Stereology of objects with internal structure:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Czech |
| Published: |
Amsterdam u.a.
Elsevier
1989
|
| Series: | Materials science monographs
50. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Tschech. übers. - EST: Stereologie vnitřní struktury objektů <engl.> |
| Physical Description: | 226 S. Ill., graph. Darst. |
| ISBN: | 0444988920 |
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Record in the Search Index
| _version_ | 1804117918435246080 |
|---|---|
| adam_text | MATERIALS SCIENCE MONOGRAPHS, 50
STEREOLOGY
OF OBJECTS
WITH INTERNAL
STRUCTURE
IVAN SAXL
Institute of Geophysics,
Prague, Czechoslovakia
ELSEVIER
Amsterdam - Oxford - New York - Tokyo 1989
CONTENTS
PREFACE 9
LIST OF SYMBOLS 11
1 INTRODUCTION 17
2 MODELS OF STRUCTURAL ELEMENTS AND THEIR MEASURES 24
2 1 Internal structure of natural objects 24
2 2 Mathematical model of structural features 29
221 Compact sets 29
222 Convex bodies 31
223 Convex ring 9t 33
224 Regular model Sf 34
225 Topological properties of structural features 35
2 3 Invariant measures of point sets - 41
231 Lebesgue measure of a point set 41
232 Content of the boundary of a compact point set 45
233 Linear characteristics of compact point sets, boundary curvatures 50
234 Invariant measures of convex bodies 53
2341 Properties of Minkowski functional of convex bodies 57
235 Extension of Minkowski functionals to sets of the convex ring 61
2 4 Mathematical models of the analysis of object structure 67
241 System of subsets of the object, projections 67
242 Dimension of intersections and projections 70
243 Kinematic measure- 71
244 Kinematic measure of r-flats and linear subspaces 78
245 Kinematic densities of linear subspaces and r-flats 82
2 5 Determination of invariant measures of an object from the measures of its parts 86
251 Comprehensive system of kinematic relations: compact probes 86
252 Comprehensive system of kinematic relations: r-flats 90
253 Projection of objects into linear subspaces, Cauchy s formula 91
254 Invariant measures of an internal structure • 94
255 General relations concerning adjoined functionals 96
256 Examples 97
3 STEREOLOGY OF OBJECTS WITH INTERNAL STRUCTURE 104
3 1 Randomization of the probe or r-flat positions and orientations 105
3 2 Basic stereological formulae 111
321 Relations valid for arbitrary structures 111
Contents
322 Ratio characteristics 119
323 Relations valid for structures formed by aggregates of particles 122
3 3 Statistical estimates of stereological quantities 126
331 Stereological estimators, simple random sampling 126
332 Weighted random sampling and ratio estimators 130
333 Variances of stereological estimators 133
3 4 Practice of geometric sampling 140
341 Simple (uniform) random sampling 140
342 Weighted sampling 147
343 Lattices and coherent testing systems: systematic sampling 149
344 Edge effects and their corrections 155
3 5 Stereological models and sampling designs 161
351 Restricted deterministic case - 162
352 Extended deterministic case 166
353 Random case 168
354 Sampling of particles 176
APPENDICES 177
A I Minkowski algebra of sets 177
A 2 The notation of geometric objects in En 182
A 3 The Euler-Poincare characteristic and related topological quantities 185
A 4 Monte Carlo methods of estimating the values of integrals 194
BIBLIOGRAPHY 201
TABLES 211
INDEX 223
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:02:02Z |
| institution | BVB |
| isbn | 0444988920 |
| language | English Czech |
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| physical | 226 S. Ill., graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Elsevier |
| record_format | marc |
| series | Materials science monographs |
| series2 | Materials science monographs |
| spelling | Saxl, Ivan Verfasser aut Stereologie vnitřní struktury objektů Stereology of objects with internal structure Amsterdam u.a. Elsevier 1989 226 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Materials science monographs 50. Aus d. Tschech. übers. - EST: Stereologie vnitřní struktury objektů <engl.> Matière - Structure ram Stéréologie ram Matter Constitution Stereology Stereologie (DE-588)4183122-6 gnd rswk-swf Stereologie (DE-588)4183122-6 s DE-604 Materials science monographs 50. (DE-604)BV000008462 50. HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002271140&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saxl, Ivan Stereology of objects with internal structure Materials science monographs Matière - Structure ram Stéréologie ram Matter Constitution Stereology Stereologie (DE-588)4183122-6 gnd |
| subject_GND | (DE-588)4183122-6 |
| title | Stereology of objects with internal structure |
| title_alt | Stereologie vnitřní struktury objektů |
| title_auth | Stereology of objects with internal structure |
| title_exact_search | Stereology of objects with internal structure |
| title_full | Stereology of objects with internal structure |
| title_fullStr | Stereology of objects with internal structure |
| title_full_unstemmed | Stereology of objects with internal structure |
| title_short | Stereology of objects with internal structure |
| title_sort | stereology of objects with internal structure |
| topic | Matière - Structure ram Stéréologie ram Matter Constitution Stereology Stereologie (DE-588)4183122-6 gnd |
| topic_facet | Matière - Structure Stéréologie Matter Constitution Stereology Stereologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002271140&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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