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The elements of Cantor sets : with applications / / Robert W. Vallin
| The elements of Cantor sets : with applications / / Robert W. Vallin |
| Autore | Vallin Robert W |
| Edizione | [First edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , [2013] |
| Descrizione fisica | 1 online resource (248 p.) |
| Disciplina | 515.8 |
| Soggetto topico |
Cantor sets
Measure theory Mathematical analysis MATHEMATICS / Mathematical Analysis |
| ISBN |
1-118-40743-1
1-118-54874-4 1-118-54870-1 |
| Classificazione | MAT034000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright Page; CONTENTS; Foreword; Preface; Acknowledgments; Introduction; 1 A Quick Biography of Cantor; 2 Basics; 2.1 Review; Exercises; 3 Introducing the Cantor Set; 3.1 Some Definitions and Basics; 3.2 Size of a Cantor Set; 3.2.1 Cardinality; 3.2.2 Category; 3.2.3 Measure; 3.3 Large and Small; Exercises; 4 Cantor Sets and Continued Fractions; 4.1 Introducing Continued Fractions; 4.2 Constructing a Cantor Set; 4.3 Diophantine Equations; 4.4 Miscellaneous; Exercises; 5 p-adic Numbers and Valuations; 5.1 Some Abstract Algebra; 5.2 p-adic Numbers
5.2.1 An Analysis Point of View5.2.2 An Algebra Point of View; 5.3 p-adic Integers and Cantor Sets; 5.4 p-adic Rational Numbers; Exercises; 6 Self-Similar Objects; 6.1 The Meaning of Self-Similar; 6.2 Metric Spaces; 6.3 Sequences in (S, d); 6.4 Affine Transformations; 6.5 An Application for an IFS; Exercises; 7 Various Notions of Dimension; 7.1 Limit Supremum and Limit Infimum; 7.2 Topological Dimension; 7.3 Similarity Dimension; 7.4 Box-Counting Dimension; 7.5 Hausdorff Measure and Dimension; 7.6 Miscellaneous Notions of Dimension; Exercises; 8 Porosity and Thickness-Looking at the Gaps 8.1 The Porosity of a Set8.2 Symmetric Sets and Symmetric Porosity; 8.3 A New and Different Definition of Cantor Set; 8.4 Thickness of a Cantor Set; 8.5 Applying Thickness; 8.6 A Bit More on Thickness; 8.7 Porosity in a Metric Space; Exercises; 9 Creating Pathological Functions via C; 9.1 Sequences of Functions; 9.2 The Cantor Function; 9.3 Space-Filling Curves; 9.4 Baire Class One Functions; 9.5 Darboux Functions; 9.6 Linearly Continuous Functions; Exercises; 10 Generalizations and Applications; 10.1 Generalizing Cantor Sets; 10.2 Fat Cantor Sets; 10.3 Sums of Cantor Sets 10.4 Differences of Cantor Sets10.5 Products of Cantor Sets; 10.6 Cantor Target; 10.7 Ana Sets; 10.8 Average Distance; 10.9 Non-Averaging Sets; 10.10 Cantor Series and Cantor Sets; 10.11 Liouville Numbers and Irrationality Exponents; 10.12 Sets of Sums of Convergent Alternating Series; 10.13 The Monty Hall Problem; 11 Epilogue; References; Index |
| Record Nr. | UNINA-9910139035303321 |
Vallin Robert W
|
||
| Hoboken, New Jersey : , : Wiley, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The elements of Cantor sets : with applications / / Robert W. Vallin
| The elements of Cantor sets : with applications / / Robert W. Vallin |
| Autore | Vallin Robert W |
| Edizione | [First edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , [2013] |
| Descrizione fisica | 1 online resource (248 p.) |
| Disciplina | 515.8 |
| Soggetto topico |
Cantor sets
Measure theory Mathematical analysis MATHEMATICS / Mathematical Analysis |
| ISBN |
1-118-40743-1
1-118-54874-4 1-118-54870-1 |
| Classificazione | MAT034000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright Page; CONTENTS; Foreword; Preface; Acknowledgments; Introduction; 1 A Quick Biography of Cantor; 2 Basics; 2.1 Review; Exercises; 3 Introducing the Cantor Set; 3.1 Some Definitions and Basics; 3.2 Size of a Cantor Set; 3.2.1 Cardinality; 3.2.2 Category; 3.2.3 Measure; 3.3 Large and Small; Exercises; 4 Cantor Sets and Continued Fractions; 4.1 Introducing Continued Fractions; 4.2 Constructing a Cantor Set; 4.3 Diophantine Equations; 4.4 Miscellaneous; Exercises; 5 p-adic Numbers and Valuations; 5.1 Some Abstract Algebra; 5.2 p-adic Numbers
5.2.1 An Analysis Point of View5.2.2 An Algebra Point of View; 5.3 p-adic Integers and Cantor Sets; 5.4 p-adic Rational Numbers; Exercises; 6 Self-Similar Objects; 6.1 The Meaning of Self-Similar; 6.2 Metric Spaces; 6.3 Sequences in (S, d); 6.4 Affine Transformations; 6.5 An Application for an IFS; Exercises; 7 Various Notions of Dimension; 7.1 Limit Supremum and Limit Infimum; 7.2 Topological Dimension; 7.3 Similarity Dimension; 7.4 Box-Counting Dimension; 7.5 Hausdorff Measure and Dimension; 7.6 Miscellaneous Notions of Dimension; Exercises; 8 Porosity and Thickness-Looking at the Gaps 8.1 The Porosity of a Set8.2 Symmetric Sets and Symmetric Porosity; 8.3 A New and Different Definition of Cantor Set; 8.4 Thickness of a Cantor Set; 8.5 Applying Thickness; 8.6 A Bit More on Thickness; 8.7 Porosity in a Metric Space; Exercises; 9 Creating Pathological Functions via C; 9.1 Sequences of Functions; 9.2 The Cantor Function; 9.3 Space-Filling Curves; 9.4 Baire Class One Functions; 9.5 Darboux Functions; 9.6 Linearly Continuous Functions; Exercises; 10 Generalizations and Applications; 10.1 Generalizing Cantor Sets; 10.2 Fat Cantor Sets; 10.3 Sums of Cantor Sets 10.4 Differences of Cantor Sets10.5 Products of Cantor Sets; 10.6 Cantor Target; 10.7 Ana Sets; 10.8 Average Distance; 10.9 Non-Averaging Sets; 10.10 Cantor Series and Cantor Sets; 10.11 Liouville Numbers and Irrationality Exponents; 10.12 Sets of Sums of Convergent Alternating Series; 10.13 The Monty Hall Problem; 11 Epilogue; References; Index |
| Record Nr. | UNINA-9910808180303321 |
|
Vallin Robert W
|
||
| Hoboken, New Jersey : , : Wiley, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Intersections of thick Cantor sets / / Roger Kraft
| Intersections of thick Cantor sets / / Roger Kraft |
| Autore | Kraft Roger <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1992 |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina | 515/.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Cantor sets
Difference sets Bifurcation theory |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0894-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table Of Contents""; ""Introduction""; ""1. Theorems and Examples""; ""2. Cantor Sets and Thickness""; ""3. Proof of Theorem 1.2""; ""4. Third Kind of Overlapped Point""; ""5. Second Kind of Overlapped Point""; ""6. First Kind of Overlapped Point""; ""7. The Dynamics of Ï?[sub(rr')]""; ""8. Results About The Geometric Process""; ""9. Proof of Theorem 6.1(1)""; ""10. The Boundary Between â?[sub(1)]andâ?[sub(2)]""; ""11. Proof of Theorem 1.1""; ""Appendix 1""; ""Appendix 2""; ""References"" |
| Record Nr. | UNINA-9910480679603321 |
|
Kraft Roger <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Intersections of thick Cantor sets / / Roger Kraft
| Intersections of thick Cantor sets / / Roger Kraft |
| Autore | Kraft Roger <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1992 |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina | 515/.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Cantor sets
Difference sets Bifurcation theory |
| ISBN | 1-4704-0894-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table Of Contents""; ""Introduction""; ""1. Theorems and Examples""; ""2. Cantor Sets and Thickness""; ""3. Proof of Theorem 1.2""; ""4. Third Kind of Overlapped Point""; ""5. Second Kind of Overlapped Point""; ""6. First Kind of Overlapped Point""; ""7. The Dynamics of Ï?[sub(rr')]""; ""8. Results About The Geometric Process""; ""9. Proof of Theorem 6.1(1)""; ""10. The Boundary Between â?[sub(1)]andâ?[sub(2)]""; ""11. Proof of Theorem 1.1""; ""Appendix 1""; ""Appendix 2""; ""References"" |
| Record Nr. | UNINA-9910788878003321 |
|
Kraft Roger <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Intersections of thick Cantor sets / / Roger Kraft
| Intersections of thick Cantor sets / / Roger Kraft |
| Autore | Kraft Roger <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1992 |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina | 515/.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Cantor sets
Difference sets Bifurcation theory |
| ISBN | 1-4704-0894-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table Of Contents""; ""Introduction""; ""1. Theorems and Examples""; ""2. Cantor Sets and Thickness""; ""3. Proof of Theorem 1.2""; ""4. Third Kind of Overlapped Point""; ""5. Second Kind of Overlapped Point""; ""6. First Kind of Overlapped Point""; ""7. The Dynamics of Ï?[sub(rr')]""; ""8. Results About The Geometric Process""; ""9. Proof of Theorem 6.1(1)""; ""10. The Boundary Between â?[sub(1)]andâ?[sub(2)]""; ""11. Proof of Theorem 1.1""; ""Appendix 1""; ""Appendix 2""; ""References"" |
| Record Nr. | UNINA-9910812412103321 |
|
Kraft Roger <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nová infinitní matematika . I Velká iluze matematiky 20. století / / Petr Vopěnka
| Nová infinitní matematika . I Velká iluze matematiky 20. století / / Petr Vopěnka |
| Autore | Vopěnka Petr |
| Pubbl/distr/stampa | Praze, [Czech Republic] : , : Karolinum, , 2015 |
| Descrizione fisica | 1 online resource (126 pages) |
| Disciplina | 515.8 |
| Soggetto topico |
Cantor sets
Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN | 80-246-3221-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | cze |
| Record Nr. | UNINA-9910136727303321 |
|
Vopěnka Petr
|
||
| Praze, [Czech Republic] : , : Karolinum, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nová infinitní matematika . I Velká iluze matematiky 20. století / / Petr Vopěnka
| Nová infinitní matematika . I Velká iluze matematiky 20. století / / Petr Vopěnka |
| Autore | Vopěnka Petr |
| Pubbl/distr/stampa | Praze, [Czech Republic] : , : Karolinum, , 2015 |
| Descrizione fisica | 1 online resource (126 pages) |
| Disciplina | 515.8 |
| Soggetto topico |
Cantor sets
Mathematics |
| ISBN | 80-246-3221-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | cze |
| Record Nr. | UNINA-9910798703203321 |
|
Vopěnka Petr
|
||
| Praze, [Czech Republic] : , : Karolinum, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nová infinitní matematika . I Velká iluze matematiky 20. století / / Petr Vopěnka
| Nová infinitní matematika . I Velká iluze matematiky 20. století / / Petr Vopěnka |
| Autore | Vopěnka Petr |
| Pubbl/distr/stampa | Praze, [Czech Republic] : , : Karolinum, , 2015 |
| Descrizione fisica | 1 online resource (126 pages) |
| Disciplina | 515.8 |
| Soggetto topico |
Cantor sets
Mathematics |
| ISBN | 80-246-3221-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | cze |
| Record Nr. | UNINA-9910823282703321 |
|
Vopěnka Petr
|
||
| Praze, [Czech Republic] : , : Karolinum, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
