Relevant bibliographies by topics / Integral geometry. Polygons. Convex bodies

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Integral geometry. Polygons. Convex bodies'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Integral geometry. Polygons. Convex bodies"

1

Santaló, L. A. "Affine integral geometry and convex bodies." Journal of Microscopy 151, no. 3 (1988): 229–33. http://dx.doi.org/10.1111/j.1365-2818.1988.tb04683.x.

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Guàrdia, Roser, and Ferran Hurtado. "On the equipartition of plane convex bodies and convex polygons." Journal of Geometry 83, no. 1-2 (2005): 32–45. http://dx.doi.org/10.1007/s00022-005-0006-0.

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Weil, Wolfgang. "Integral geometry of translation invariant functionals, II: The case of general convex bodies." Advances in Applied Mathematics 83 (February 2017): 145–71. http://dx.doi.org/10.1016/j.aam.2016.09.005.

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Bauer, Christina, and Rolf Schneider. "Extremal problems for geometric probabilities involving convex bodies." Advances in Applied Probability 27, no. 01 (1995): 20–34. http://dx.doi.org/10.1017/s000186780004619x.

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The theory of geometric probabilities is concerned with randomly generated geometric objects. The aim is to compute probabilities of certain geometric events or distributions of random variables defined in a geometric way. Very often the computation even of simple expectations is too difficult, and one has to be satisfied with establishing estimates and, if possible, sharp inequalities. In geometric probabilities, convex sets play a prominent role, since often the convexity assumptions simplify the situation considerably. Extremal problems for geometric probabilities involving convex bodies ca
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Bauer, Christina, and Rolf Schneider. "Extremal problems for geometric probabilities involving convex bodies." Advances in Applied Probability 27, no. 1 (1995): 20–34. http://dx.doi.org/10.2307/1428092.

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The theory of geometric probabilities is concerned with randomly generated geometric objects. The aim is to compute probabilities of certain geometric events or distributions of random variables defined in a geometric way. Very often the computation even of simple expectations is too difficult, and one has to be satisfied with establishing estimates and, if possible, sharp inequalities. In geometric probabilities, convex sets play a prominent role, since often the convexity assumptions simplify the situation considerably. Extremal problems for geometric probabilities involving convex bodies ca
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Goodey, Paul, Markus Kiderlen, and Wolfgang Well. "Section means, integral transforms, and Boolean models." Advances in Applied Probability 28, no. 2 (1996): 332–33. http://dx.doi.org/10.1017/s0001867800048254.

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For a stationary particle process X with convex particles in ℝdd ≧ 2, a mean body M(X) can be defined by where h(M,·) denotes the support function of the convex body M, γ the intensity of X, and P0 is the distribution of the typical particle of X (a probability measure on the set of convex bodies with Steiner point at the origin). Replacing the support function h(M,·) by the surface area measure S(M,·) (see Schneider (1993), for the basic notions from convex geometry), we get the Blaschke body B(X) of X, After normalization, the left-hand side represents the mean normal distribution of X. The
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7

Ushakov, V. N., and M. V. Pershakov. "On estimation of Hausdorff deviation of convex polygons in $\mathbb{R}^2$ from their differences with disks." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 30, no. 4 (2020): 585–603. http://dx.doi.org/10.35634/vm200404.

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We study a problem concerning the estimation of the Hausdorff deviation of convex polygons in $\mathbb R^2$ from their geometric difference with circles of sufficiently small radius. Problems with such a subject, in which not only convex polygons but also convex compacts in the Euclidean space $\mathbb R^n$ are considered, arise in various fields of mathematics and, in particular, in the theory of differential games, control theory, convex analysis. Estimates of Hausdorff deviations of convex compact sets in $\mathbb R^n$ in their geometric difference with closed balls in $\mathbb R^n$ are pre
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SHEN, JINGFANG, and WENLI WEI. "FRACTAL CHARACTERISTIC AND DOMAIN EXTENSION FACTOR STUDY ON CONTACT MODEL OF ROUGH SURFACE." Fractals 28, no. 08 (2020): 2040024. http://dx.doi.org/10.1142/s0218348x20400241.

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Machine joint surface has an important impact on the performance of mechanical systems. Based on fractal theory, joint surface is assumed to be the contact between absolute smooth surface and rough surface. Through the analysis of the contact process, the contact mechanics model, the contact stiffness model and the three-dimensional surface micro-contact model are studied. To obtain fractal characteristic, the factors and laws affecting the contact characteristics are indicated through digital simulation. The concept of micro-convex body hierarchy is proposed. The critical values are related t
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9

Hug, Daniel, Jan Rataj, and Wolfgang Weil. "A product integral representation of mixed volumes of two convex bodies." Advances in Geometry 13, no. 4 (2013). http://dx.doi.org/10.1515/advgeom-2012-0044.

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Dissertations / Theses on the topic "Integral geometry. Polygons. Convex bodies"

1

Treuden, Mark Richard. "Collision probabilities of convex polygons in spherical two-space /." 1994. http://hdl.handle.net/1957/16813.

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Bonnet, Gilles. "Poisson hyperplane tessellation: Asymptotic probabilities of the zero and typical cells." Doctoral thesis, 2017. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2017021715545.

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We consider the distribution of the zero and typical cells of a (homogeneous) Poisson hyperplane tessellation. We give a direct proof adapted to our setting of the well known Complementary Theorem. We provide sharp bounds for the tail distribution of the number of facets. We also improve existing bounds for the tail distribution of size measurements of the cells, such as the volume or the mean width. We improve known results about the generalised D.G. Kendall's problem, which asks about the shape of large cells. We also show that cells with many facets cannot be close to a lower dimensional co
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Books on the topic "Integral geometry. Polygons. Convex bodies"

1

International Conference in "Stochastic Geometry, Convex Bodies and Empirical Measures" (2nd 1996 Agrigento, Italy). II International Conference in "Stochastic Geometry, Convex Bodies and Empirical Measures": Agrigento, September 9-14, 1996. Sede della società, 1997.

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International Conference in "Stochastic Geometry, Convex Bodies and Empirical Measures" (3rd 1999 Mazara del Vallo, Italy). III International Conference in "Stochastic Geometry, Convex Bodies and Empirical Measures": Mazara del Vallo, May 24-29, 1999. Sede della Societa, 2000.

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International Conference in "Stochastic Geometry, Convex Bodies Empirical Measures & Applications to Engineering Science" (4th 2001 Tropea, Italy). IV International Conference in "Stochastic Geometry, Convex Bodies, Empirical Measures & Applications to Engineering Science": Tropea, September 24-29, 2001. Sede della società, 2002.

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International Conference of Stochastic Geometry, Convex Bodies, Empirical Measures & Applications to Engineering, Medical, and Earth Sciences (5th 2004 Mondello, Italy). V International Conference os Stochastic Geometry, Convex Bodies, Empirical Measures & Applications to Engineering, Medical, and Earth Sciences, Mondello (Palermo), 6-11 settembre 2004. Sede della Società, 2006.

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International Conference on Stochastic Geometry, Convex Bodies and Empirical Measures (1st 1993 Palermo, Italy). First International Conference on Stochastic Geometry, Convex Bodies and Empirical Measures, Palermo, Italy, 25 April-2 May 1993. Sede della Società, 1994.

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Convegno italiano di geometria integrale, probabilità geometriche e corpi convessi (5th 1995 Milan, Italy). V Convegno italiano di geometria integrale, probabilità geometriche e corpi convessi: Milano, 19-22 aprile 1995. Sede della società, 1996.

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Convegno, italiano di geometria integrale probabilità geometriche e. corpi convessi (4th 1994 Bari Italy). IV Convegno italiano di geometria integrale, probabilità geometriche e corpi convessi: Bari, 2-5 maggio 1994. Sede della società, 1995.

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8

Treuden, Mark Richard. Collision probabilities of convex polygons in spherical two-space. 1994.

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Book chapters on the topic "Integral geometry. Polygons. Convex bodies"

1

Sakai, T., C. Nara, and J. Urrutia. "Equal Area Polygons in Convex Bodies." In Combinatorial Geometry and Graph Theory. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-30540-8_17.

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Oda, Tadao. "Integral Convex Polytopes and Toric Projective Varieties." In Convex Bodies and Algebraic Geometry. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-72547-0_2.

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