Introduction to crystallographic statistics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
1995
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| Schriftenreihe: | International Union of Crystallography: International Union of Crystallography monographs on crystallography
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 173 S. graph. Darst. |
| ISBN: | 0198559267 |
Internformat
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Datensatz im Suchindex
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| adam_text | INTRODUCTION TO CRYSTALLOGRAPHIC STATISTICS URI SHMUELI PROFESSOR OF
CHEMISTRY TEL AVIV UNIVERSITY GEORGE H. WEISS CHIEF, PHYSICAL SCIENCES
LABORATORY DIVISION OF COMPUTER RESEARCH AND TECHNOLOGY NATIONAL
INSTITUTES OF HEALTH INTERNATIONAL UNION OF CRYSTALLOGRAPHY OXFORD
UNIVERSITY PRESS 1995 CONTENTS 1 INTRODUCTORY MATERIAL 1 1.1 PURPOSE AND
SCOPE OF THE BOOK 1 1.2 REPRESENTATIONS OF THE STRUCTURE FACTOR 3 1.3
THE ROLE OF STATISTICS 8 1.4 FUNDAMENTAL IDEAS IN PROBABILITY THEORY 11
1.4.1 THE PROBABILITY DENSITY FUNCTION (PDF) AND ITS MOMENTS 12 1.4.2
THE CHARACTERISTIC FUNCTION 13 1.4.3 CUMULANTS AND MOMENTS 14 1.4.4 AN
EXAMPLE 15 1.4.5 PDFS, CHARACTERISTIC FUNCTIONS AND MOMENTS OF VECTOR
RANDOM VARIABLES 16 1.4.6 CONDITIONAL PDFS . 17 1.4.7 INDEPENDENT RANDOM
VARIABLES 18 1.4.8 CHARACTERISTIC FUNCTIONS FOR SUMS OF INDEPENDENT
RANDOM VARIABLES 18 2 SOME ELEMENTARY PDFS 21 2.1 THE PDF OF E IN
SPACE GROUP P 21 2.2 THE PDF OF E IN SPACE GROUP PL 2 6 3 IDEAL
DISTRIBUTIONS 29 3.1 THE CENTRAL LIMIT THEOREM 29 3.2 THE IDEAL CENTRIC
AND ACENTRIC PDFS 39 3.3 EFFECTS OF NON-CRYSTALLOGRAPHIC SYMMETRY 44 3.4
IDEAL SUBCENTRIC DISTRIBUTION 46 3.5 CONDITIONAL DENSITY OF A
THREE-PHASE INVARIANT 51 4 HIGHER-ORDER APPROXIMATIONS 54 4.1
MATHEMATICAL BACKGROUND 54 4.1.1 EXPANSION IN ORTHOGONAL POLYNOMIALS 54
4.1.2 EXPONENTIATED PDFS 63 4.1.3 THE SADDLEPOINT APPROXIMATION 64 4.2
MOMENTS OF THE STRUCTURE FACTOR 69 4.2.1 EXAMPLES 72 VIII CONTENTS
4.2.2 EFFECTS OF SPACE-GROUP SYMMETRY AND ATOMIC HETEROGENEITY ON THE
FOURTH MOMENT OF E 76 4.2.3 MOMENTS OF THE STRUCTURE FACTOR FROM
MOMENT-CUMULANT RELATIONSHIPS 77 4.3 SOME APPROXIMATE NON-IDEAL
DISTRIBUTIONS 79 4.3.1 DISPERSIONLESS CENTRIC AND ACENTRIC PDFS 79 4.3.2
PDFS ALLOWING FOR DISPERSION 82 5 FOURIER REPRESENTATIONS OF PDFS 85 5.1
PRINCIPLE OF THE METHOD 85 5.2 GENERAL EXPRESSIONS OF FOURIER PDFS 88
5.2.1 CENTROSYMMETRIC SPACE GROUPS 89 5.2.2 NON-CENTROSYMMETRIC SPACE
GROUPS 89 5.3 FOURIER COEFFICIENTS FOR DIFFERENT SYMMETRIES 91 5.3.1
SPACE GROUP PI 91 5.3.2 SPACE GROUP PMMM AND RELATED SYMMETRIES 92 5.3.3
PLANE GROUP P3 93 5.3.4 SPACE GROUP P6/MCC 95 5.4 EXACT AND APPROXIMATE
PDFS OF E 97 5.5 REMARKS ON NUMERICAL IMPLEMENTATIONS 102 5.6 HEAVY
ATOMS IN SPECIAL POSITIONS 104 5.7 FOURIER PDFS FOR NON-CRYSTALLOGRAPHIC
SYMMETRY 107 5.7.1 THE FOURIER SERIES FOR THE BICENTRIC PDF IN PI 108
5.7.2 PARTIALLY BICENTRIC FOURIER PDF OF E 109 5.7.3 MULTICENTRIC PDFS
OF E IN SPACE GROUP PI 111 5.8 UNEQUALLY BOUNDED A AND B , 115 5.8.1
PDF OF E WHEN A AND B ARE UNEQUALLY BOUNDED 116 5.8.2 DERIVATION OF
THE FOURIER COEFFICIENTS AND ILLUSTRATIVE EXAMPLES 119 6 FOURIER
REPRESENTATIONS OF PDFS IN DIRECT METHODS OF PHASE DETERMINATION 126 6.1
INTRODUCTION 126 6.2 EXACT CONDITIONAL PROBABILITY FOR EI IN PI 127
6.2.1 DERIVATION 128 6.2.2 REDUCTION OF THE EXACT RESULT TO THE
HYPERBOLIC TANGENT FORMULA 133 6.2.3 ILLUSTRATIVE EXAMPLES 135 6.3 EXACT
CONDITIONAL PROBABILITY FOR 2 IN PI 139 6.3.1 INTRODUCTION 139 6.3.2
DERIVATION 140 CONTENTS 6.3.3 ILLUSTRATIVE EXAMPLES . - - 143 6.4 EXACT
CONDITIONAL PDF OF A THREE-PHASE INVARIANT 145 6.4.1 JV-PHASE INVARIANTS
145 6.4.2 DERIVATION OF THE CONDITIONAL JOINT PDF OF $ 147 6.4.3
DERIVATION OF FOURIER COEFFICIENTS 149 6.4.4 REDUCTION OF THE EXACT
RESULT TO COCHRAN S (1955) APPROXIMATION 153 6.4.5 PROGRAMMING
CONSIDERATIONS AND ILLUSTRATIVE EXAMPLES 154 6.4.6 A SIMPLE APPLICATION
OF COMPLICATED FORMULAE 159 APPENDIX A 162 REFERENCES 163 INDEX 171
|
| any_adam_object | 1 |
| author | Shmueli, Uri Weiss, George H. |
| author_facet | Shmueli, Uri Weiss, George H. |
| author_role | aut aut |
| author_sort | Shmueli, Uri |
| author_variant | u s us g h w gh ghw |
| building | Verbundindex |
| bvnumber | BV010481601 |
| classification_rvk | UQ 5300 VC 6100 |
| ctrlnum | (OCoLC)246890668 (DE-599)BVBBV010481601 |
| dewey-full | 548.81015195 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 548 - Crystallography |
| dewey-raw | 548.81015195 |
| dewey-search | 548.81015195 |
| dewey-sort | 3548.81015195 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:53:15Z |
| institution | BVB |
| isbn | 0198559267 |
| language | Undetermined |
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| physical | IX, 173 S. graph. Darst. |
| publishDate | 1995 |
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| publisher | Oxford Univ. Press |
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| series | International Union of Crystallography: International Union of Crystallography monographs on crystallography |
| series2 | International Union of Crystallography: International Union of Crystallography monographs on crystallography |
| spelling | Shmueli, Uri Verfasser aut Introduction to crystallographic statistics Uri Shmueli ; George H. Weiss Oxford Oxford Univ. Press 1995 IX, 173 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International Union of Crystallography: International Union of Crystallography monographs on crystallography 6 Molekülstruktur (DE-588)4170383-2 gnd rswk-swf Kristallographie (DE-588)4033217-2 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Computational chemistry (DE-588)4290091-8 gnd rswk-swf Kristallographie (DE-588)4033217-2 s Computational chemistry (DE-588)4290091-8 s DE-604 Molekülstruktur (DE-588)4170383-2 s Statistik (DE-588)4056995-0 s Weiss, George H. Verfasser aut International Union of Crystallography: International Union of Crystallography monographs on crystallography 6 (DE-604)BV005455767 6 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006984773&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shmueli, Uri Weiss, George H. Introduction to crystallographic statistics International Union of Crystallography: International Union of Crystallography monographs on crystallography Molekülstruktur (DE-588)4170383-2 gnd Kristallographie (DE-588)4033217-2 gnd Statistik (DE-588)4056995-0 gnd Computational chemistry (DE-588)4290091-8 gnd |
| subject_GND | (DE-588)4170383-2 (DE-588)4033217-2 (DE-588)4056995-0 (DE-588)4290091-8 |
| title | Introduction to crystallographic statistics |
| title_auth | Introduction to crystallographic statistics |
| title_exact_search | Introduction to crystallographic statistics |
| title_full | Introduction to crystallographic statistics Uri Shmueli ; George H. Weiss |
| title_fullStr | Introduction to crystallographic statistics Uri Shmueli ; George H. Weiss |
| title_full_unstemmed | Introduction to crystallographic statistics Uri Shmueli ; George H. Weiss |
| title_short | Introduction to crystallographic statistics |
| title_sort | introduction to crystallographic statistics |
| topic | Molekülstruktur (DE-588)4170383-2 gnd Kristallographie (DE-588)4033217-2 gnd Statistik (DE-588)4056995-0 gnd Computational chemistry (DE-588)4290091-8 gnd |
| topic_facet | Molekülstruktur Kristallographie Statistik Computational chemistry |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006984773&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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