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  • 39B40  (1)
  • Crack-profile  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Aequationes mathematicae 42 (1991), S. 137-153 
    ISSN: 1420-8903
    Keywords: 39B40 ; 39A70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper deals with the problem of characterizing higher order Cauchy differences of mappings on groups and semigroups. Symmetric, first order Cauchy differencesf(x + y)−f(x)−f(y) for mapsf between groups were characterized by Jessen, Karpf, and Thorup [8] through the use of first partial Cauchy differences. Our results are similar and extend their result to higher order differences. Our results also extend those of Heuvers [6] for mappings between vector spaces over the rationals.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of nondestructive evaluation 13 (1994), S. 155-163 
    ISSN: 1573-4862
    Keywords: Crack-profile ; crack aspect ratio ; alternating current field measurement ; boundary element method ; pseudo-random error ; smoothing technique
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract The alternating current field measurement technique has been employed in the present study to predict cracks of different profiles. Profiles used included surface thumb-nail cracks of semi-circular, semi-elliptical, asymmetrical and rectangular shape with aspect ratios ranging from 2 to 10. From the potential ratios measured experimentally, a numerical approach was employed to compute the crack profiles. Crack profiles were also computed from theoretical potential profiles obtained using boundary element method. The present study shows that with high aspect ratios, the crack profiles predicted using theoretical data bore great resemblance to that of the actual. The underpredictions at the centre-line position of the cracks were small. Using experimentally measured potentials with 1-dimensional interpretation, all predicted profiles showed an under estimation of the actual. The errors appeared generally lower for the narrower plate and decreased with increase in aspect ratio. Pseudo-random errors were introduced to the theoretical potentials to simulate measurement errors that may occur in practice, to improve the error handling capability of the computer programme designed for the study. In addition, a smoothing technique was also applied to improve the accuracy of the crack profile prediction. By “freezing” some of the distant potential field, a significant computer processing time reduction of 25–35% has been achieved.
    Type of Medium: Electronic Resource
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