Geodesic
Covariogram of a right parallelepiped
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 101-108.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we obtain explicit expressions for the covariogram and the orientation-dependent chord length distribution of a right parallelepiped with square base.
Keywords: Оrientation dependent chord length distribution, convex body. 
@article{UZERU_2019_53_2_a3,
     author = {V. K. Ohanyan and G. K. Adamyan},
     title = {Covariogram of a right parallelepiped},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {101--108},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2019_53_2_a3/}
}
TY  - JOUR
AU  - V. K. Ohanyan
AU  - G. K. Adamyan
TI  - Covariogram of a right parallelepiped
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2019
SP  - 101
EP  - 108
VL  - 53
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2019_53_2_a3/
LA  - en
ID  - UZERU_2019_53_2_a3
ER  - 
%0 Journal Article
%A V. K. Ohanyan
%A G. K. Adamyan
%T Covariogram of a right parallelepiped
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2019
%P 101-108
%V 53
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2019_53_2_a3/
%G en
%F UZERU_2019_53_2_a3
V. K. Ohanyan; G. K. Adamyan. Covariogram of a right parallelepiped. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 101-108. http://geodesic.mathdoc.fr/item/UZERU_2019_53_2_a3/

[1] R. J. Gardner, Geometric Tomography, Encyclopedia of Mathematics and its Applications, 58, Second edition, Cambridge University Press, N.Y., 2006 | MR

[2] G. Matheron, Random Sets and Integral Geometry, Wiley, New York, 1975 | MR | Zbl

[3] H. S. Harutyunyan, V. K. Ohanyan, “Chord Length Distribution Function for Regular Polygons”, Advances in Applied Probability, 41 (2009), 358–366 | DOI | MR | Zbl

[4] N. G. Aharonyan, V. K. Ohanyan, “Chord Length Distributions for Polygons”, Journal of Conteporary Math. Anal. (Armenian Academy of Sciences), 40:4 (2005), 43–56 | MR

[5] A. G. Gasparyan, V. K. Ohanyan, “Recognition of Triangles by Covariogram”, Journal of Conteporary Math. Anal. (Armenian Academy of Sciences), 48:3 (2013), 110–122 | MR

[6] W. Gille, N. G. Aharonyan, H. S. Harutyunyan, “Chord Length Distribution of Pentagonal and Hexagonal Rods: Relation to Small Angle Scattering”, Journal of Appl. Crystallography, 42 (2009), 326–328 | DOI

[7] H. S. Harutyunyan, V. K. Ohanyan, “Orientation-Dependent Section Distributions for Convex Bodies”, J. of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 49:3 (2014) | MR

[8] N. G. Aharonyan, H. O. Harutyunyan, “Geometric Probability Calculation for a Triangle”, Proceedings of the YSU. Physical and Mathematical Sciences, 51:3 (2017), 211–216

[9] R. Schneider, W. Weil, Stochastic and Integral Geometry, Probability and its Applications, Springer-Verlag, Berlin-Heidelberg, 2008 | DOI | MR | Zbl

[10] G. Bianchi, “The Covariogram Determines Three-Dimensional Convex Polytopes”, Adv. Math., 220:6 (2009), 1771–1808 | MR

[11] H. S. Harutyunyan, V. K. Ohanyan, “Orientation-Dependent Sections Distributions for Convex Bodies”, Journal of Conteporary Math. Anal. (Armenian Academy of Sciences), 49:3 (2014), 139–156 | MR