Graphs and Cubes / Ovchinnikov, Sergei (2011)  

Público ISBD Título : Graphs and Cubes Tipo de documento: documento electrónico Autores: Ovchinnikov, Sergei ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XIII, 287 p. 172 illus Il.: online resource ISBN/ISSN/DL: 978-1-4614-0797-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Graph  theory  Theory Clasificación: 51 Matemáticas Resumen: This introductory text in graph theory focuses on partial cubes, which are graphs that are isometrically embeddable into hypercubes of an arbitrary dimension, as well as bipartite graphs, and cubical graphs. This branch of graph theory has developed rapidly during the past three decades, producing exciting results and establishing links to other branches of mathematics.   Currently, Graphs and Cubes is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories.  Many exercises, along with historical notes, are included at the end of every chapter, and readers are encouraged to explore the exercises fully, and use them as a basis for research projects.   The prerequisites for this text include familiarity with basic mathematical concepts and methods on the level of undergraduate courses in discrete mathematics, linear algebra, group theory, and topology of Euclidean spaces. While the book is intended for lower-division graduate students in mathematics, it will be of interest to a much wider audience; because of their rich structural properties, partial cubes appear in theoretical computer science, coding theory, genetics, and even the political and social sciences Nota de contenido: Preface -- 1 Graphs -- 2 Bipartite Graphs -- 3 Cubes -- 4 Cubical Graphs -- 5 Partial Cubes -- 6 Lattice Embeddings -- 7 Hyperplane Arrangements -- 8 Token Systems -- Notation -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-0797-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33232 Graphs and Cubes [documento electrónico] / Ovchinnikov, Sergei ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XIII, 287 p. 172 illus : online resource. - (Universitext, ISSN 0172-5939) . ISBN : 978-1-4614-0797-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Graph  theory  Theory Clasificación: 51 Matemáticas Resumen: This introductory text in graph theory focuses on partial cubes, which are graphs that are isometrically embeddable into hypercubes of an arbitrary dimension, as well as bipartite graphs, and cubical graphs. This branch of graph theory has developed rapidly during the past three decades, producing exciting results and establishing links to other branches of mathematics.   Currently, Graphs and Cubes is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories.  Many exercises, along with historical notes, are included at the end of every chapter, and readers are encouraged to explore the exercises fully, and use them as a basis for research projects.   The prerequisites for this text include familiarity with basic mathematical concepts and methods on the level of undergraduate courses in discrete mathematics, linear algebra, group theory, and topology of Euclidean spaces. While the book is intended for lower-division graduate students in mathematics, it will be of interest to a much wider audience; because of their rich structural properties, partial cubes appear in theoretical computer science, coding theory, genetics, and even the political and social sciences Nota de contenido: Preface -- 1 Graphs -- 2 Bipartite Graphs -- 3 Cubes -- 4 Cubical Graphs -- 5 Partial Cubes -- 6 Lattice Embeddings -- 7 Hyperplane Arrangements -- 8 Token Systems -- Notation -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-0797-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33232

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Measure, Integral, Derivative / Ovchinnikov, Sergei (2013)  

Público ISBD Título : Measure, Integral, Derivative : A Course on Lebesgue's Theory Tipo de documento: documento electrónico Autores: Ovchinnikov, Sergei ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: X, 146 p. 16 illus Il.: online resource ISBN/ISSN/DL: 978-1-4614-7196-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Measure  theory  Functions  of  real  variables  and  Integration  Real Clasificación: 51 Matemáticas Resumen: This classroom-tested text is intended for a one-semester course in Lebesgue’s theory.  With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students.  The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text.  The presentation is elementary, where s-algebras are not used in the text on measure theory and Dini’s derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue’s theory are found in the book Nota de contenido: 1 Preliminaries -- 2 Lebesgue Measure -- 3  Lebesgue Integration -- 4 Differentiation and Integration -- A Measure and Integral over Unbounded Sets -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7196-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32341 Measure, Integral, Derivative : A Course on Lebesgue's Theory [documento electrónico] / Ovchinnikov, Sergei ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - X, 146 p. 16 illus : online resource. - (Universitext, ISSN 0172-5939) . ISBN : 978-1-4614-7196-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Measure  theory  Functions  of  real  variables  and  Integration  Real Clasificación: 51 Matemáticas Resumen: This classroom-tested text is intended for a one-semester course in Lebesgue’s theory.  With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students.  The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text.  The presentation is elementary, where s-algebras are not used in the text on measure theory and Dini’s derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue’s theory are found in the book Nota de contenido: 1 Preliminaries -- 2 Lebesgue Measure -- 3  Lebesgue Integration -- 4 Differentiation and Integration -- A Measure and Integral over Unbounded Sets -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7196-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32341

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Media Theory / Eppstein, David (2008)  

Público ISBD Título : Media Theory : Interdisciplinary Applied Mathematics Tipo de documento: documento electrónico Autores: Eppstein, David ; SpringerLink (Online service) ; Falmagne, Jean-Claude ; Ovchinnikov, Sergei Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Número de páginas: X, 328 p Il.: online resource ISBN/ISSN/DL: 978-3-540-71697-6 Idioma : Inglés (eng) Palabras clave: Mathematics  Computers  Artificial  intelligence  Applied  mathematics  Engineering  Combinatorics  Applications  of  Theory  Computation  Intelligence  (incl.  Robotics) Clasificación: 51 Matemáticas Resumen: The focus of this book is a mathematical structure modeling a physical or biological system that can be in any of a number of `states.' Each state is characterized by a set of binary features, and differs from some other neighbor state or states by just one of those feature. A simple example of a `state’ is a partial solution of a jigsaw puzzle, which can be transformed into another partial solution or into the final solution just by adding or removing a single adjoining piece. The evolution of such a system over time is considered. Such a structure is analyzed from algebraic and probabilistic (stochastic) standpoints Nota de contenido: Examples and Preliminaries -- Basic Concepts -- Media and Well-graded Families -- Closed Media and ?-Closed Families -- Well-Graded Families of Relations -- Mediatic Graphs -- Media and Partial Cubes -- Media and Integer Lattices -- Hyperplane arrangements and their media -- Algorithms -- Visualization of Media -- Random Walks on Media -- Applications En línea: http://dx.doi.org/10.1007/978-3-540-71697-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34326 Media Theory : Interdisciplinary Applied Mathematics [documento electrónico] / Eppstein, David ; SpringerLink (Online service) ; Falmagne, Jean-Claude ; Ovchinnikov, Sergei . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - X, 328 p : online resource. ISBN : 978-3-540-71697-6 Idioma : Inglés (eng) Palabras clave: Mathematics  Computers  Artificial  intelligence  Applied  mathematics  Engineering  Combinatorics  Applications  of  Theory  Computation  Intelligence  (incl.  Robotics) Clasificación: 51 Matemáticas Resumen: The focus of this book is a mathematical structure modeling a physical or biological system that can be in any of a number of `states.' Each state is characterized by a set of binary features, and differs from some other neighbor state or states by just one of those feature. A simple example of a `state’ is a partial solution of a jigsaw puzzle, which can be transformed into another partial solution or into the final solution just by adding or removing a single adjoining piece. The evolution of such a system over time is considered. Such a structure is analyzed from algebraic and probabilistic (stochastic) standpoints Nota de contenido: Examples and Preliminaries -- Basic Concepts -- Media and Well-graded Families -- Closed Media and ?-Closed Families -- Well-Graded Families of Relations -- Mediatic Graphs -- Media and Partial Cubes -- Media and Integer Lattices -- Hyperplane arrangements and their media -- Algorithms -- Visualization of Media -- Random Walks on Media -- Applications En línea: http://dx.doi.org/10.1007/978-3-540-71697-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34326

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