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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Fresenius' journal of analytical chemistry 361 (1998), S. 15-22 
    ISSN: 1432-1130
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract In the Tucker3 model of N-way principal components analysis (NPCA), a so-called core matrix describes the possible interactions between components from different modes. For an easy interpretation of solutions, it is necessary to have as few interactions as possible (in conventional PCA of data tables, such interactions can always be avoided). This goal may be realized by various approaches of core matrix transformations. At the same time, it is desirable to have simple component (or loading) matrices. Usually, the simplicity of the core conflicts to a certain degree with the simplicity of the components. The paper demonstrates how the conditional optimization of both goals can be used to find a compromise. For the purpose of illustration, the procedure is first applied to a small three-way data array from heavy metal analysis of tissues in different samples of game. Later, a data array of bigger size from a three-way interlaboratory study is considered.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 84 (1999), S. 55-88 
    ISSN: 1436-4646
    Keywords: Key words: stochastic programming – probabilistic constraints – metric regularity – nonsmooth analysis – quadratic growth – quantitative stability – empirical approximation Mathematics Subject Classification (1991): 90C15, 90C30, 49J52
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Set-valued analysis 5 (1997), S. 323-349 
    ISSN: 1572-932X
    Keywords: cone increasing constraints ; nonsmooth analysis ; metric regularity ; chance constraints ; genericity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate stability (in terms of metric regularity) for the specific class of cone increasing constraint mappings. This class is of interest in problems with additional knowledge on some nondecreasing behavior of the constraints (e.g. in chance constraints, where the occurring distribution function of some probability measure is automatically nondecreasing). It is demonstrated, how this extra information may lead to sharper characterizations. In the first part, general cone increasing constraint mappings are studied by exploiting criteria for metric regularity, as recently developed by Mordukhovich. The second part focusses on genericity investigations for global metric regularity (i.e. metric regularity at all feasible points) of nondecreasing constraints in finite dimensions. Applications to chance constraints are given.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    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.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 4 (1990), S. 187-189 
    ISSN: 0886-9383
    Keywords: Analysis of correlation ; Common latent features ; Trace elements in human tissues ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: If in two data tables X and Y objects are characterized by the same variables (measured at different occasions), then looking for common latent features should be more appropriate than choosing latent features in X and Y separately (e.g. as in canonical correlation or PLS). The procedure to be proposed here is a slight modification of the method of linear characteristics (according to De Groot and Li) by disclaiming the assumption of equal inner-block covariance matrices. In order to find weights defining a latent feature with maximal correlation between X and Y, a system of non-linear equations has to be solved. The procedure is applied to the investigation of heavy metal concentrations in different human tissues.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 3 (1989), S. 537-540 
    ISSN: 0886-9383
    Keywords: Cluster analysis ; Display ; Interlaboratory test ; Ultrametrics ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ultrametric inter-object distances found by hierarchical clustering may be used to generate and appropriate constellation of points in a plane. A configuration of points which reproduce the ultrametric distances in a low-dimensional space as closely as possible can be found by Torgerson's method of multidimensional scaling. The resulting display supports the cognition of clusters very well, and for this purpose it seems to be superior to, for instance, the frequently applied principal components display. In certain situations dedrograms are expected to become simpler to interpret when such complementary ‘cluster display’ is also consulted. An example from analytical chemistry is presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 41 (1995), S. 161-173 
    ISSN: 1432-5217
    Keywords: Approximate subdifferential ; topological properties ; partial approximate subdifferential ; nonsmooth optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Topological properties of the approximate Subdifferential introduced by Mordukhovich are studied. Apart from formulating a sufficient condition for connectedness, it is shown that, up to homeomorphy, each compact subset of ℝp may occur as the approximate subdifferential of some Lipschitz function. Furthermore, even an exact result is possible when considering the partial approximate Subdifferential, which was introduced as a parametric extension by Jourani and Thibault: Given any compact subset of ℝp, there is a locally Lipschitzian function realizing this set as its partial approximate Subdifferential at some predefined point.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1040-0397
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This work addresses the problem of signal resolution by partial least-squares regression (PLS) for differential pulse stripping voltammograms. The performance of PLS is demonstrated for an example of calibration with mixtures of two analytes (Tl+ and Pb2+) with strongly overlapping voltammograms. The accuracy of the determination of concentrations for validation mixtures was found to be considerably higher with PLS than with simple evaluation using currents observed at two potentials (requiring resolution of a system of two linear equations with two unknowns). Hence, PLS is recommended for computer-assisted, on-line voltammetric analysis of multicomponent systems.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Title: Stochastic Optimization for Operating Chemical Processes Under Uncertainty /; ZIB-Report 01-04
    Author: Henrion, Rene
    Contributer: Li, Pu , Möller, Andris , Steinbach, Marc C. , Wendt, Moritz , Wozny, Günter
    Publisher: Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Year of publication: 2001
    Series Statement: ZIB-Report ZIB-Report 01-04
    ISSN: 1438-0064
    Type of Medium: Book
    Language: English
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  • 10
    Publication Date: 2021-03-16
    Description: The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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