Neighbourhood relations, sections and completion times for random tessellations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Freiberg (Sachsen), Techn. Univ., Diss., 1995 |
| Physical Description: | V, 95 S. |
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|---|---|
| adam_text |
CONTENTS
ACKNOWLEDGEMENTS
I
1
INTRODUCTION
1
1.1
TESSELLATIONS
.
1
1.2
TYPICALITY
.
2
1.2.1
HEURISTICS
.
2
1.2.2
ERGODIC
AND
PALM
METHODS
.
2
1.3
RECENT
PROGRESS
OF
THE
THEORY
OF
RANDOM
TESSELLATIONS
.
3
1.4
OUTLINE
OF
THE
THESIS
.
5
2
THE
NEIGHBOURHOOD
OF
THE
TYPICAL
CELL
OF
A
RANDOM
TESSELLATION
7
2.1
ABOAV
'
S
LAW
AND
LEWIS
'
S
LAW
-
A
REVIEW
.
7
2.1.1
INTRODUCTION
.
7
2.1.2
ABOAV-WEAIRE
'
S
LAW
.
8
2.1.3
AN
EXACT
IDENTITY
.
11
2.1.4
RIVIER
'
S
MICROREVERSIBLE
SYSTEM
AND
MAXIMUM
ENTROPY
METHOD
11
2.1.5
LEWIS
'
S
LAW
-
RIVIER
'
S
MAXIMUM
ENTROPY
METHOD
.
13
2.1.6
SOME
EMPIRICAL
STUDIES
OF
LEWIS
'
S
LAW
.
15
2.1.7
THE
FUNDAMENTAL
REGION
.
16
2.2
MEAN
VALUE
FORMULAE
BY
USING
MECKE
'
S
(1980)
PALM
METHOD
.
17
2.2.1
INTRODUCTION
.
17
2.2.2
NOTATION
.
17
2.2.3
WEAIRE
'
S
SUM
RULE
AND
ABOAV
'
S
LAW
.
19
2.2.4
RESULTS
IN
HIGHER
DIMENSIONAL
SPACE
.
21
2.3
A
CRITICISM
ON
RIVIER
'
S
MAXIMUM
ENTROPY
METHOD
.
25
2.3.1
INTRODUCTION
.
25
2.3.2
A
REVIEW
OF
LEWIS
'
S
LAW
AND
THE
MAXIMUM
ENTROPY
METHOD
.
.
26
2.3.3
ABOAV
'
S
LAW
.
28
2.3.4
A
MAXIMUM
ENTROPY
PREDICTION
OF
ABOAV
'
S
LAW
.
30
2.3.5
OTHER
ENTROPIC
PREDICTIONS
OF
ABOAV
'
S
LAW
.
32
2.3.6
A
GENERAL
MAXIMUM
ENTROPY
METHOD
.
35
2.3.7
PROPERTIES
OF
MAXIMUM
ENTROPY
SELECTION
.
35
2.3.8
INFINITELY
MANY
POSSIBILITIES
OF
THE
FUNCTIONAL
FORM
OF
H(N)
.
.
36
2.3.9
CONCLUSION
AND
DISCUSSION
.
37
CONTENTS
IN
3
LIMIT
THEOREMS
FOR
THE
TIME
OF
COMPLETION
OF
JOHNSON-MEHL
TES
SELLATIONS
39
3.1
INTRODUCTION
.
39
3.2
THE
BOOLEAN
MODELS
.
42
3.3
THE
FUNDAMENTAL
THEOREM
.
43
3.4
IMPORTANT
SPECIAL
MODELS
.
49
3.5
UNBOUNDED
A
.
51
3.6
BOUNDED
A
.
52
3.7
NON-CONSTANT
GROWTH
SPEED
.
54
3.8
SECTIONAL
TESSELLATIONS
.
54
3.9
AN
EXAMPLE
OF
A
FRACTAL
AS
THE
RESULT
OF
A
BIRTH-GROWTH
PROCESS
.
57
3.10
PROOF
OF
THEOREM
3.1
.
59
3.11
EXTREME
VALUE
APPROACH
.
62
3.11.1
TIME
OF
COMPLETION
OF
LINEAR
VORONOI
TESSELLATIONS
GENERATED
BY
STATIONARY
RENEWAL
PROCESSES
.
62
3.11.2
RATE
OF
CONVERGENCE
OF
VORONOI
CASES
.
64
3.11.3
SIMULATION
.
65
4
THE
SECTIONAL
POISSON
VORONOI
TESSELLATION
IS
NOT
A
VORONOI
TESSEL
LATION.
66
4.1
INTRODUCTION
.
66
4.2
VORONOI
AND
SECTIONAL
VORONOI
TESSELLATIONS:
DEFINITIONS
.
68
4.3
MAIN
THEOREM
1:
THE
EXISTENCE
OF
NON-VORONOI
CELLS
.
70
4.4
VORONOI
AND
SECTIONAL
VORONOI
TESSELLATIONS:
FUNDAMENTAL
RESULTS
.
73
4.4.1
VERTICES
AND
POINT
DISTRIBUTIONS
.
73
4.4.2
THE
GENERATING
POINTS
.
73
4.5
MAIN
THEOREM
2:
ALL
CELLS
ARE
NON-VORONOI
.
75
4.5.1
CASE
(I):
PLANAR
SECTIONS
(1
=
2)
.
76
4.5.2
CASE
(II):
3
T
D
-
1
.
81
4.6
THE
NATURE
OF
THE
POINT
PROCESS
4
.
83
REFERENCES
85
KURZBIOGRAPHIE
95 |
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| spelling | Chiu, Sung Nok Verfasser aut Neighbourhood relations, sections and completion times for random tessellations vorgelegt von Sung Nok Chiu 1995 V, 95 S. txt rdacontent n rdamedia nc rdacarrier Freiberg (Sachsen), Techn. Univ., Diss., 1995 Parkettierung (DE-588)4126296-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Parkettierung (DE-588)4126296-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007044535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chiu, Sung Nok Neighbourhood relations, sections and completion times for random tessellations Parkettierung (DE-588)4126296-7 gnd |
| subject_GND | (DE-588)4126296-7 (DE-588)4113937-9 |
| title | Neighbourhood relations, sections and completion times for random tessellations |
| title_auth | Neighbourhood relations, sections and completion times for random tessellations |
| title_exact_search | Neighbourhood relations, sections and completion times for random tessellations |
| title_full | Neighbourhood relations, sections and completion times for random tessellations vorgelegt von Sung Nok Chiu |
| title_fullStr | Neighbourhood relations, sections and completion times for random tessellations vorgelegt von Sung Nok Chiu |
| title_full_unstemmed | Neighbourhood relations, sections and completion times for random tessellations vorgelegt von Sung Nok Chiu |
| title_short | Neighbourhood relations, sections and completion times for random tessellations |
| title_sort | neighbourhood relations sections and completion times for random tessellations |
| topic | Parkettierung (DE-588)4126296-7 gnd |
| topic_facet | Parkettierung Hochschulschrift |
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