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Analysis of planar anisotropy by means of the Steiner compact

Published online by Cambridge University Press:  14 July 2016

Jan Rataj  and
Ivan Saxl
Jan Rataj
Affiliation:
Institute of Geophysics, Czechoslovak Academy of Sciences
Ivan Saxl*
Affiliation:
Institute of Geophysics, Czechoslovak Academy of Sciences
*
∗Postal address for both authors: Institute of Geophysics, Czechoslovak Academy of Sciences, Βο ční II. čp. 1401, 141 31 Praha 4, Czechoslovakia.
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Abstract

A graphical method for the estimation of the anisotropy of planar fibre systems based on the Steiner compact set is proposed and discussed. Upper bounds for the deviation in probability of the graphical estimate of the Steiner compact are given and a consistency theorem is proved.

Keywords

PLANAR FIBRE SYSTEMCONVEX SETSUPPORT FUNCTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 490 - 502
Copyright
Copyright © Applied Probability Trust 1989 

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References

[1] Digabel, H. (1975) Détermination practique de la rose des directions; 15 fascicules de morphologie mathématique appliquée (6), Fontainebleau.Google Scholar
[2] Feller, W. (1970) An Introduction to Probability Theory and its Applications Vol. 1, 3rd edn. Wiley, New York.Google Scholar
[3] Kanatani, K. I. (1984) Stereological determination of structural anisotropy. Int. J. Eng. Sci. 22, 531–546.Google Scholar
[4] Marriott, F. H. (1971) Buffon's problem for non-random directions. Biometrics 27, 233.Google Scholar
[5] Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
[6] Nguyen, X. X. and Zessin, H. (1979) Ergodic theorems for spatial processes. Z. Wahrscheinlichkeitsth. 48, 133–158.Google Scholar
[7] Serra, J. (1975) Anisotropy fast characterization. 15 fascicules de morphologie mathématique appliquée (8), Fontainebleau.Google Scholar
[8] Stoyan, D., Kendall, W. S. and Mecke, J. (1987) Stochastic Geometry and its Applications. Akademie-Verlag, Berlin.Google Scholar
[9] Valentine, F. A. (1964) Convex Sets. McGraw-Hill, New York.Google Scholar
[10] Weibel, E. R. (1980) Stereological Methods, Vol. 2. Academic Press, London.Google Scholar
[11] Weil, W. (1987) Point processes of cylinders, particles and flats. Acta Appl. Math. 9, 103–136.Google Scholar