Random Tessellations in RdDepartment of Theoretical Statistics, Institute of Mathematics, University of Aarhus, 1986 - Geometric probabilities - 79 pages |
From inside the book
Results 1-3 of 5
Page
... Quermass- W S Wo ( K ) = λa ( K ) W1 ( k ) = √ va ( ok ) √ W2 ( K ) = M ( K ) ய Wd - 1 ( K ) ud 5 ( x ) = Wa ( K ) ... Quermassintegrals are important because is a non - negative d - s " dimensional " functional on C ( K ) which is ...
... Quermass- W S Wo ( K ) = λa ( K ) W1 ( k ) = √ va ( ok ) √ W2 ( K ) = M ( K ) ய Wd - 1 ( K ) ud 5 ( x ) = Wa ( K ) ... Quermassintegrals are important because is a non - negative d - s " dimensional " functional on C ( K ) which is ...
Page 5-5
... Quermassintegral of u s - flat containing see section 2. In other words w.r.t. the N ( m , x ) is the number of s - facets contained in or containing the facet X of m . Notice that ω Ν S S u w ( s ) ( x ) when € ( m ) , = V cf. section ...
... Quermassintegral of u s - flat containing see section 2. In other words w.r.t. the N ( m , x ) is the number of s - facets contained in or containing the facet X of m . Notice that ω Ν S S u w ( s ) ( x ) when € ( m ) , = V cf. section ...
Page 5-17
... Corollary 5.6 applies also to these two cases . The following corollary states a mean value relation con- cerning the 2th Quermassintegral of the typical cell . Corollary 5.7 . For d≥ 3 and Bend , d ( d − 1 ) Ja2¿ ( B ) - 5.17.
... Corollary 5.6 applies also to these two cases . The following corollary states a mean value relation con- cerning the 2th Quermassintegral of the typical cell . Corollary 5.7 . For d≥ 3 and Bend , d ( d − 1 ) Ja2¿ ( B ) - 5.17.
Contents
Flat sections of random tessellations | 5-20 |
Voronoi and Delaunay tessellations generated by | 7-1 |
References | |
Common terms and phrases
AARHUS According arbitrary associated assume ball boundary called centres centroids choice closed Combining concerning consider contained convex Corollary covariant d-polytope defined definition Delaunay tessellation denote depend easily equal ergodic estimate example expected facet characteristics Finally finite follows Formula Furthermore Geometry given Hence hyperplanes imply inside integral intensities interior intersection introduced invariant isotropic JtEt La-s lines mean value relations measurable function measure Mecke Miles Note Notice observed obtain orthogonal Palm distribution Palm measure particular Poisson point process precisely present Proof properties prove random tessellation relations relative respectively right hand side s-content s-facet s-flat satisfied space stationary stationary Poisson point studied subsets Suppose tessellation in Rd Theorem 6.3 theory translations typical cell typical s-facet unit vertices volume Voronoi tessellation Ε Σ Σ Σ