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AuthorBeneลก, Viktor. author
TitleStochastic Geometry: Selected Topics [electronic resource] / by Viktor Beneลก, Jan Rataj
ImprintBoston, MA : Springer US, 2004
Connect tohttp://dx.doi.org/10.1007/b129604
Descript XI, 221 p. online resource

SUMMARY

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


CONTENT

Preliminaries -- Random Measures and Point Processes -- Random Fibre and Surface Systems -- Vertical Sampling Schemes -- Fibre and Surface Anisotropy -- Particle Systems


Mathematics Measure theory Convex geometry Discrete geometry Probabilities Statistics Materials science Mathematics Probability Theory and Stochastic Processes Statistics general Convex and Discrete Geometry Measure and Integration Characterization and Evaluation of Materials



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