Topics in random polynomials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow
Longman
1998
|
| Schriftenreihe: | Pitman research notes in mathematics series
393 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 163 S. graph. Darst. |
| ISBN: | 0582356229 |
Internformat
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Datensatz im Suchindex
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| adam_text | Contents
Preface
1 Introduction 1
1.1 Behaviour 2
1.2 Distribution of coefficients 6
1.2.1 Non-identical coefficients 7
1.2.2 Dependence coefficients 8
1.2.3 Complex coefficients and complex roots 9
2 Level crossings of stochastic processes 10
2.1 Definitions 10
2.2 Level crossings 11
2.2.1 Sharp crossings 13
2.2.2 Local maxima 14
2.2.3 Exceedance measure 15
2.2.4 Complex case 15
2.3 Gaussian processes 16
2.3.1 Level crossings 17
2.3.2 Sharp crossings 18
2.3.3 Local maxima 18
2.3.4 Exceedance measure 20
2.3.5 Complex case 21
2.4 Higher moments 21
2.4.1 Variance of the number of real zeros 24
2.5 Real zeros of random polynomials 25
3 Algebraic polynomials 29
3.1 Definitions and general formulae 30
3.2 Real zeros 32
3.2.1 Asymptotic expansion 34
3.3 Level crossings 35
3.3.1 Bounded-level crossings 36
3.3.2 Unbounded level crossings 40
3.3.3 Large level crossings 41
3.4 Coefficients with non-zero means 42
3.4.1 Identically distributed coefficients 42
3.4.2 Coefficients with non-equal means 45
3.5 Dependent coefficients 52
3.6 Slope crossings 54
3.7 Sharp crossings 55
3.8 Maxima (minima) 59
3.8.1 Local maxima 61
3.8.2 Non-zero mean 63
3.9 Points of inflection 64
3.10 Exceedance measure 64
3.10.1 Axis crossings 65
3.10.2 Exceedance measure of the level K 68
3.10.3 Numerical result 70
3.11 Variance of number of real zeros 70
4 Trigonometric polynomials 72
4.1 Moments 73
4.2 Level crossings 75
4.2.1 Asymptotic expansion 79
4.3 Non-identical coefficients 80
4.3.1 Two groups of coefficients 80
4.3.2 Coefficients with different distributions 84
4.4 Dependent coefficients 89
4.5 Slope crossings 91
4.6 Maxima (minima) 91
4.6.1 Asymptotic expansion 92
4.6.2 Local maxima 92
4.7 Exceedance measure 93
4.7.1 Numerical result 94
4.8 Variance of the number of real zeros 94
5 Orthogonal polynomials 100
5.1 Level crossings 100
5.2 Non-identical coefficients 105
6 Hyperbolic polynomials 110
6.1 Moments Ill
6.2 Level crossing 113
6.3 Coefficients with non-zero means 115
6.3.1 Non-identical coefficients 118
6.4 Maxima and minima 121
7 Other distributions 125
7.1 Algebraic polynomials 125
7.1.1 Non-degenerate stable distribution 127
7.1.2 Numerical results 133
7.1.3 Maxima (minima) 136
7.1.4 Non-zero location parameter 137
7.2 General distribution 139
7.3 Trigonometric polynomial 140
8 Complex coefficients and complex roots 142
8.1 Complex coefficients 142
8.1.1 Algebraic polynomials 143
8.1.2 Trigonometric polynomials 147
8.2 Complex roots 148
8.2.1 Asymptotic analysis 152
Bibliography 154
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.942 |
| dewey-search | 512.942 |
| dewey-sort | 3512.942 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV024975913 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:24:53Z |
| institution | BVB |
| isbn | 0582356229 |
| language | English |
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| oclc_num | 833396099 |
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| physical | 163 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Longman |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Farahmand, Kambiz Verfasser aut Topics in random polynomials Kambiz Farahmand Harlow Longman 1998 163 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 393 Pitman research notes in mathematics series 393 (DE-604)BV000022845 393 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019643307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farahmand, Kambiz Topics in random polynomials Pitman research notes in mathematics series |
| title | Topics in random polynomials |
| title_auth | Topics in random polynomials |
| title_exact_search | Topics in random polynomials |
| title_full | Topics in random polynomials Kambiz Farahmand |
| title_fullStr | Topics in random polynomials Kambiz Farahmand |
| title_full_unstemmed | Topics in random polynomials Kambiz Farahmand |
| title_short | Topics in random polynomials |
| title_sort | topics in random polynomials |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019643307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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