Number theory and the Periodicity of Matter:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
2008
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 374 S. graph. Darst. |
| ISBN: | 9781402066597 9781402066603 1402066597 |
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| 245 | 1 | 0 | |a Number theory and the Periodicity of Matter |c Jan C. Boeyens ; Demitrius C. Levendis |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Springer |c 2008 | |
| 300 | |a XV, 374 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text | Contents
Preface
v
1 Introduction 1
1.1 Number Magic .......................... 1
1.2 Periodic Structures........................ 3
1.3 Nuclear Synthesis......................... 5
1.4 Nuclidic Periodicity and Stability................ 6
1.5 Hidden Symmetry......................... 8
1.6 Number Patterns......................... 10
1.7 Cosmic Structure......................... 12
1.8 Nuclear Structure and Properties................ 13
1.8.1 Nuclide Abundance.................... 13
1.8.2 Nuclear Spin and Parity................. 14
1.8.3 Neutron Scattering.................... 14
1.8.4 Radioactivity....................... 15
1.8.5 Nuclear Structure..................... 15
1.9 Holistic Symmetry ........................ 17
2 Number Theory Primer 19
2.1 Introduction............................ 19
2.2 Numbers and Arithmetic..................... 20
2.2.1 Arithmetic......................... 21
2.2.2 Divisibility......................... 23
2.2.3 Prime Numbers...................... 24
2.2.4 Magic Numbers...................... 26
2.2.5 Fundamental Theorem of Arithmetic.......... 30
2.2.6 Gaussian Integers..................... 32
2.2.7 The Binomial Equation.................. 33
2.2.8 Algebraic Number Theory................ 34
2.3 Distribution of Prime Numbers ................. 36
2.3.1 Twin Primes ....................... 38
2.3.2 The Sieve Revisited.................... 40
XI
xii CONTENTS
2.3.3 Prime-generating Polynomials.............. 41
2.4 Fibonacci Numbers........................ 43
2.4.1 The Golden Ratio..................... 44
2.4.2 Phyllotaxis and Growth ................. 47
2.5 Rational Fractions ........................ 48
2.5.1 The Farey Sequence ................... 50
2.6 Modular Arithmetic........................ 52
2.6.1 Congruences........................ 52
2.6.2 Higher Congruences.................... 55
2.6.3 Partitions and Equivalence Relations.......... 61
2.7 Periodic Arithmetic Functions.................. 61
2.7.1 The Lagrange Resolvent...............•. . 63
2.7.2 Gaussian Sums...................... 64
2.7.3 Finite Fourier Series ................... 66
2.7.4 Periodic Functions .................... 67
3 Periodic Table of the Elements 71
3.1 Historical Development...................... 71
3.1.1 The Theory of Combustion ............... 73
3.1.2 Atomic Theory...................... 76
3.1.3 Measurement of Atomic Weights ............ 81
3.1.4 The Periodic Law..................... 84
3.1.5 Interlude.......................... 91
3.1.6 Atomic Structure..................... 93
3.1.7 Atomic Number...................... 98
3.2 Theoretical Development..................... 101
3.2.1 Atomic Line Spectra................... 101
3.2.2 Quantum Theory..................... 102
3.2.3 The Bohr Model ..................... 106
3.2.4 Static Model of the Atom ................ 109
3.2.5 The Sommerfeld Model.................. 113
3.2.6 Wave-mechanical Atomic Model............. 114
3.2.7 Aufbau Procedure .................... 126
3.3 Conclusion............................. 128
4 Structure of Atomic Nuclei 131
4.1 Introduction............................ 131
4.2 Mass and Binding Energy.................... 132
4.2.1 Models of the Nucleus.................. 134
4.2.2 The Semi-empirical Mass Formula............ 136
4.2.3 Nuclear Stability..................... 138
CONTENTS xiii
4.2.4 Nuclear Synthesis and Abundance............142
4.3 Theoretical Models........................152
4.3.1 The Shell Model .....................152
4.3.2 Strong Interaction ....................154
4.4 Particle Physics..........................157
4.4.1 Antimatter ........................158
4.4.2 The CPT Theorem....................161
4.4.3 The Quark Model.....................165
4.4.4 Deep Inelastic Scattering.................171
4.4.5 Quantum Chromodynamics...............178
4.4.6 Primary Structure ....................180
5 Elements of Cosmography 183
5.1 Historical .............................184
5.2 Cosmological Paradoxes .....................187
5.2.1 Olbers Paradox......................187
5.2.2 Zwicky Paradox......................189
5.2.3 Antimatter Paradox ...................190
5.3 Cosmological Models.......................190
5.3.1 The Expanding Universe.................191
5.3.2 Plasma Cosmology....................196
5.3.3 Curved-space Cosmology.................197
5.3.4 The Anthropic Principle.................198
5.3.5 Elemental Synthesis ...................199
5.4 Chirality of Space-time......................200
5.4.1 The Helicoid........................201
5.4.2 The Chiral Plane.....................202
5.4.3 General Theory......................202
5.5 The Vacuum Substratum.....................204
5.5.1 Implicate Order and Holomovement...........205
5.5.2 Information Theory....................206
6 The Periodic Laws 209
6.1 Introduction............................209
6.2 Number Spiral and Periodic Laws................215
6.3 General Periodic Function....................222
6.4 Hidden Symmetry.........................225
6.5 Neutron Periodicity........................228
6.5.1 The Magic Diagram ...................233
6.6 Nuclide Periodicity........................235
xiv CONTENTS
7 Periodicity and Number Theory 237
7.1 Introduction............................237
7.2 Nuclear Synthesis by a-particle Addition............238
7.3 Nuclides in Farey Sequence....................240
7.4 Triangle of Stability........................242
7.4.1 Nuclidic Periodicity....................245
7.5 Nuclear Stability.........................247
7.5.1 Nuclear Binding Energy.................250
7.5.2 0-Stability.........................252
7.6 Golden Parabola .........................255
8 Properties of Atomic Matter 259
8.1 Periodicity............................. 259
8.2 Nuclear Stability ......................... 262
8.2.1 Cosmic Abundance.................... 264
8.3 Nuclear Structure......................... 266
8.3.1 Bound-state f3~ Decay.................. 267
8.3.2 Nuclear Spin ....................... 268
8.3.3 Packing of Nucleons ................... 278
8.3.4 Nuclear Size and Shape.................. 281
8.3.5 Parity........................... 285
8.3.6 a-Instability........................ 288
9 The Grand Pattern 291
9.1 The Golden Ratio.........................291
9.2 Nuclear Structure.........................293
9.3 The Five Domains ........................294
9.3.1 A Golden Diagram....................297
9.4 Matter Transformation......................298
9.4.1 The Cosmic Phase Diagram...............300
10 The Golden Excess 303
10.1 Introduction............................303
10.2 Nuclide Periodicity........................304
10.2.1 Superconducting Nuclides................305
10.2.2 Periodic Effects......................308
10.3 Superfluidity............................309
10.4 Structure of the Nucleus.....................312
10.5 Superconductivity.........................314
10.5.1 The Phase Transition...................314
10.5.2 The Critical Temperature................317
CONTENTS xv
10.5.3 Crystal Chemistry ....................317
10.5.4 An Alternative Mechanism................325
10.5.5 Hall Effect.........................331
10.6 Nuclear Stability.........................332
11 Chemical Periodicity 335
11.1 Introduction............................335
11.2 Electronegativity.........................336
11.2.1 The Quantum-Potential Scale..............338
11.2.2 Derivation of a Common Scale..............342
11.3 Chemical Bonding ........................342
11.3.1 Point-Charge Model ...................346
11.3.2 The Diatomic Energy Function .............350
11.3.3 Bond Order........................352
11.3.4 Molecular Mechanics...................355
11.4 Epilogue..............................355
Bibliography 357
|
| adam_txt |
Contents
Preface
v
1 Introduction 1
1.1 Number Magic . 1
1.2 Periodic Structures. 3
1.3 Nuclear Synthesis. 5
1.4 Nuclidic Periodicity and Stability. 6
1.5 Hidden Symmetry. 8
1.6 Number Patterns. 10
1.7 Cosmic Structure. 12
1.8 Nuclear Structure and Properties. 13
1.8.1 Nuclide Abundance. 13
1.8.2 Nuclear Spin and Parity. 14
1.8.3 Neutron Scattering. 14
1.8.4 Radioactivity. 15
1.8.5 Nuclear Structure. 15
1.9 Holistic Symmetry . 17
2 Number Theory Primer 19
2.1 Introduction. 19
2.2 Numbers and Arithmetic. 20
2.2.1 Arithmetic. 21
2.2.2 Divisibility. 23
2.2.3 Prime Numbers. 24
2.2.4 Magic Numbers. 26
2.2.5 Fundamental Theorem of Arithmetic. 30
2.2.6 Gaussian Integers. 32
2.2.7 The Binomial Equation. 33
2.2.8 Algebraic Number Theory. 34
2.3 Distribution of Prime Numbers . 36
2.3.1 Twin Primes . 38
2.3.2 The Sieve Revisited. 40
XI
xii CONTENTS
2.3.3 Prime-generating Polynomials. 41
2.4 Fibonacci Numbers. 43
2.4.1 The Golden Ratio. 44
2.4.2 Phyllotaxis and Growth . 47
2.5 Rational Fractions . 48
2.5.1 The Farey Sequence . 50
2.6 Modular Arithmetic. 52
2.6.1 Congruences. 52
2.6.2 Higher Congruences. 55
2.6.3 Partitions and Equivalence Relations. 61
2.7 Periodic Arithmetic Functions. 61
2.7.1 The Lagrange Resolvent.•. . 63
2.7.2 Gaussian Sums. 64
2.7.3 Finite Fourier Series . 66
2.7.4 Periodic Functions . 67
3 Periodic Table of the Elements 71
3.1 Historical Development. 71
3.1.1 The Theory of Combustion . 73
3.1.2 Atomic Theory. 76
3.1.3 Measurement of Atomic Weights . 81
3.1.4 The Periodic Law. 84
3.1.5 Interlude. 91
3.1.6 Atomic Structure. 93
3.1.7 Atomic Number. 98
3.2 Theoretical Development. 101
3.2.1 Atomic Line Spectra. 101
3.2.2 Quantum Theory. 102
3.2.3 The Bohr Model . 106
3.2.4 Static Model of the Atom . 109
3.2.5 The Sommerfeld Model. 113
3.2.6 Wave-mechanical Atomic Model. 114
3.2.7 Aufbau Procedure . 126
3.3 Conclusion. 128
4 Structure of Atomic Nuclei 131
4.1 Introduction. 131
4.2 Mass and Binding Energy. 132
4.2.1 Models of the Nucleus. 134
4.2.2 The Semi-empirical Mass Formula. 136
4.2.3 Nuclear Stability. 138
CONTENTS xiii
4.2.4 Nuclear Synthesis and Abundance.142
4.3 Theoretical Models.152
4.3.1 The Shell Model .152
4.3.2 Strong Interaction .154
4.4 Particle Physics.157
4.4.1 Antimatter .158
4.4.2 The CPT Theorem.161
4.4.3 The Quark Model.165
4.4.4 Deep Inelastic Scattering.171
4.4.5 Quantum Chromodynamics.178
4.4.6 Primary Structure .180
5 Elements of Cosmography 183
5.1 Historical .184
5.2 Cosmological Paradoxes .187
5.2.1 Olbers Paradox.187
5.2.2 Zwicky Paradox.189
5.2.3 Antimatter Paradox .190
5.3 Cosmological Models.190
5.3.1 The Expanding Universe.191
5.3.2 Plasma Cosmology.196
5.3.3 Curved-space Cosmology.197
5.3.4 The Anthropic Principle.198
5.3.5 Elemental Synthesis .199
5.4 Chirality of Space-time.200
5.4.1 The Helicoid.201
5.4.2 The Chiral Plane.202
5.4.3 General Theory.202
5.5 The Vacuum Substratum.204
5.5.1 Implicate Order and Holomovement.205
5.5.2 Information Theory.206
6 The Periodic Laws 209
6.1 Introduction.209
6.2 Number Spiral and Periodic Laws.215
6.3 General Periodic Function.222
6.4 Hidden Symmetry.225
6.5 Neutron Periodicity.228
6.5.1 The Magic Diagram .233
6.6 Nuclide Periodicity.235
xiv CONTENTS
7 Periodicity and Number Theory 237
7.1 Introduction.237
7.2 Nuclear Synthesis by a-particle Addition.238
7.3 Nuclides in Farey Sequence.240
7.4 Triangle of Stability.242
7.4.1 Nuclidic Periodicity.245
7.5 Nuclear Stability.247
7.5.1 Nuclear Binding Energy.250
7.5.2 0-Stability.252
7.6 Golden Parabola .255
8 Properties of Atomic Matter 259
8.1 Periodicity. 259
8.2 Nuclear Stability . 262
8.2.1 Cosmic Abundance. 264
8.3 Nuclear Structure. 266
8.3.1 Bound-state f3~ Decay. 267
8.3.2 Nuclear Spin . 268
8.3.3 Packing of Nucleons . 278
8.3.4 Nuclear Size and Shape. 281
8.3.5 Parity. 285
8.3.6 a-Instability. 288
9 The Grand Pattern 291
9.1 The Golden Ratio.291
9.2 Nuclear Structure.293
9.3 The Five Domains .294
9.3.1 A Golden Diagram.297
9.4 Matter Transformation.298
9.4.1 The Cosmic Phase Diagram.300
10 The Golden Excess 303
10.1 Introduction.303
10.2 Nuclide Periodicity.304
10.2.1 Superconducting Nuclides.305
10.2.2 Periodic Effects.308
10.3 Superfluidity.309
10.4 Structure of the Nucleus.312
10.5 Superconductivity.314
10.5.1 The Phase Transition.314
10.5.2 The Critical Temperature.317
CONTENTS xv
10.5.3 Crystal Chemistry .317
10.5.4 An Alternative Mechanism.325
10.5.5 Hall Effect.331
10.6 Nuclear Stability.332
11 Chemical Periodicity 335
11.1 Introduction.335
11.2 Electronegativity.336
11.2.1 The Quantum-Potential Scale.338
11.2.2 Derivation of a Common Scale.342
11.3 Chemical Bonding .342
11.3.1 Point-Charge Model .346
11.3.2 The Diatomic Energy Function .350
11.3.3 Bond Order.352
11.3.4 Molecular Mechanics.355
11.4 Epilogue.355
Bibliography 357 |
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| author | Boeyens, Jan C. A. 1934-2015 |
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| author_role | aut |
| author_sort | Boeyens, Jan C. A. 1934-2015 |
| author_variant | j c a b jca jcab |
| building | Verbundindex |
| bvnumber | BV023089532 |
| classification_rvk | SK 950 UQ 1300 |
| ctrlnum | (OCoLC)255618225 (DE-599)DNB985051140 |
| discipline | Chemie / Pharmazie Physik Mathematik |
| discipline_str_mv | Chemie / Pharmazie Physik Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV023089532 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:40:26Z |
| indexdate | 2024-07-09T21:10:45Z |
| institution | BVB |
| isbn | 9781402066597 9781402066603 1402066597 |
| language | English |
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| physical | XV, 374 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| spelling | Boeyens, Jan C. A. 1934-2015 Verfasser (DE-588)135717884 aut Number theory and the Periodicity of Matter Jan C. Boeyens ; Demitrius C. Levendis 1. ed. Berlin Springer 2008 XV, 374 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Periodizität (DE-588)4248522-8 gnd rswk-swf Kernstruktur (DE-588)4030351-2 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Kosmologie (DE-588)4114294-9 gnd rswk-swf Atombau (DE-588)4068920-7 gnd rswk-swf Atombau (DE-588)4068920-7 s Kernstruktur (DE-588)4030351-2 s Kosmologie (DE-588)4114294-9 s Periodizität (DE-588)4248522-8 s Zahlentheorie (DE-588)4067277-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016292419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boeyens, Jan C. A. 1934-2015 Number theory and the Periodicity of Matter Periodizität (DE-588)4248522-8 gnd Kernstruktur (DE-588)4030351-2 gnd Zahlentheorie (DE-588)4067277-3 gnd Kosmologie (DE-588)4114294-9 gnd Atombau (DE-588)4068920-7 gnd |
| subject_GND | (DE-588)4248522-8 (DE-588)4030351-2 (DE-588)4067277-3 (DE-588)4114294-9 (DE-588)4068920-7 |
| title | Number theory and the Periodicity of Matter |
| title_auth | Number theory and the Periodicity of Matter |
| title_exact_search | Number theory and the Periodicity of Matter |
| title_exact_search_txtP | Number theory and the Periodicity of Matter |
| title_full | Number theory and the Periodicity of Matter Jan C. Boeyens ; Demitrius C. Levendis |
| title_fullStr | Number theory and the Periodicity of Matter Jan C. Boeyens ; Demitrius C. Levendis |
| title_full_unstemmed | Number theory and the Periodicity of Matter Jan C. Boeyens ; Demitrius C. Levendis |
| title_short | Number theory and the Periodicity of Matter |
| title_sort | number theory and the periodicity of matter |
| topic | Periodizität (DE-588)4248522-8 gnd Kernstruktur (DE-588)4030351-2 gnd Zahlentheorie (DE-588)4067277-3 gnd Kosmologie (DE-588)4114294-9 gnd Atombau (DE-588)4068920-7 gnd |
| topic_facet | Periodizität Kernstruktur Zahlentheorie Kosmologie Atombau |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016292419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT boeyensjanca numbertheoryandtheperiodicityofmatter |