Popularizing mathematical methods in the People's Republic of China: some personal experiences
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Birkhäuser
1989
|
| Schriftenreihe: | Mathematical modeling
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 209 S. |
| ISBN: | 3764333723 0817633723 |
Internformat
MARC
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| 245 | 1 | 0 | |a Popularizing mathematical methods in the People's Republic of China |b some personal experiences |c Hua Loo-Keng ; Wang Yuan |
| 264 | 1 | |a Boston u.a. |b Birkhäuser |c 1989 | |
| 300 | |a XXII, 209 S. | ||
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| 650 | 7 | |a Optimisation mathématique |2 ram | |
| 650 | 7 | |a Recherche opérationnelle |2 ram | |
| 650 | 7 | |a génie industriel |2 inriac | |
| 650 | 7 | |a géologie |2 inriac | |
| 650 | 7 | |a optimisation mathématique |2 inriac | |
| 650 | 7 | |a recherche opérationnelle |2 inriac | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Industrial engineering |x Mathematics | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Operations research | |
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Datensatz im Suchindex
| _version_ | 1804116312165711872 |
|---|---|
| adam_text | Contents
Acknowledgements xi
Preface xiii
Preface by the editor xvii
An Obituary of Loo Keng Hua, by H. Halberstam xix
CHAPTER 0
INTRODUCTION
§ 0.1 Three principles 1
§ 0.2 Looking for problems in the literature 3
§ 0.3 Looking for problems in the workshop 5
§0.4 Optimum seeking methods (O.S.M) 8
§0.5 The Fibonacci search 10
§ 0.6 The golden number and numerical integration 11
§ 0.7 Overall planning methods 13
§0.8 On the use of statistics 18
§ 0.9 Concluding remarks 23
CHAPTER 1
ON THE CALCULATION OF MINERAL RESERVES AND HILLSIDE
AREAS ON CONTOUR MAPS
§ 1.1 Introduction 25
§ 1.2 Calculation of mineral reserves 26
§1.3 Calculation of hillside areas 32
References 40
v
vi
CHAPTER 2
THE MESHING GEAR PAIR PROBLEM
§2.1 Introduction 41
§ 2.2 Simple continued fractions 42
§2.3 Farey series 47
§ 2.4 An algorithm for the problem 49
§ 2.5 The solution to the meshing gear pair problem 51
References 55
CHAPTER 3
OPTIMUM SEEKING METHODS (single variable)
§ 3.1 Introduction 57
§ 3.2 Unimodal functions 59
§ 3.3 Method of trials by shifting to and fro 60
§ 3.4 The golden section method 61
§3.5 The proof of Theorem 3.1 63
§ 3.6 The Fibonacci search 69
§3.7 The proof of Theorem 3.2 71
§ 3.8 The bisection method 74
§ 3.9 The parabola method 76
References 78
CHAPTER 4
OPTIMUM SEEKING METHODS (several variables)
§4.1 Introduction 79
§ 4.2 Unimodal functions (several variables) 79
§ 4.3 The bisection method 81
§ 4.4 The successive approximation method 85
§4.5 The parallel line method 87
§4.6 The discrete case with two factors 89
vii
§ 4.7 The equilateral triangle method 91
§4.8 The gradient method 94
§4.9 The paraboloid method 95
§ 4.10 Convex bodies 99
§4.11 QieKuaiFa 104
§4.12 The 0 1 variable method 106
References 109
CHAPTER 5
THE GOLDEN NUMBER AND NUMERICAL INTEGRATION
§5.1 Introduction Ill
§5.2 Lemmas 113
§ 5.3 Error estimation for the quadrature formula 117
§ 5.4 A result for Q and a lower bound for the quadrature
formula 120
§5.5 Remarks 122
References 124
CHAPTER 6
OVERALL PLANNING METHODS
§ 6.1 Introduction 125
§6.2 Critical Path Method 125
§6.3 Float 127
§ 6.4 Parallel operations and overlapping operations 130
§6.5 Manpower scheduling 134
References 136
CHAPTER 7
PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT)
§ 7.1 Introduction 137
viii
§ 7.2 Estimation of the probability 138
§ 7.3 Computation process 142
§7.4 An elementary approach 145
§ 7.5 Remarks 147
References 149
CHAPTER 8
MACHINE SCHEDULING
§ 8.1 Introduction 151
§8.2 Two machine problem 151
§ 8.3 A lemma. 154
§ 8.4 Proof of Theorem 8.1 156
References 158
CHAPTER 9
THE TRANSPORTATION PROBLEM (GRAPHICAL METHOD)
§ 9.1 Introduction 159
§ 9.2 One cycle 167
§9.3 Proof of Theorem 9.1 170
References 172
CHAPTER 10
THE TRANSPORTATION PROBLEM (SIMPLEX METHOD)
§ 10.1 Introduction 173
§ 10.2 Eliminated unknowns and feasible solutions 179
§ 10.3 Criterion numbers 182
§ 10.4 A criterion for optimality 188
§10.5 Characteristic numbers 189
§ 10.6 Substitution 193
§ 10.7 Linear programming 197
References 198
ix
CHAPTER 11
THE POSTMAN PROBLEM
§ 11.1 Introduction 201
§ 11.2 Euler paths 204
§ 11.3 A necessary and sufficient criterion for an optimum
solution 205
References 208
|
| any_adam_object | 1 |
| author | Hua, Luogeng 1910-1985 Wang, Yuan 1930- |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| geographic | China (DE-588)4009937-4 gnd |
| geographic_facet | China |
| id | DE-604.BV001843603 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:36:30Z |
| institution | BVB |
| isbn | 3764333723 0817633723 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001223187 |
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| physical | XXII, 209 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Mathematical modeling |
| series2 | Mathematical modeling |
| spelling | Hua, Luogeng 1910-1985 Verfasser (DE-588)119001500 aut Popularizing mathematical methods in the People's Republic of China some personal experiences Hua Loo-Keng ; Wang Yuan Boston u.a. Birkhäuser 1989 XXII, 209 S. txt rdacontent n rdamedia nc rdacarrier Mathematical modeling 2 Chine inriac Génie industriel - Mathématiques ram Optimisation mathématique ram Recherche opérationnelle ram génie industriel inriac géologie inriac optimisation mathématique inriac recherche opérationnelle inriac Mathematik Industrial engineering Mathematics Mathematical optimization Operations research Implementation (DE-588)4026661-8 gnd rswk-swf Wirtschaft (DE-588)4066399-1 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf China (DE-588)4009937-4 gnd rswk-swf China (DE-588)4009937-4 g Operations Research (DE-588)4043586-6 s Implementation (DE-588)4026661-8 s Wirtschaft (DE-588)4066399-1 s DE-604 Wang, Yuan 1930- Verfasser (DE-588)120999072 aut Mathematical modeling 2 (DE-604)BV021847616 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001223187&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hua, Luogeng 1910-1985 Wang, Yuan 1930- Popularizing mathematical methods in the People's Republic of China some personal experiences Mathematical modeling Chine inriac Génie industriel - Mathématiques ram Optimisation mathématique ram Recherche opérationnelle ram génie industriel inriac géologie inriac optimisation mathématique inriac recherche opérationnelle inriac Mathematik Industrial engineering Mathematics Mathematical optimization Operations research Implementation (DE-588)4026661-8 gnd Wirtschaft (DE-588)4066399-1 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4026661-8 (DE-588)4066399-1 (DE-588)4043586-6 (DE-588)4009937-4 |
| title | Popularizing mathematical methods in the People's Republic of China some personal experiences |
| title_auth | Popularizing mathematical methods in the People's Republic of China some personal experiences |
| title_exact_search | Popularizing mathematical methods in the People's Republic of China some personal experiences |
| title_full | Popularizing mathematical methods in the People's Republic of China some personal experiences Hua Loo-Keng ; Wang Yuan |
| title_fullStr | Popularizing mathematical methods in the People's Republic of China some personal experiences Hua Loo-Keng ; Wang Yuan |
| title_full_unstemmed | Popularizing mathematical methods in the People's Republic of China some personal experiences Hua Loo-Keng ; Wang Yuan |
| title_short | Popularizing mathematical methods in the People's Republic of China |
| title_sort | popularizing mathematical methods in the people s republic of china some personal experiences |
| title_sub | some personal experiences |
| topic | Chine inriac Génie industriel - Mathématiques ram Optimisation mathématique ram Recherche opérationnelle ram génie industriel inriac géologie inriac optimisation mathématique inriac recherche opérationnelle inriac Mathematik Industrial engineering Mathematics Mathematical optimization Operations research Implementation (DE-588)4026661-8 gnd Wirtschaft (DE-588)4066399-1 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Chine Génie industriel - Mathématiques Optimisation mathématique Recherche opérationnelle génie industriel géologie optimisation mathématique recherche opérationnelle Mathematik Industrial engineering Mathematics Mathematical optimization Operations research Implementation Wirtschaft Operations Research China |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001223187&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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