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Stochastic Geometry

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  • Book
  • © 2004

Overview

Authors:
  1. Viktor Beneš

    1. Faculty of Mathematics and Physics, Charles University, Prague

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    You can also search for this author in PubMed   Google Scholar

  2. Jan Rataj

    1. Faculty of Mathematics and Physics, Charles University, Prague

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
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  2. Preliminaries

    Pages 1-20

  3. Random Measures and Point Processes

    Pages 21-44

  4. Random Fibre and Surface Systems

    Pages 45-92

  5. Vertical Sampling Schemes

    Pages 93-134

  6. Fibre and Surface Anisotropy

    Pages 135-167

  7. Particle Systems

    Pages 169-210

  8. Back Matter

    Pages 211-221
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Keywords

About this book

Stochastic geometry, based on current developments in geometry, probability and measure theory, makes possible modeling of two- and three-dimensional random objects with interactions as they appear in the microstructure of materials, biological tissues, macroscopically in soil, geological sediments etc. In combination with spatial statistics it is used for the solution of practical problems such as the description of spatial arrangements and the estimation of object characteristics. A related field is stereology, which makes possible inference on the structures, based on lower-dimensional observations. Unfolding problems for particle systems and extremes of particle characteristics are studied. The reader can learn about current developments in stochastic geometry with mathematical rigor on one hand and find applications to real microstructure analysis in natural and material sciences on the other hand.

Reviews

From the reviews:

"To write a text on stochastic geometry and its applications requires that an author successfully address a number of issues involving material and audience. … Viktor Beneš and Jan Rataj have produced an interesting text which successfully addresses the challenges involved in writing such a book. ... The text will be a valuable addition to the library of those who have an interest in applications … . the authors provide interesting examples. Each chapter of the text contains a number of exercises … ." (Patrick T. McDonald, Mathematical Reviews, 2005g)

Authors and Affiliations

  • Faculty of Mathematics and Physics, Charles University, Prague

    Viktor Beneš, Jan Rataj

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