Distribution of sequences: a sampler
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Frankfurt am Main [u.a.]
Lang
2005
|
| Series: | Slovenská Akadémia Vied <Bratislava>: Schriftenreihe der Slowakischen Akademie der Wissenschaften
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | Getr. Zählung |
| ISBN: | 3631540132 0820477311 |
Staff View
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Record in the Search Index
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| adam_text | OTO STRAUCH STEFAN PORUBSKY DISTRIBUTION OF SEQUENCES: A SAMPLER PETER
LANG EUROPAISCHER VERLAG DER WISSENSCHAFTEN CONTENTS PREFACE VII LIST OF
SYMBOLS AND ABBREVIATIONS XV 1 BASIC DEFINITIONS AND PROPERTIES 1 * 1
1.1 SEQUENCES 1-1 1.2 COUNTING FUNCTIONS 1-2 1.3 STEP DISTRIBUTION
FUNCTION OF X N , N = 1, 2,..., N 1-3 1.4 UNIFORM DISTRIBUTION 1-4 1.5
OTHER TYPES OF U.D 1-5 1.6 DISTRIBUTION FUNCTIONS 1-7 1.7 DISTRIBUTION
FUNCTIONS OF A GIVEN SEQUENCE 1-8 1.8 VARIOUS TYPES OF DISTRIBUTION OF
SEQUENCES 1-11 1.8.1 (/-DISTRIBUTED SEQUENCES, ASYMPTOTIC DIS- TRIBUTION
FUNCTIONS 1-11 1.8.2 DISTRIBUTION WITH RESPECT TO A SUMMA- TION METHOD
1-13 1.8.3 MATRIX ASYMPTOTIC DISTRIBUTION 1-13 1.8.4 WEIGHTED ASYMPTOTIC
DISTRIBUTION 1-14 1.8.5 I^OO-UNIFORM DISTRIBUTION 1-15 1.8.6 ABEL
ASYMPTOTIC DISTRIBUTION 1-15 1.8.7 ZETA ASYMPTOTIC DISTRIBUTION 1-15
1.8.8 STATISTICALLY CONVERGENT SEQUENCES 1 * 16 1.8.9 STATISTICALLY
INDEPENDENT SEQUENCES 1 * 17 1.8.10 MALDISTRIBUTED SEQUENCES 1-19 1.8.11
(A, A )-DISTRIBUTION 1-19 1.8.12 COMPLETELY U.D. SEQUENCES 1-20 1.8.13
COMPLETELY DENSE SEQUENCES 1-21 1.8.14 RELATIVELY DENSE UNIVERSAL
SEQUENCES 1-21 CONTENTS 1.8.15 LOW DISCREPANCY SEQUENCES 1-22 1.8.16 LOW
DISPERSION SEQUENCES 1-22 1.8.17 {T,M, S)-NETS 1-23 1.8.18 (T,
S)-SEQUENCES 1-23 1.8.19 GOOD LATTICE POINTS SEQUENCES 1-24 1.8.20
LATTICE RULES 1-25 1.8.21 RANDOM NUMBERS 1-26 1.8.22 PSEUDORANDOM
NUMBERS 1 * 27 1.8.23 BLOCK SEQUENCES 1-28 1.8.24 NORMAL NUMBERS 1-31
1.8.25 HOMOGENEOUSLY U.D. SEQUENCES 1-35 1.8.26 U.D. SEQUENCES WITH
RESPECT TO DIVISORS 1-35 1.8.27 EUTAXIC SEQUENCES 1-36 1.8.28 UNIFORMLY
QUICK SEQUENCES 1-36 1.8.29 POISSONIAN SEQUENCES 1-38 1.8.30 U.D. OF
MATRIX SEQUENCES 1 * 39 1.8.31 U.D. OF QUADRATIC FORMS 1-39 1.9
CLASSICAL DISCREPANCIES 1-40 1.10 OTHER DISCREPANCIES 1-47 1.10.1
DISCREPANCY FOR ^-DISTRIBUTED SEQUENCES 1-47 1.10.2 DIAPHONY 1-49 1.10.3
L 2 DISCREPANCY OF STATISTICALLY INDEPEN- DENT SEQUENCES 1 * 51 1.10.4
POLYNOMIAL DISCREPANCY 1-52 1.10.5 A-DISCREPANCY 1-53 1.10.6 WEIGHTED
DISCREPANCIES 1-53 1.10.7 LOGARITHMIC DISCREPANCY 1-54 1.10.8 ABEL
DISCREPANCY 1-54 1.10.9 DISCREPANCY WITH RESPECT TO A SET OF DIS-
TRIBUTION FUNCTIONS 1-56 1.10.10 DISCREPANCY OF DISTRIBUTION FUNCTIONS
1-57 1.10.11 DISPERSION 1-57 1.11 THE MULTI-DIMENSIONAL CASE 1-60 1.11.1
U.D. SEQUENCES 1-62 CONTENTS III 1.11.2 EXTREMAL AND STAR DISCREPANCY
1-62 1.11.3 THE MULTI-DIMENSIONAL NUMERICAL INTEGRATION . . . .1 * 66
1.11.4 L 2 DISCREPANCY 1-71 1.11.5 DIAPHONY 1-74 1.11.6 DISCREPANCY
RELATIVE TO SETS SYSTEMS X 1 * 76 1.11.7 DISCREPANCY RELATIVE TO CUBES
(CUBE-DISCREPANCY) . .1-76 1.11.8 DISCREPANCY RELATIVE TO BALLS 1-76
1.11.9 ISOTROPIC DISCREPANCY 1-77 1.11.10 SPHERICAL-CAP DISCREPANCY 1-78
1.11.11 L 2 DISCREPANCY RELATIVE TO A COUNTING FUNCTION . . . .1-78
1.11.12 DISCREPANCY RELATIVE TO REPRODUCING KERNEL 1-79 1.11.13
NON-UNIFORMITY 1-81 1.11.14 PARTITION DISCREPANCY 1*82 1.11.15 ABEL
DISCREPANCY 1-83 1.11.16 POLYNOMIAL DISCREPANCY 1-83 1.11.17 DISPERSION
1-84 1.11.18 SPECTRAL TEST 1-86 1.12 QUASI-MONTE CARLO APPLICATIONS 1-87
2 ONE*DIMENSIONAL SEQUENCES 2 * 1 2.1 CRITERIA FOR ASYMPTOTIC
DISTRIBUTION FUNCTIONS 2-1 2.2 SUFFICIENT OR NECESSARY CONDITIONS FOR
A.D.F. S 2-8 2.3 GENERAL OPERATIONS WITH SEQUENCES 2-24 2.4 SUBSEQUENCES
2-41 2.5 TRANSFORMATIONS OF SEQUENCES 2-44 2.6 SEQUENCES INVOLVING
CONTINUOUS FUNCTIONS 2-49 2.7 SEQUENCES OF ITERATIONS 2-69 2.8 SEQUENCES
OF THE FORM A(N)0 2-72 2.9 SEQUENCE INVOLVING SUM-OF-DIGITS FUNCTION
2-89 2.10 SEQUENCES INVOLVING (/-ADDITIVE FUNCTIONS 2-98 2.11
VANDERCORPUT SEQUENCES 2-102 2.12 SEQUENCES INVOLVING LOGARITHMIC
FUNCTION 2-109 2.13 SEQUENCES INVOLVING TRIGONOMETRIC FUNCTIONS 2-130
2.14 SEQUENCES INVOLVING POLYNOMIALS 2-135 IV CONTENTS 2.15 POWER
SEQUENCES 2-141 2.16 SEQUENCES INVOLVING THE INTEGER PART FUNCTION 2-145
2.17 EXPONENTIAL SEQUENCES 2-149 2.18 NORMAL NUMBERS 2-158 2.19
SEQUENCES INVOLVING PRIMES 2-170 2.20 SEQUENCES INVOLVING
NUMBER-THEORETICAL FUNCTIONS 2-183 2.21 SEQUENCES INVOLVING SPECIAL
FUNCTIONS 2-212 2.22 SEQUENCES OF RATIONAL NUMBERS 2-213 2.23 SEQUENCES
OF REDUCED RATIONAL NUMBERS 2 - 230 2.24 RECURRING SEQUENCES 2 - 236
2.25 PSEUDORANDOM NUMBERS CONGRUENTIAL GENERATORS 2 - 243 2.26 BINARY
SEQUENCES 2 - 255 3 MULTI*DIMENSIONAL SEQUENCES 3 * 1 3.1 CRITERIA AND
BASIC PROPERTIES 3-1 3.2 GENERAL OPERATIONS WITH SEQUENCES 3-2 3.3
GENERAL SEQUENCES 3-7 3.4 SEQUENCES OF THE FORM A(N)0 3-9 3.5 SEQUENCES
INVOLVING SUM-OF-DIGITS FUNCTIONS 3-16 3.6 SEQUENCES INVOLVING PRIMES
3-19 3.7 SEQUENCES INVOLVING NUMBER-THEORETICAL FUNCTIONS 3-25 3.8
POLYNOMIAL SEQUENCES 3-32 3.9 POWER SEQUENCES 3-35 3.10 EXPONENTIAL
SEQUENCES 3-36 3.11 CIRCLE SEQUENCES 3-43 3.12 SEQUENCES INVOLVING
TRIGONOMETRIC FUNCTIONS 3-49 3.13 SEQUENCES INVOLVING LOGARITHMIC
FUNCTION 3-49 3.14 SEQUENCES OF RATIONAL NUMBERS 3-52 3.15 GOOD LATTICE
POINTS 3-55 3.16 LATTICE POINTS INVOLVING RECURRING SEQUENCES 3-66 3.17
LATTICE RULES 3-69 3.18 SEQUENCES INVOLVING RADICAL INVERSE FUNCTION
3-72 3.19 (T, M, S)-NETS AND (T, S)-SEQUENCES 3-76 3.20 PSEUDORANDOM
NUMBERS CONGRUENTIAL GENERATORS 3-90 3.21 MISCELLANEOUS ITEMS 3-92
CONTENTS 4 APPENDIX 4 * 1 4.1 TECHNICAL THEOREMS 4-1 4.2 INTEGRAL
IDENTITIES 4-8 4.3 BASIC STATISTICAL NOTIONS 4-13 BIBLIOGRAPHY 5-1 NAME
INDEX 6 * 1 SUBJECT INDEX 7 * 1
|
| adam_txt |
OTO STRAUCH STEFAN PORUBSKY DISTRIBUTION OF SEQUENCES: A SAMPLER PETER
LANG EUROPAISCHER VERLAG DER WISSENSCHAFTEN CONTENTS PREFACE VII LIST OF
SYMBOLS AND ABBREVIATIONS XV 1 BASIC DEFINITIONS AND PROPERTIES 1 * 1
1.1 SEQUENCES 1-1 1.2 COUNTING FUNCTIONS 1-2 1.3 STEP DISTRIBUTION
FUNCTION OF X N , N = 1, 2,., N 1-3 1.4 UNIFORM DISTRIBUTION 1-4 1.5
OTHER TYPES OF U.D 1-5 1.6 DISTRIBUTION FUNCTIONS 1-7 1.7 DISTRIBUTION
FUNCTIONS OF A GIVEN SEQUENCE 1-8 1.8 VARIOUS TYPES OF DISTRIBUTION OF
SEQUENCES 1-11 1.8.1 (/-DISTRIBUTED SEQUENCES, ASYMPTOTIC DIS- TRIBUTION
FUNCTIONS 1-11 1.8.2 DISTRIBUTION WITH RESPECT TO A SUMMA- TION METHOD
1-13 1.8.3 MATRIX ASYMPTOTIC DISTRIBUTION 1-13 1.8.4 WEIGHTED ASYMPTOTIC
DISTRIBUTION 1-14 1.8.5 I^OO-UNIFORM DISTRIBUTION 1-15 1.8.6 ABEL
ASYMPTOTIC DISTRIBUTION 1-15 1.8.7 ZETA ASYMPTOTIC DISTRIBUTION 1-15
1.8.8 STATISTICALLY CONVERGENT SEQUENCES 1 * 16 1.8.9 STATISTICALLY
INDEPENDENT SEQUENCES 1 * 17 1.8.10 MALDISTRIBUTED SEQUENCES 1-19 1.8.11
(A, A')-DISTRIBUTION 1-19 1.8.12 COMPLETELY U.D. SEQUENCES 1-20 1.8.13
COMPLETELY DENSE SEQUENCES 1-21 1.8.14 RELATIVELY DENSE UNIVERSAL
SEQUENCES 1-21 CONTENTS 1.8.15 LOW DISCREPANCY SEQUENCES 1-22 1.8.16 LOW
DISPERSION SEQUENCES 1-22 1.8.17 {T,M, S)-NETS 1-23 1.8.18 (T,
S)-SEQUENCES 1-23 1.8.19 GOOD LATTICE POINTS SEQUENCES 1-24 1.8.20
LATTICE RULES 1-25 1.8.21 RANDOM NUMBERS 1-26 1.8.22 PSEUDORANDOM
NUMBERS 1 * 27 1.8.23 BLOCK SEQUENCES 1-28 1.8.24 NORMAL NUMBERS 1-31
1.8.25 HOMOGENEOUSLY U.D. SEQUENCES 1-35 1.8.26 U.D. SEQUENCES WITH
RESPECT TO DIVISORS 1-35 1.8.27 EUTAXIC SEQUENCES 1-36 1.8.28 UNIFORMLY
QUICK SEQUENCES 1-36 1.8.29 POISSONIAN SEQUENCES 1-38 1.8.30 U.D. OF
MATRIX SEQUENCES 1 * 39 1.8.31 U.D. OF QUADRATIC FORMS 1-39 1.9
CLASSICAL DISCREPANCIES 1-40 1.10 OTHER DISCREPANCIES 1-47 1.10.1
DISCREPANCY FOR ^-DISTRIBUTED SEQUENCES 1-47 1.10.2 DIAPHONY 1-49 1.10.3
L 2 DISCREPANCY OF STATISTICALLY INDEPEN- DENT SEQUENCES 1 * 51 1.10.4
POLYNOMIAL DISCREPANCY 1-52 1.10.5 A-DISCREPANCY 1-53 1.10.6 WEIGHTED
DISCREPANCIES 1-53 1.10.7 LOGARITHMIC DISCREPANCY 1-54 1.10.8 ABEL
DISCREPANCY 1-54 1.10.9 DISCREPANCY WITH RESPECT TO A SET OF DIS-
TRIBUTION FUNCTIONS 1-56 1.10.10 DISCREPANCY OF DISTRIBUTION FUNCTIONS
1-57 1.10.11 DISPERSION 1-57 1.11 THE MULTI-DIMENSIONAL CASE 1-60 1.11.1
U.D. SEQUENCES 1-62 CONTENTS III 1.11.2 EXTREMAL AND STAR DISCREPANCY
1-62 1.11.3 THE MULTI-DIMENSIONAL NUMERICAL INTEGRATION . . . .1 * 66
1.11.4 L 2 DISCREPANCY 1-71 1.11.5 DIAPHONY 1-74 1.11.6 DISCREPANCY
RELATIVE TO SETS SYSTEMS X 1 * 76 1.11.7 DISCREPANCY RELATIVE TO CUBES
(CUBE-DISCREPANCY) . .1-76 1.11.8 DISCREPANCY RELATIVE TO BALLS 1-76
1.11.9 ISOTROPIC DISCREPANCY 1-77 1.11.10 SPHERICAL-CAP DISCREPANCY 1-78
1.11.11 L 2 DISCREPANCY RELATIVE TO A COUNTING FUNCTION . . . .1-78
1.11.12 DISCREPANCY RELATIVE TO REPRODUCING KERNEL 1-79 1.11.13
NON-UNIFORMITY 1-81 1.11.14 PARTITION DISCREPANCY 1*82 1.11.15 ABEL
DISCREPANCY 1-83 1.11.16 POLYNOMIAL DISCREPANCY 1-83 1.11.17 DISPERSION
1-84 1.11.18 SPECTRAL TEST 1-86 1.12 QUASI-MONTE CARLO APPLICATIONS 1-87
2 ONE*DIMENSIONAL SEQUENCES 2 * 1 2.1 CRITERIA FOR ASYMPTOTIC
DISTRIBUTION FUNCTIONS 2-1 2.2 SUFFICIENT OR NECESSARY CONDITIONS FOR
A.D.F.'S 2-8 2.3 GENERAL OPERATIONS WITH SEQUENCES 2-24 2.4 SUBSEQUENCES
2-41 2.5 TRANSFORMATIONS OF SEQUENCES 2-44 2.6 SEQUENCES INVOLVING
CONTINUOUS FUNCTIONS 2-49 2.7 SEQUENCES OF ITERATIONS 2-69 2.8 SEQUENCES
OF THE FORM A(N)0 2-72 2.9 SEQUENCE INVOLVING SUM-OF-DIGITS FUNCTION
2-89 2.10 SEQUENCES INVOLVING (/-ADDITIVE FUNCTIONS 2-98 2.11
VANDERCORPUT SEQUENCES 2-102 2.12 SEQUENCES INVOLVING LOGARITHMIC
FUNCTION 2-109 2.13 SEQUENCES INVOLVING TRIGONOMETRIC FUNCTIONS 2-130
2.14 SEQUENCES INVOLVING POLYNOMIALS 2-135 IV CONTENTS 2.15 POWER
SEQUENCES 2-141 2.16 SEQUENCES INVOLVING THE INTEGER PART FUNCTION 2-145
2.17 EXPONENTIAL SEQUENCES 2-149 2.18 NORMAL NUMBERS 2-158 2.19
SEQUENCES INVOLVING PRIMES 2-170 2.20 SEQUENCES INVOLVING
NUMBER-THEORETICAL FUNCTIONS 2-183 2.21 SEQUENCES INVOLVING SPECIAL
FUNCTIONS 2-212 2.22 SEQUENCES OF RATIONAL NUMBERS 2-213 2.23 SEQUENCES
OF REDUCED RATIONAL NUMBERS 2 - 230 2.24 RECURRING SEQUENCES 2 - 236
2.25 PSEUDORANDOM NUMBERS CONGRUENTIAL GENERATORS 2 - 243 2.26 BINARY
SEQUENCES 2 - 255 3 MULTI*DIMENSIONAL SEQUENCES 3 * 1 3.1 CRITERIA AND
BASIC PROPERTIES 3-1 3.2 GENERAL OPERATIONS WITH SEQUENCES 3-2 3.3
GENERAL SEQUENCES 3-7 3.4 SEQUENCES OF THE FORM A(N)0 3-9 3.5 SEQUENCES
INVOLVING SUM-OF-DIGITS FUNCTIONS 3-16 3.6 SEQUENCES INVOLVING PRIMES
3-19 3.7 SEQUENCES INVOLVING NUMBER-THEORETICAL FUNCTIONS 3-25 3.8
POLYNOMIAL SEQUENCES 3-32 3.9 POWER SEQUENCES 3-35 3.10 EXPONENTIAL
SEQUENCES 3-36 3.11 CIRCLE SEQUENCES 3-43 3.12 SEQUENCES INVOLVING
TRIGONOMETRIC FUNCTIONS 3-49 3.13 SEQUENCES INVOLVING LOGARITHMIC
FUNCTION 3-49 3.14 SEQUENCES OF RATIONAL NUMBERS 3-52 3.15 GOOD LATTICE
POINTS 3-55 3.16 LATTICE POINTS INVOLVING RECURRING SEQUENCES 3-66 3.17
LATTICE RULES 3-69 3.18 SEQUENCES INVOLVING RADICAL INVERSE FUNCTION
3-72 3.19 (T, M, S)-NETS AND (T, S)-SEQUENCES 3-76 3.20 PSEUDORANDOM
NUMBERS CONGRUENTIAL GENERATORS 3-90 3.21 MISCELLANEOUS ITEMS 3-92
CONTENTS 4 APPENDIX 4 * 1 4.1 TECHNICAL THEOREMS 4-1 4.2 INTEGRAL
IDENTITIES 4-8 4.3 BASIC STATISTICAL NOTIONS 4-13 BIBLIOGRAPHY 5-1 NAME
INDEX 6 * 1 SUBJECT INDEX 7 * 1 |
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| author | Strauch, Oto Porubský, Štefan |
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| id | DE-604.BV021572409 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:38:52Z |
| indexdate | 2024-07-09T20:38:56Z |
| institution | BVB |
| isbn | 3631540132 0820477311 |
| language | English |
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| publisher | Lang |
| record_format | marc |
| series | Slovenská Akadémia Vied <Bratislava>: Schriftenreihe der Slowakischen Akademie der Wissenschaften |
| series2 | Slovenská Akadémia Vied <Bratislava>: Schriftenreihe der Slowakischen Akademie der Wissenschaften |
| spelling | Strauch, Oto Verfasser aut Distribution of sequences a sampler Oto Strauch ; Štefan Porubský Frankfurt am Main [u.a.] Lang 2005 Getr. Zählung txt rdacontent n rdamedia nc rdacarrier Slovenská Akadémia Vied <Bratislava>: Schriftenreihe der Slowakischen Akademie der Wissenschaften 1 Distribution (Probability theory) Sequences (Mathematics) Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Gleichverteilung (DE-588)4157566-0 gnd rswk-swf Gleichverteilung (DE-588)4157566-0 s Algebraische Zahlentheorie (DE-588)4001170-7 s DE-604 Porubský, Štefan Verfasser aut Slovenská Akadémia Vied <Bratislava>: Schriftenreihe der Slowakischen Akademie der Wissenschaften 1 (DE-604)BV021607757 1 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014788195&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strauch, Oto Porubský, Štefan Distribution of sequences a sampler Slovenská Akadémia Vied <Bratislava>: Schriftenreihe der Slowakischen Akademie der Wissenschaften Distribution (Probability theory) Sequences (Mathematics) Algebraische Zahlentheorie (DE-588)4001170-7 gnd Gleichverteilung (DE-588)4157566-0 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4157566-0 |
| title | Distribution of sequences a sampler |
| title_auth | Distribution of sequences a sampler |
| title_exact_search | Distribution of sequences a sampler |
| title_exact_search_txtP | Distribution of sequences a sampler |
| title_full | Distribution of sequences a sampler Oto Strauch ; Štefan Porubský |
| title_fullStr | Distribution of sequences a sampler Oto Strauch ; Štefan Porubský |
| title_full_unstemmed | Distribution of sequences a sampler Oto Strauch ; Štefan Porubský |
| title_short | Distribution of sequences |
| title_sort | distribution of sequences a sampler |
| title_sub | a sampler |
| topic | Distribution (Probability theory) Sequences (Mathematics) Algebraische Zahlentheorie (DE-588)4001170-7 gnd Gleichverteilung (DE-588)4157566-0 gnd |
| topic_facet | Distribution (Probability theory) Sequences (Mathematics) Algebraische Zahlentheorie Gleichverteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014788195&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021607757 |
| work_keys_str_mv | AT strauchoto distributionofsequencesasampler AT porubskystefan distributionofsequencesasampler |