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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 69 (1995), S. 1-43 
    ISSN: 1436-4646
    Keywords: Mathematical programming ; Cutting planes ; Analytic center
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Anoracle for a convex setS ⊂ ℝ n accepts as input any pointz in ℝ n , and ifz ∈S, then it returns ‘yes’, while ifz ∉S, then it returns ‘no’ along with a separating hyperplane. We give a new algorithm that finds a feasible point inS in cases where an oracle is available. Our algorithm uses the analytic center of a polytope as test point, and successively modifies the polytope with the separating hyperplanes returned by the oracle. The key to establishing convergence is that hyperplanes judged to be ‘unimportant’ are pruned from the polytope. If a ball of radius 2−L is contained inS, andS is contained in a cube of side 2 L+1, then we can show our algorithm converges after O(nL 2) iterations and performs a total of O(n 4 L 3+TnL 2) arithmetic operations, whereT is the number of arithmetic operations required for a call to the oracle. The bound is independent of the number of hyperplanes generated in the algorithm. An important application in which an oracle is available is minimizing a convex function overS.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0935-6304
    Keywords: Vinyl chloride ; Ion mobility spectrometry ; GC/IMS ; Chemical field screening ; Environmental chemical analysis ; Chemical analysis of air ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The objective of this research was to evaluate, in the laboratory, the potential of gas chromatography/ion mobility spectrometry (GC/IMS) for monitoring vinyl chloride and other organic compounds in air samples in the field. It was determined that GC/IMS has the potential to directly detect vinyl chloride in air at the 2 ppbv level, and when concentrated on an adsorbent trap from a 1 L sample of air, detection could be lowered to the 0.02 ppbv level. From a comparative investigation of 18 EPA priority pollutants and 34 common vapor-phase organic compounds, many compounds were found to provide a more sensitive response in IMS than vinyl chloride, indicating that GC/IMS would be broadly applicable to the direct detection of vapor-phase organics in air.Operating parameters including drift gas, spectrometer temperature, and sample-inlet position were evaluated and discussed with respect to sensitivity and resolution. High temperature dramatically increased sensitivity to vinyl chloride. Vinyl chloride was shown to produce both negative and positive ion mobility spectra, with the negative-mode spectra resulting from electron-capture dissociation of the vinyl chloride. The limit of detection for vinyl chloride was found to be 7 pg/s. Limits of detection for 18 EPA priority pollutants were determined and compared to vinyl chloride. The responses of 34 other vapor-phase organic compounds were also compared to that of vinyl chloride. Non-selective, positive-ion detection of 30 of the 34 compounds was demonstrated along with selective, electron-capture-type detection of 29 of them. Chloride-specific and bromide-specific detection illustrated the advantages of selected-ion monitoring in IMS.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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