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] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
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
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Hoboken, New Jersey : , : Wiley, , [2013] | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
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From Measures to Itô Integrals / / Ekkehard Kopp [[electronic resource]] |
Autore | Kopp P. E. <1944-> |
Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2011 |
Descrizione fisica | 1 online resource (vii, 120 pages) : digital, PDF file(s) |
Disciplina | 515/.42 |
Collana | AIMS library series |
Soggetto topico | Measure theory |
ISBN |
1-107-22245-1
1-139-07659-0 9786613111180 1-139-07087-8 1-139-08114-4 1-139-08341-4 1-139-07887-9 1-283-11118-7 0-511-81311-2 |
Classificazione | MAT034000 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Probability and measure -- Measures and distribution functions -- Measurable functions/random variables -- Integration and expectation -- Lp-spaces and conditional expectation -- Discrete-time martingales -- Brownian motion -- Stochastic integrals. |
Record Nr. | UNINA-9910791903003321 |
Kopp P. E. <1944->
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Cambridge : , : Cambridge University Press, , 2011 | ||
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Lo trovi qui: Univ. Federico II | ||
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From Measures to Itô Integrals / / Ekkehard Kopp [[electronic resource]] |
Autore | Kopp P. E. <1944-> |
Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2011 |
Descrizione fisica | 1 online resource (vii, 120 pages) : digital, PDF file(s) |
Disciplina | 515/.42 |
Collana | AIMS library series |
Soggetto topico | Measure theory |
ISBN |
1-107-22245-1
1-139-07659-0 9786613111180 1-139-07087-8 1-139-08114-4 1-139-08341-4 1-139-07887-9 1-283-11118-7 0-511-81311-2 |
Classificazione | MAT034000 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Probability and measure -- Measures and distribution functions -- Measurable functions/random variables -- Integration and expectation -- Lp-spaces and conditional expectation -- Discrete-time martingales -- Brownian motion -- Stochastic integrals. |
Record Nr. | UNINA-9910826084403321 |
Kopp P. E. <1944->
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Cambridge : , : Cambridge University Press, , 2011 | ||
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Lo trovi qui: Univ. Federico II | ||
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Greedy approximation / / Vladimir Temlyakov [[electronic resource]] |
Autore | Temlyakov Vladimir <1953-> |
Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2011 |
Descrizione fisica | 1 online resource (xiv, 418 pages) : digital, PDF file(s) |
Disciplina | 518/.5 |
Collana | Cambridge monographs on applied and computational mathematics |
Soggetto topico |
Approximation theory
Compressed sensing (Telecommunication) |
ISBN |
1-107-22690-2
1-283-34243-X 1-139-16037-0 9786613342430 0-511-76229-1 1-139-16137-7 1-139-15580-6 1-139-15932-1 1-139-15755-8 |
Classificazione | MAT034000 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1. Greedy approximation with respect to bases -- 2. Greedy approximation with respect to dictionaries: Hilbert spaces -- 3. Entropy -- 4. Approximation in learning theory -- 5. Approximation in compressed sensing -- 6. Greedy approximation with respect to dictionaries: Banach spaces. |
Record Nr. | UNINA-9910781574003321 |
Temlyakov Vladimir <1953->
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Cambridge : , : Cambridge University Press, , 2011 | ||
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Lo trovi qui: Univ. Federico II | ||
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Greedy approximation / / Vladimir Temlyakov [[electronic resource]] |
Autore | Temlyakov Vladimir <1953-> |
Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2011 |
Descrizione fisica | 1 online resource (xiv, 418 pages) : digital, PDF file(s) |
Disciplina | 518/.5 |
Collana | Cambridge monographs on applied and computational mathematics |
Soggetto topico |
Approximation theory
Compressed sensing (Telecommunication) |
ISBN |
1-107-22690-2
1-283-34243-X 1-139-16037-0 9786613342430 0-511-76229-1 1-139-16137-7 1-139-15580-6 1-139-15932-1 1-139-15755-8 |
Classificazione | MAT034000 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1. Greedy approximation with respect to bases -- 2. Greedy approximation with respect to dictionaries: Hilbert spaces -- 3. Entropy -- 4. Approximation in learning theory -- 5. Approximation in compressed sensing -- 6. Greedy approximation with respect to dictionaries: Banach spaces. |
Record Nr. | UNINA-9910827212903321 |
Temlyakov Vladimir <1953->
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Cambridge : , : Cambridge University Press, , 2011 | ||
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Lo trovi qui: Univ. Federico II | ||
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Induced representations of locally compact groups / / Eberhard Kaniuth, University of Paderborn, Germany, Keith F. Taylor, Dalhousie University, Nova Scotia [[electronic resource]] |
Autore | Kaniuth Eberhard |
Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
Descrizione fisica | 1 online resource (xiii, 343 pages) : digital, PDF file(s) |
Disciplina | 512/.25 |
Collana | Cambridge tracts in mathematics |
Soggetto topico |
Locally compact groups
Topological spaces Representations of groups |
ISBN |
1-107-23320-8
1-139-04539-3 1-139-85355-4 1-139-84559-4 1-139-84446-6 1-139-83972-1 1-139-84210-2 1-283-74656-5 1-139-84091-6 |
Classificazione | MAT034000 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Basics -- Induced representations -- The imprimitivity theorem -- Mackey analysis -- Topologies on dual spaces -- Topological Frobenius properties -- Further applications. |
Record Nr. | UNINA-9910779344003321 |
Kaniuth Eberhard
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Cambridge : , : Cambridge University Press, , 2013 | ||
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Lo trovi qui: Univ. Federico II | ||
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Induced representations of locally compact groups / / Eberhard Kaniuth, University of Paderborn, Germany, Keith F. Taylor, Dalhousie University, Nova Scotia [[electronic resource]] |
Autore | Kaniuth Eberhard |
Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
Descrizione fisica | 1 online resource (xiii, 343 pages) : digital, PDF file(s) |
Disciplina | 512/.25 |
Collana | Cambridge tracts in mathematics |
Soggetto topico |
Locally compact groups
Topological spaces Representations of groups |
ISBN |
1-107-23320-8
1-139-04539-3 1-139-85355-4 1-139-84559-4 1-139-84446-6 1-139-83972-1 1-139-84210-2 1-283-74656-5 1-139-84091-6 |
Classificazione | MAT034000 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Basics -- Induced representations -- The imprimitivity theorem -- Mackey analysis -- Topologies on dual spaces -- Topological Frobenius properties -- Further applications. |
Record Nr. | UNINA-9910827666803321 |
Kaniuth Eberhard
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Cambridge : , : Cambridge University Press, , 2013 | ||
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Lo trovi qui: Univ. Federico II | ||
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An introduction to SAGE programming : with applications to SAGE interacts for numerical methods / / Razvan A. Mezei |
Autore | Mezei Razvan A. <1982-> |
Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2016 |
Descrizione fisica | 1 online resource (245 p.) |
Disciplina | 518/.6 |
Soggetto topico |
Mathematics - Data processing
Numerical analysis - Data processing Computer programming |
ISBN |
1-119-12280-5
1-119-12279-1 |
Classificazione | MAT034000 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Machine generated contents note: Preface vii 1. INTRODUCTION 1 1.1 What is Sage Math? 1 1.2 Various Flavors of Sage Math 1 1.2.1 Sage Math on your Machine 1 1.2.2 Sage Cell 2 1.2.3 Sage Cloud 2 2. USING SAGE MATH AS A CALCULATOR 5 2.1 First Sage Math Examples 5 2.2 Computations 6 2.2.1 Basic Arithmetic Operators 6 2.2.2 Decimals vs Exact Values 10 2.2.3 Constants 11 2.2.4 Breaking Long Lines of Code 12 2.2.5 Comments 13 2.2.6 Library Functions 14 2.2.7 Working with Strings 17 2.2.8 Solving equations and inequalities 19 2.2.9 Calculus Functions 21 2.2.10 Exercises 25 2.3 Graphs 28 2.3.1 2D Graphs 28 2.3.2 3D Graphs 53 2.3.3 Exercises 54 3. INTRODUCTION TO PROGRAMMING IN SAGE 57 3.1 Variables 58 3.1.1 Exercises 61 3.2 More on Operators 61 3.2.1 Exercises 63 3.3 Making Decisions 64 3.3.1 Boolean Expressions 64 3.3.2 If statements 66 3.3.3 Exercises 73 3.4 Loops 75 3.4.1 For loops 75 3.4.2 Strings 82 3.4.3 While loops 84 3.4.4 Nested loops 88 3.4.5 Lists 91 3.4.6 Exercises 96 3.5 Functions 99 3.5.1 Using library functions. Random, Scipy, Numpy 104 3.5.2 Exercises 105 3.6 Interacts 107 3.6.1 Exercises 123 3.7 Application to Data Security: Caesar's Cipher. Interacts, strings, and encryption 125 3.7.1 Exercises 127 3.8 Application to Business: Present Value of an Annuity. Amortization127 3.8.1 Exercises 133 3.9 Application to Elementary Statistics. Mean, Median, Histograms, and Bar Charts. 134 3.9.1 Exercises 142 4. SAGE INTERACTS FOR NUMERICAL METHODS 143 4.1 Equations of Lines 143 4.1.1 Exercises 145 4.2 Tangent Lines and Plots 145 4.2.1 Exercises 149 4.3 Taylor Polynomials 149 4.3.1 Exercises 155 4.4 Riemann Sum and De nite Integrals 156 4.4.1 Exercises 162 4.5 Trapezoidal Rule for Numerical Integration 162 4.5.1 Exercises 170 4.6 Bisection Algorithm for Solving Equations 170 4.6.1 Exercises 179 4.7 Newton-Raphson Algorithm for Solving Equations 179 4.7.1 Exercises 191 4.8 Polynomial Interpolation 192 4.8.1 Exercises 198 4.9 Linear Spline Interpolation 198 4.9.1 Exercises 202 4.10 Cubic Spline Interpolation 203 4.10.1 Exercises 212 4.11 SAGE for solving Differential Equations 212 4.12 Numerical Methods for Ordinary Differential Equations 215 4.12.1 Exercises 221 4.13 Numerical Methods for Partial Di¤erential Equations 222 4.13.1 Exercises 227 4.14 Scatter plots. Line of Best Fit and More 228 4.14.1 Exercises 236 4.15 Matrices, Eigenvalues, and Eigenvectors 236 4.15.1 Exercises 243 4.16 Solving Matrix Equations 243 4.16.1 Exercises 245 Bibliography 247 Index 249 . |
Record Nr. | UNINA-9910137424103321 |
Mezei Razvan A. <1982->
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Hoboken, New Jersey : , : Wiley, , 2016 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
An introduction to SAGE programming : with applications to SAGE interacts for numerical methods / / Razvan A. Mezei |
Autore | Mezei Razvan A. <1982-> |
Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2016 |
Descrizione fisica | 1 online resource (245 p.) |
Disciplina | 518/.6 |
Soggetto topico |
Mathematics - Data processing
Numerical analysis - Data processing Computer programming |
ISBN |
1-119-12280-5
1-119-12279-1 |
Classificazione | MAT034000 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Machine generated contents note: Preface vii 1. INTRODUCTION 1 1.1 What is Sage Math? 1 1.2 Various Flavors of Sage Math 1 1.2.1 Sage Math on your Machine 1 1.2.2 Sage Cell 2 1.2.3 Sage Cloud 2 2. USING SAGE MATH AS A CALCULATOR 5 2.1 First Sage Math Examples 5 2.2 Computations 6 2.2.1 Basic Arithmetic Operators 6 2.2.2 Decimals vs Exact Values 10 2.2.3 Constants 11 2.2.4 Breaking Long Lines of Code 12 2.2.5 Comments 13 2.2.6 Library Functions 14 2.2.7 Working with Strings 17 2.2.8 Solving equations and inequalities 19 2.2.9 Calculus Functions 21 2.2.10 Exercises 25 2.3 Graphs 28 2.3.1 2D Graphs 28 2.3.2 3D Graphs 53 2.3.3 Exercises 54 3. INTRODUCTION TO PROGRAMMING IN SAGE 57 3.1 Variables 58 3.1.1 Exercises 61 3.2 More on Operators 61 3.2.1 Exercises 63 3.3 Making Decisions 64 3.3.1 Boolean Expressions 64 3.3.2 If statements 66 3.3.3 Exercises 73 3.4 Loops 75 3.4.1 For loops 75 3.4.2 Strings 82 3.4.3 While loops 84 3.4.4 Nested loops 88 3.4.5 Lists 91 3.4.6 Exercises 96 3.5 Functions 99 3.5.1 Using library functions. Random, Scipy, Numpy 104 3.5.2 Exercises 105 3.6 Interacts 107 3.6.1 Exercises 123 3.7 Application to Data Security: Caesar's Cipher. Interacts, strings, and encryption 125 3.7.1 Exercises 127 3.8 Application to Business: Present Value of an Annuity. Amortization127 3.8.1 Exercises 133 3.9 Application to Elementary Statistics. Mean, Median, Histograms, and Bar Charts. 134 3.9.1 Exercises 142 4. SAGE INTERACTS FOR NUMERICAL METHODS 143 4.1 Equations of Lines 143 4.1.1 Exercises 145 4.2 Tangent Lines and Plots 145 4.2.1 Exercises 149 4.3 Taylor Polynomials 149 4.3.1 Exercises 155 4.4 Riemann Sum and De nite Integrals 156 4.4.1 Exercises 162 4.5 Trapezoidal Rule for Numerical Integration 162 4.5.1 Exercises 170 4.6 Bisection Algorithm for Solving Equations 170 4.6.1 Exercises 179 4.7 Newton-Raphson Algorithm for Solving Equations 179 4.7.1 Exercises 191 4.8 Polynomial Interpolation 192 4.8.1 Exercises 198 4.9 Linear Spline Interpolation 198 4.9.1 Exercises 202 4.10 Cubic Spline Interpolation 203 4.10.1 Exercises 212 4.11 SAGE for solving Differential Equations 212 4.12 Numerical Methods for Ordinary Differential Equations 215 4.12.1 Exercises 221 4.13 Numerical Methods for Partial Di¤erential Equations 222 4.13.1 Exercises 227 4.14 Scatter plots. Line of Best Fit and More 228 4.14.1 Exercises 236 4.15 Matrices, Eigenvalues, and Eigenvectors 236 4.15.1 Exercises 243 4.16 Solving Matrix Equations 243 4.16.1 Exercises 245 Bibliography 247 Index 249 . |
Record Nr. | UNINA-9910828587203321 |
Mezei Razvan A. <1982->
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Hoboken, New Jersey : , : Wiley, , 2016 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
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