimine and 1,3,4-thiadiazine derivatives was studied in detail under electron ionizing conditions by means of accurate mass measurements, deuterium-labelling experiments and metastable ion studies. The resultant fragmentation patterns were highly complicated with cleavage of the amine bond and of the thiazoline ring. The main differences between the decomposition mechanism of thiazoline and thiadiazine derivatives lies in the retro-synthetic ring transformation processes, observed in the case of thiadiazine compounds only.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 435-439 
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    Topics: Physics
    Notes: Various isomer matrices were used for laser-desorption ionization of mixtures of oligomers. It was found that the efficiency of production of oligomer ions changed drastically when different isomers were used as matrices. For selected matrix materials, parent oligomer ions with sizes up to 64 bases were observed.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 446-448 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The desorption rate for ‘spontaneous desorption’ (SD) has been investigated using various grids with different geometrical dimensions (line width, line distance). The experimental results can be understood if one assumes that the keV ions which sputter ions from the sample in an SD process originate exclusively at the grid via field-enhanced desorption of adsorbates (FEDA). This means that SD is a two-step process. The first step is FEDA, the second step is a sputter process.
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  • 81
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    Notes: Electron ionization mass spectrometry is shown to provide a valid analytical toot for the structural characterization of the title compounds. Diagnostic fragmentation pathways of an unsymmetrically substituted 2,5-furan dicarbonyl dichloride and dianilide were observed.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 462-464 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Clenbuterol is a β-agonist drug used illegally as a growth stimulant in meat-producing animals and human athletes. The analysis of clenbuterol in spiked human plasma was performed using on-line liquid chromatography/atmospheric-pressure chemical-ionization mass spectrometry (LC/APCI-MS) using a conventional bore LC column (flow rate = 1.0 mL/min). At low sampling cone voltages, the mass spectrum was predominantly the [M + H]+ ion but diagnostic fragment ions were formed upon incremental increases in sampling cone voltage. The detection limit (signal-to-noise ratio of 3) using selected-ion monitoring of the [M + H]+ ion was 0.1 ng on-column (l0 ppb). This is a 50-fold better sensitivity of detection than that previously reported for an on-line thermospray LC/MS method. The extraction procedures were not optimized for maximum sensitivity and the lack of interferences suggests that much lower detection limits for clenbuterol in plasma are attainable.
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  • 83
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    Notes: The 70 eV electron ionization mass spectra of 27 2-aryl substituted octahydro-1,3- and -3,1-benzoxazines have been recorded in order to find out how the site and stereochemistry of the ring fusion and especially the nature of the substitutent X on the 2-phenyl group affect their fragmentation patterns. The structural isomers showed clearly different spectra; however, stereoisomeric differentiation was possible only with 1,3-derivatives. The fragment-ion peaks connected with the ionized ring and open chain forms of the compounds studied were clearly present in all the spectra. Analogously to the results obtained in solution, the electron-withdrawing ability of X increased the abundance of the fragments originating from the ring form. Also, the relative importance of different fragmentation channels varied according to the electron donating or withdrawing ability of the substituent X.
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  • 84
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1037-1040 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: A new type of curved-field reflectron has been developed for the energy focusing of ions formed after initial acceleration in time-of-flight (TOF) mass spectrometers. These include ions generated in the dissociation region of a tandem TOF, as well as metastable decay products formed in the field-free drift region prior to their reflection. Unlike conventional linear-field reflectrons, which focus product ions to different focal lengths that are proportional to the mass (energy) of the fragment, the new curved-field reflectron energy focuses all ions to within a small region near the exit of the reflectron. Thus, the collection of resolved fragment peaks is possible without scanning or stepping the potential gradient of the reflectron, enabling faster acquisition of the production spectrum and, more importantly, true multiplex recording of the spectra from each ionization event. Theoretical considerations of the design are discussed along with an evaluation of collision-induced dissociation data, demonstrating the performance of the new reflectron in a tandem TOF instrument.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1048-1050 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: We confirm the cleavage at position B16-17 of porcine insulin which occurs during in vitrio digestion by insulin proteinase. The fragment A14-21-B17-30 was purified by reversed-phase high performance liquid chromatography and characterized by electrospray ionization mass spectrometry. Fast-atom bombardment mass spectrometry, on the other hand, failed todetect the presence of this fragment.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1041-1047 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: A number of different low molecule weight and volatile compounds have been tested and compared as matrices in 252Cf plasma-desorption mass spectrometry (PDMS) measurements of oligosaccharides. Some heteroaromatic amines (2-aminothiazole and 3-aminopyridine), hydroxyanthraquinones (alizarin and quinalizarin) and phthaleins (fluorescein) proved to be especially suited to enhancing the quasimolecular ion intensity of oligosaccharides. Discrimination effects could be reduced by matrix addition and thus, quantitative results of PDMS could be improved. Oligosaccharides with broad molecular weight distribution (dextrin 10 and dextran T 1.5) have been successfully analyzed by PDMS. The mass spectra obtained compared quite well with ion chromatograms of the respective oligosaccharides.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1051-1054 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Despite the presence of the ions at m/z 242 and m/z 243 in the electron ionization (EI) and chemical ionization (CI) mass spectra of tetryl, respectively, no such daughter ions were observed in the collision-induced dissociation spectra of the M+· ion in EI and of the [M+H]+ ion in CI. This supports the thesis that these ions are formed through hydrolysis of tetryl to N-methylpicramide in the ion source before ionization. It was found that the hydrolysis is considerably stronger under CI consitions, but can be minirnized in EI. The structure of the molecular ion at m/z 242 in the EI mass spectrum of N-methylpicramide was found to be similar to that of the [MH-NO2]+ ion in the CI mass spectrum of tetryl.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. ii 
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    Rapid Communications in Mass Spectrometry 7 (1993) 
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1067-1069 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: A liquid chromatography/thermospray ionization tandem mass spectrometry (LC/TSP-MS/MS) method was developed for the quantification of abscisic acid (ABA) in crude plant extracts without derivatization. By this technique interfering chemical background ions are eliminated and a detection limit for ABA olf 0.2 ng is achieved. Reproducibility for quantification is attained by parallel reaction monitoring of ABA and added ABA-d6 used as an internal standard. The standard curve is linear over the range 200 pg to 10 ng of injected ABA. As examples of the application of the methodology, the quantification of ABA in some plant tissues is given.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1077-1081 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Negative-ion electrospray mass spectrcmetry for the detection of higher fullerene anions is discussed. The fullerenes were reduced in dimethoxyethane/aromatic solvent using NaK amalgam and analyzed by electrospray ionization mass spectrometry using a double-focusing mass spectrometer. All the Cn- ions (n = 2k, and k is an integer) could be detected up to n = 102 except for 60 〈 n 〈 70 and n = 72. The detection efficiency of C76 is found to be considerably lower than that for C78, probably because the C76- ion reacts further in solution and is converted to undetectable reaction products. In addition to the fullerene anions, large peaks due to methoxy-substituted fullerene anions, Cn(OCH3)m-, are observed. The intensities of these ions grow with time.
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  • 92
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    Notes: For the first time, molecular ions from two different compounds have been simultaneously isolated in an ion-trap mass spectrometer and their subsequent tandem mass spectra (MS/MS) obtained. Isolation was achieved by applying a filtered-noise field (FNF) to the end-caps of a FinniganMAT ion-trap mass spectrometer (ITMS) using the Teledyne MEC/Hitachi HST-1000 Enhancement Kit. The HST-1000 generates a broadband waveform that would normally eject all ions from the trap. However, by setting notches in the waveform that correspond to certain resonant frequencies, individual masses can be isolated and stored in the trap without the need for the conventional DC voltage on the ring electrode. Using this FNF technique, the molecular ions of p-dichlorobenzene (m/z 146) and 1,3,5-trimethylbcnzene (m/z 120) were simultaneously isolated from a 42-component mixture of volatile organic compounds. Each molecular ion was collisionally dissociated by applying a resonance excitation (‘tickle’) voltage from the HST-1000, and the spectrum for each molecular ion was obtained by scanning the RF voltage to the ring electrode.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1095-1098 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The resolution of single- and double-stage, homogeneous electric mirror time-of-flight mass spectrometers can be calculated with the derived formulae for detectors located normally to the ion flight direction or parallel to the mirror face. These formulae account for contributions to the peak width from ion initial velocity and position in the source (‘turn around’ time included), from ion-packet longitudinal and transverse size at the source final grid, as well as due to the angular ion spread. Third-order terms are included for beam size, angular aperture and velocity spread, the incidence angle being small. The field-free space needed to obtain energy focusing in time is connected with the length of the accelerating space inside the source.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1108-1112 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Direct peptide mapping of sickle-cell hemoglobin (Hb S) using electrospray mass spectrometry is demonstrated to be a rapid, sensitive and useful technique for providing information concerning the location of variation. By fully comparing electrospray mass spectra of digests of sickle-cell and normal hemoglobins, using L-l-tosylamide-2-phenylethyl chloromeihyl ketone (TPCK)-treated trypsin, the point mutation of B1 fragment of β-chain in Hb S can be confirmed, taking into consideration that all the other fragments are completely identical in the two proteins.
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    Rapid Communications in Mass Spectrometry 7 (1993), S. 1118-1120 
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    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The female sex pheromone of the China corn borer, Ostrinia furnacalis (Lepidoptera: Pyralidae), was confirmed as Δ12-tetradecenyl acetate by a ‘fuzzy’ similarity analysis of gas chromatograph/mass Spectrometry data.
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Mass spectral fragmentations of two cyclopentane, four cyclohexane/ene and four norbornane/ene ß-amino acids were studied under electron ionization by low-resolution, high-resolution, metastable ion analysis and collision-induced dissociation techniques. All stereoisomeric compounds gave rise to identical 70 eV electron-ionization mass spectra. The major fragmentation pathway for the saturated compounds began as an α-cleavage reaction with respect to the nitrogen atom. For the unsaturated compounds, a retro-Diels-Alder reaction was favoured. In addition to a normal retro-Diels-Alder fragmentation reaction, the norbornene compounds underwent a retro-Diels-Alder fragmentation reaction accompanied by the migration of one hydrogen atom. In the case of the chemical ionization mass spectra, differences between stereoisomers were observed only under methane chemical ionization, where monocyclic trans isomers decomposed more readily than the corresponding cis isomers. All the [M + H]+ ions decomposed mainly by dehydration and deamination reactions. The fragmentation in the chemical-ionization ion source resulted in the same elimination ratio [M + H — H2O]/{[M + H — H2O] + [M + H — NH3]} as observed under kinetic control in the collision region.
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  • 97
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Rapid Communications in Mass Spectrometry 7 (1993), S. 1131-1135 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: This paper describes implementation of a storage waveform technique for manipulation of ions in a quadrupole ion trap. The technique is similar to the well established storage waveform inverse Fourier-transform (SWIFT) technology for controlling ion motion in Fourier-transform ion cyclotron resonance (FT-ICR). These techniques allow one to manipulate ions stored in the trap through computer control. The focus of this paper is the application of the storage waveform technique to the chemical noise problems associated with the analytical applications of atmospheric-pressure ionization/ion-trap mass spectrometry. In particular, the wave function described results in selected-ion accumulation in the trap in a mass window of ∼ 100 u. The position of the mass window can easily be adjusted across the mass range, thus providing selective accumulation in the trap only for ions of interest, while removing all others. The technique is easily implemented for routine use with on-line separations, resulting in improved sensitivity by significantly reducing ion current from interfering chemical background.
    Additional Material: 4 Ill.
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  • 98
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Rapid Communications in Mass Spectrometry 7 (1993), S. 542-547 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The utility of charge-inversion Spectrometry in the state analysis of diatomic cation beams is demonstrated by a brief summary and by reference to novel work on beams of NO+, SH+, CS+ and CI2+. A previously unknown state, of 3.5 eV relative energy and presumably of 4Σ+ symmetry was observed to be populated in a beam of CS+ ions formed from CS2. Evidence for the longevity ( 〉 10-5s) of the Ã2II state of CS+ and the b̃3II state of NO+ is also presented.
    Additional Material: 4 Ill.
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  • 99
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Rapid Communications in Mass Spectrometry 7 (1993), S. 528-537 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Cyclic nucleotides are biochemical second messengers which mediate the actions of many hormones and neurotransmitters. Fast-atom bombardment (FAB) mass spectrometry and mass-analysed ion kinetic energy (MIKE) spectra have provided a means of unambiguous identification of these compounds, and in addition to identifying endogenous putative cyclic nueleotides and their synthetic analogues FAB/MIKE analysis has now been applied to good effect to both qualitative and quantitative studies of cyclic nuclcotide-related enzymes. Here the application of this mass spectrometric technique to cyclic nucleotides is described and its impact upon this field reviewed.
    Additional Material: 11 Ill.
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  • 100
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Rapid Communications in Mass Spectrometry 7 (1993), S. 538-541 
    ISSN: 0951-4198
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: Mass analysis of ions emanating from a laser-produced plasma requires some means of overcoming their wide energy spread, such as, for example, through the use of an ion reflector in time-of-flight spectrometers. An alternative approach to this problem is to allow the ions to move freely from the plasma into a spectrometer in which a radial deflection field varies in time in such a way that the deflection trajectory of an ion is independent of its energy. This paper describes the theory of such a spectrometer and investigates the focusing properties of the system. It is found that the required time-varying field does not destroy the focusing features known for a radial field system except that under these new conditions first-order focusing occurs at a turning angle of 144°, which contrasts with a focusing angle of 127° for a radial-field spectrometer operating with a constant deflection field. The ion trajectories for the time-varying field have been sutdied using numerical methods and results from these are presented. An approximate theory is also included which is in excellent agreement with the numerical computations and which yields simple results for use in spectrometer design.
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