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Titre : Advanced Engineering Mathematics : A Second Course with MatLab Type de document : document électronique Auteurs : Duffy Dean G. Editeur : Boca Raton : CRC Press Année de publication : 2022 Importance : 1 vol (447 p.) ISBN/ISSN/EAN : 978-1-00-055125-9 Langues : Français (fre) Catégories : Bibliothèque numérique:Mathématique Mots-clés : Engineering mathematics Résumé :
Through four previous editions of Advanced Engineering Mathematics with MATLAB, the author presented a wide variety of topics needed by today's engineers. The fifth edition of that book, available now, has been broken into two parts: topics currently needed in mathematics courses and a new stand-alone volume presenting topics not often included in these courses and consequently unknown to engineering students and many professionals.The overall structure of this new book consists of two parts: transform methods and random processes. Built upon a foundation of applied complex variables, the first part covers advanced transform methods, as well as z-transforms and Hilbert transforms--transforms of particular interest to systems, communication, and electrical engineers. This portion concludes with Green's function, a powerful method of analyzing systems. The second portion presents random processes--processes that more accurately model physical and biological engineering. Of particular interest is the inclusion of stochastic calculus. The author continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of his previous books. As before, theory is presented first, then examples, and then drill problems. Answers are given in the back of the book. This book is all about the future: The purpose of this book is not only to educate the present generation of engineers but also the next.'The main strength is the text is written from an engineering perspective. The majority of my students are engineers. The physical examples are related to problems of interest to the engineering students.'--Lea Jenkins, Clemson UniversityNote de contenu :
TABLE OF CONTENTS
List of Definitions
Chapter 1: Complex Variables
Chapter 2: Transform Methods
Chapter 3: The Z-transform
Chapter 4: The Hilbert Transform
Chapter 5: Green’s Functions
Chapter 6: Probability
Chapter 7: Random Processes
Chapter 8: Itô’s Stochastic Calculus
Answers to Odd Numbered ProblemsCôte titre : E-Fs/0054 En ligne : https://sciences-courses.univ-setif.dz/login/index.php Advanced Engineering Mathematics : A Second Course with MatLab [document électronique] / Duffy Dean G. . - Boca Raton : CRC Press, 2022 . - 1 vol (447 p.).
ISBN : 978-1-00-055125-9
Langues : Français (fre)
Catégories : Bibliothèque numérique:Mathématique Mots-clés : Engineering mathematics Résumé :
Through four previous editions of Advanced Engineering Mathematics with MATLAB, the author presented a wide variety of topics needed by today's engineers. The fifth edition of that book, available now, has been broken into two parts: topics currently needed in mathematics courses and a new stand-alone volume presenting topics not often included in these courses and consequently unknown to engineering students and many professionals.The overall structure of this new book consists of two parts: transform methods and random processes. Built upon a foundation of applied complex variables, the first part covers advanced transform methods, as well as z-transforms and Hilbert transforms--transforms of particular interest to systems, communication, and electrical engineers. This portion concludes with Green's function, a powerful method of analyzing systems. The second portion presents random processes--processes that more accurately model physical and biological engineering. Of particular interest is the inclusion of stochastic calculus. The author continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of his previous books. As before, theory is presented first, then examples, and then drill problems. Answers are given in the back of the book. This book is all about the future: The purpose of this book is not only to educate the present generation of engineers but also the next.'The main strength is the text is written from an engineering perspective. The majority of my students are engineers. The physical examples are related to problems of interest to the engineering students.'--Lea Jenkins, Clemson UniversityNote de contenu :
TABLE OF CONTENTS
List of Definitions
Chapter 1: Complex Variables
Chapter 2: Transform Methods
Chapter 3: The Z-transform
Chapter 4: The Hilbert Transform
Chapter 5: Green’s Functions
Chapter 6: Probability
Chapter 7: Random Processes
Chapter 8: Itô’s Stochastic Calculus
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Titre : Algorithm and Design Complexity Type de document : document électronique Auteurs : Sherine Anli ; Jasmine Mary ; Peter Geno Editeur : Boca Raton : CRC Press Année de publication : 2023 Importance : 1 vol (181 p.) ISBN/ISSN/EAN : 978-1-00-086551-6 Langues : Français (fre) Catégories : Bibliothèque numérique:Informatique Mots-clés : Computer algorithms
Computational complexityIndex. décimale : 004 Informatique Résumé :
Computational complexity is critical in analysis of algorithms and is important to be able to select algorithms for efficiency and solvability. Algorithm and Design Complexity initiates with discussion of algorithm analysis, time-space trade-off, symptotic notations, and so forth. It further includes algorithms that are definite and effective, known as computational procedures. Further topics explored include divide-and-conquer, dynamic programming, and backtracking.Features: Includes complete coverage of basics and design of algorithms Discusses algorithm analysis techniques like divide-and-conquer, dynamic programming, and greedy heuristics Provides time and space complexity tutorials Reviews combinatorial optimization of Knapsack problem Simplifies recurrence relation for time complexity This book is aimed at graduate students and researchers in computers science, information technology, and electrical engineering.Note de contenu :
TABLE OF CONTENTS
chapter 1 Algorithm Analysis
chapter 2 Divide and Conquer
chapter 3 Dynamic Programming
chapter 4 Backtracking
chapter 5 GraphCôte titre : E-Fs/0038 En ligne : https://sciences-courses.univ-setif.dz/login/index.php Algorithm and Design Complexity [document électronique] / Sherine Anli ; Jasmine Mary ; Peter Geno . - Boca Raton : CRC Press, 2023 . - 1 vol (181 p.).
ISBN : 978-1-00-086551-6
Langues : Français (fre)
Catégories : Bibliothèque numérique:Informatique Mots-clés : Computer algorithms
Computational complexityIndex. décimale : 004 Informatique Résumé :
Computational complexity is critical in analysis of algorithms and is important to be able to select algorithms for efficiency and solvability. Algorithm and Design Complexity initiates with discussion of algorithm analysis, time-space trade-off, symptotic notations, and so forth. It further includes algorithms that are definite and effective, known as computational procedures. Further topics explored include divide-and-conquer, dynamic programming, and backtracking.Features: Includes complete coverage of basics and design of algorithms Discusses algorithm analysis techniques like divide-and-conquer, dynamic programming, and greedy heuristics Provides time and space complexity tutorials Reviews combinatorial optimization of Knapsack problem Simplifies recurrence relation for time complexity This book is aimed at graduate students and researchers in computers science, information technology, and electrical engineering.Note de contenu :
TABLE OF CONTENTS
chapter 1 Algorithm Analysis
chapter 2 Divide and Conquer
chapter 3 Dynamic Programming
chapter 4 Backtracking
chapter 5 GraphCôte titre : E-Fs/0038 En ligne : https://sciences-courses.univ-setif.dz/login/index.php Exemplaires (1)
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Titre : Algorithm Design: A Methodological Approach - 150 Problems and Detailed Solutions Type de document : document électronique Auteurs : Bosc Patrick ; Guyom Marc ; Miclet Laurent Editeur : Boca Raton : CRC Press Année de publication : 2022 Importance : 1 vol (807 p.) ISBN/ISSN/EAN : 978-1-00-083479-6 Langues : Français (fre) Catégories : Bibliothèque numérique:Informatique Mots-clés : Algorithm Programming
Algorithms:Problems, exercises, etcIndex. décimale : 004 Informatique Résumé :
A bestseller in its French edition, this book is original in its construction and its success in the French market demonstrates its appeal. It is based on three principles: (1) An organization of the chapters by families of algorithms: exhaustive search, divide and conquer, etc. On the contrary, there is no chapter devoted only to a systematic exposure of, say, algorithms on strings. Some of these will be found in different chapters. (2) For each family of algorithms, an introduction is given to the mathematical principles and the issues of a rigorous design, with one or two pedagogical examples. (3) For the most part, the book details 150 problems, spanning seven families of algorithms. For each problem, a precise and progressive statement is given. More importantly, a complete solution is detailed, with respect to the design principles that have been presented; often, some classical errors are pointed out. Roughly speaking, two-thirds of the book is devoted to the detailed rational construction of the solutionsNote de contenu :
Table of Contents
Preface
- Mathematics and Computer Science: Some Useful Notions
- Complexity of an Algorithm
- Specifications, Invariants, Iteration
- Reduce and Conquer, Recursion
- Generate and Test
- Branch and Bound
- Greedy Algorithms
- Divide and Conquer
- Dynamic Programming
- Notations
-List of Problems
-Bibliography
-Index
Côte titre : E-Fs/0039 En ligne : https://sciences-courses.univ-setif.dz/login/index.php Algorithm Design: A Methodological Approach - 150 Problems and Detailed Solutions [document électronique] / Bosc Patrick ; Guyom Marc ; Miclet Laurent . - Boca Raton : CRC Press, 2022 . - 1 vol (807 p.).
ISBN : 978-1-00-083479-6
Langues : Français (fre)
Catégories : Bibliothèque numérique:Informatique Mots-clés : Algorithm Programming
Algorithms:Problems, exercises, etcIndex. décimale : 004 Informatique Résumé :
A bestseller in its French edition, this book is original in its construction and its success in the French market demonstrates its appeal. It is based on three principles: (1) An organization of the chapters by families of algorithms: exhaustive search, divide and conquer, etc. On the contrary, there is no chapter devoted only to a systematic exposure of, say, algorithms on strings. Some of these will be found in different chapters. (2) For each family of algorithms, an introduction is given to the mathematical principles and the issues of a rigorous design, with one or two pedagogical examples. (3) For the most part, the book details 150 problems, spanning seven families of algorithms. For each problem, a precise and progressive statement is given. More importantly, a complete solution is detailed, with respect to the design principles that have been presented; often, some classical errors are pointed out. Roughly speaking, two-thirds of the book is devoted to the detailed rational construction of the solutionsNote de contenu :
Table of Contents
Preface
- Mathematics and Computer Science: Some Useful Notions
- Complexity of an Algorithm
- Specifications, Invariants, Iteration
- Reduce and Conquer, Recursion
- Generate and Test
- Branch and Bound
- Greedy Algorithms
- Divide and Conquer
- Dynamic Programming
- Notations
-List of Problems
-Bibliography
-Index
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Titre : An Introduction to Metric Spaces Type de document : document électronique Auteurs : Gopal Dhananjay ; Deshmukh Aniruddha ; S. Ranadive Abhay Editeur : Boca Raton : CRC Press Année de publication : 2022 Importance : 1 vol (286 p.) ISBN/ISSN/EAN : 978-1-00-008799-4 Langues : Français (fre) Catégories : Bibliothèque numérique:Mathématique Mots-clés : Metric spaces Index. décimale : 514.3 Topologie des espaces (topologie métrique) Résumé :
This book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while actively participating in the learning of this subject. In this book, the authors illustrated the strategy of the proofs of various theorems that motivate readers to complete them on their own. Bits of pertinent history are infused in the text, including brief biographies of some of the central players in the development of metric spaces. The textbook is divided into seven chapters that contain the main materials on metric spaces; namely, introductory concepts, completeness, compactness, connectedness, continuous functions and metric fixed point theorems with applications.Some of the noteworthy features of this book include· Diagrammatic illustrations that encourage readers to think geometrically· Focus on systematic strategy to generate ideas for the proofs of theorems· A wealth of remarks, observations along with a variety of exercises· Historical notes and brief biographies appearing throughout the textNote de contenu :
Conten
Preface ix
A Note to the Reader xiii
Authors xv
1 Set Theory 1
1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4 Countability of Sets . . . . . . . . . . . . . . . . . . . . . . . 39
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2 Metric Spaces 55
2.1 Review of Real Number System and Absolute Value . . . . . 55
2.2 Young, H¨older, andMinkowski Inequalities . . . . . . . . . . 57
2.3 Notion ofMetric Space . . . . . . . . . . . . . . . . . . . . . 64
2.4 Open Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.5 Closed Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2.6 Interior, Exterior, and Boundary Points . . . . . . . . . . . . 101
2.7 Limit and Cluster Points . . . . . . . . . . . . . . . . . . . . 104
2.8 Bounded Sets . . . . . . . . . . . . . . . . . . . . . . . . . . 110
2.9 Distance Between Sets . . . . . . . . . . . . . . . . . . . . . 112
2.10 EquivalentMetrics . . . . . . . . . . . . . . . . . . . . . . . . 115
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3 Complete Metric Spaces 129
3.1 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.2 Convergence of Sequence . . . . . . . . . . . . . . . . . . . . 131
3.3 CompleteMetric Spaces . . . . . . . . . . . . . . . . . . . . . 139
3.4 Completion ofMetric Spaces . . . . . . . . . . . . . . . . . . 143
3.5 Baire Category Theorem . . . . . . . . . . . . . . . . . . . . 149
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4 Compact Metric Spaces 161
4.1 Open Cover and Compact Sets . . . . . . . . . . . . . . . . . 161
4.2 General Properties of Compact Sets . . . . . . . . . . . . . . 165
4.3 Sufficient Conditions for Compactness . . . . . . . . . . . . . 169
4.4 Sequential Compactness . . . . . . . . . . . . . . . . . . . . . 172
4.5 Compactness: Characterizations . . . . . . . . . . . . . . . . 174
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5 Connected Spaces 183
5.1 Connectedness . . . . . . . . . . . . . . . . . . . . . . . . . . 183
5.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.3 Totally Disconnected Spaces . . . . . . . . . . . . . . . . . . 192
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6 Continuity 195
6.1 Continuity of Real Valued Functions . . . . . . . . . . . . . . 195
6.2 Continuous Functions in ArbitraryMetric Spaces . . . . . . 197
6.3 Uniform Continuity . . . . . . . . . . . . . . . . . . . . . . . 217
6.4 Continuous Functions on Compact Spaces . . . . . . . . . . . 224
6.5 Continuous Functions on Connected Spaces . . . . . . . . . . 229
6.6 Equicontinuity and Arzela-Ascoli’s Theorem . . . . . . . . . 242
6.7 Open and ClosedMaps . . . . . . . . . . . . . . . . . . . . . 245
6.8 Homeomorphism . . . . . . . . . . . . . . . . . . . . . . . . . 246
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 252
7 Banach Fixed Point Theorem and Its Applications 255
7.1 Banach Contraction Theorem . . . . . . . . . . . . . . . . . 255
7.2 Applications of Banach Contraction Principle . . . . . . . . . 260
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Appendix A 277
Bibliography 281
Index 283
Côte titre : E-Fs/0056 En ligne : https://sciences-courses.univ-setif.dz/login/index.php An Introduction to Metric Spaces [document électronique] / Gopal Dhananjay ; Deshmukh Aniruddha ; S. Ranadive Abhay . - Boca Raton : CRC Press, 2022 . - 1 vol (286 p.).
ISBN : 978-1-00-008799-4
Langues : Français (fre)
Catégories : Bibliothèque numérique:Mathématique Mots-clés : Metric spaces Index. décimale : 514.3 Topologie des espaces (topologie métrique) Résumé :
This book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while actively participating in the learning of this subject. In this book, the authors illustrated the strategy of the proofs of various theorems that motivate readers to complete them on their own. Bits of pertinent history are infused in the text, including brief biographies of some of the central players in the development of metric spaces. The textbook is divided into seven chapters that contain the main materials on metric spaces; namely, introductory concepts, completeness, compactness, connectedness, continuous functions and metric fixed point theorems with applications.Some of the noteworthy features of this book include· Diagrammatic illustrations that encourage readers to think geometrically· Focus on systematic strategy to generate ideas for the proofs of theorems· A wealth of remarks, observations along with a variety of exercises· Historical notes and brief biographies appearing throughout the textNote de contenu :
Conten
Preface ix
A Note to the Reader xiii
Authors xv
1 Set Theory 1
1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4 Countability of Sets . . . . . . . . . . . . . . . . . . . . . . . 39
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2 Metric Spaces 55
2.1 Review of Real Number System and Absolute Value . . . . . 55
2.2 Young, H¨older, andMinkowski Inequalities . . . . . . . . . . 57
2.3 Notion ofMetric Space . . . . . . . . . . . . . . . . . . . . . 64
2.4 Open Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.5 Closed Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2.6 Interior, Exterior, and Boundary Points . . . . . . . . . . . . 101
2.7 Limit and Cluster Points . . . . . . . . . . . . . . . . . . . . 104
2.8 Bounded Sets . . . . . . . . . . . . . . . . . . . . . . . . . . 110
2.9 Distance Between Sets . . . . . . . . . . . . . . . . . . . . . 112
2.10 EquivalentMetrics . . . . . . . . . . . . . . . . . . . . . . . . 115
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3 Complete Metric Spaces 129
3.1 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.2 Convergence of Sequence . . . . . . . . . . . . . . . . . . . . 131
3.3 CompleteMetric Spaces . . . . . . . . . . . . . . . . . . . . . 139
3.4 Completion ofMetric Spaces . . . . . . . . . . . . . . . . . . 143
3.5 Baire Category Theorem . . . . . . . . . . . . . . . . . . . . 149
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4 Compact Metric Spaces 161
4.1 Open Cover and Compact Sets . . . . . . . . . . . . . . . . . 161
4.2 General Properties of Compact Sets . . . . . . . . . . . . . . 165
4.3 Sufficient Conditions for Compactness . . . . . . . . . . . . . 169
4.4 Sequential Compactness . . . . . . . . . . . . . . . . . . . . . 172
4.5 Compactness: Characterizations . . . . . . . . . . . . . . . . 174
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5 Connected Spaces 183
5.1 Connectedness . . . . . . . . . . . . . . . . . . . . . . . . . . 183
5.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.3 Totally Disconnected Spaces . . . . . . . . . . . . . . . . . . 192
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6 Continuity 195
6.1 Continuity of Real Valued Functions . . . . . . . . . . . . . . 195
6.2 Continuous Functions in ArbitraryMetric Spaces . . . . . . 197
6.3 Uniform Continuity . . . . . . . . . . . . . . . . . . . . . . . 217
6.4 Continuous Functions on Compact Spaces . . . . . . . . . . . 224
6.5 Continuous Functions on Connected Spaces . . . . . . . . . . 229
6.6 Equicontinuity and Arzela-Ascoli’s Theorem . . . . . . . . . 242
6.7 Open and ClosedMaps . . . . . . . . . . . . . . . . . . . . . 245
6.8 Homeomorphism . . . . . . . . . . . . . . . . . . . . . . . . . 246
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 252
7 Banach Fixed Point Theorem and Its Applications 255
7.1 Banach Contraction Theorem . . . . . . . . . . . . . . . . . 255
7.2 Applications of Banach Contraction Principle . . . . . . . . . 260
Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
Biographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Appendix A 277
Bibliography 281
Index 283
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Titre : Analysis-II Type de document : document électronique Auteurs : Goel Dr M.K. Editeur : Boca Raton : CRC Press Année de publication : 2023 Importance : 1 vol (215 p.) ISBN/ISSN/EAN : 978-93-94406-60-5 Langues : Français (fre) Catégories : Bibliothèque numérique:Mathématique Mots-clés : Calculus Integral Index. décimale : 515-Analyse mathèmatique Note de contenu :
Conten
1. RIEMANN INTEGRATION
2. IMPROPER INTEGRALS
3. INTEGRAL AS A FUNCTION OF A PARAMETER
4. METRIC SPACES
5. BASES, SUB-BASES AND SUBSPACES
6. CONVERGENCE OF SEQUENCES OF METRIC SPACES
7. COMPLETENESS
8. ISOMETRY AND CONTRACTION
9. CONTINUITY AND HOMEOMORPHISM
10. COMPACTNESS AND CONNECTEDNESS
Côte titre : E-Fs/0057 En ligne : https://sciences-courses.univ-setif.dz/login/index.php Analysis-II [document électronique] / Goel Dr M.K. . - Boca Raton : CRC Press, 2023 . - 1 vol (215 p.).
ISBN : 978-93-94406-60-5
Langues : Français (fre)
Catégories : Bibliothèque numérique:Mathématique Mots-clés : Calculus Integral Index. décimale : 515-Analyse mathèmatique Note de contenu :
Conten
1. RIEMANN INTEGRATION
2. IMPROPER INTEGRALS
3. INTEGRAL AS A FUNCTION OF A PARAMETER
4. METRIC SPACES
5. BASES, SUB-BASES AND SUBSPACES
6. CONVERGENCE OF SEQUENCES OF METRIC SPACES
7. COMPLETENESS
8. ISOMETRY AND CONTRACTION
9. CONTINUITY AND HOMEOMORPHISM
10. COMPACTNESS AND CONNECTEDNESS
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