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Autor Károly Bezdek |
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Título : Classical Topics in Discrete Geometry Tipo de documento: documento electrónico Autores: Károly Bezdek ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, ISSN 1613-5237 Número de páginas: XIV, 166p Il.: online resource ISBN/ISSN/DL: 978-1-4419-0600-7 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Clasificación: 51 Matemáticas Resumen: About the author: Karoly Bezdek received his Dr.rer.nat.(1980) and Habilitation (1997) degrees in mathematics from the Eötvös Loránd University, in Budapest and his Candidate of Mathematical Sciences (1985) and Doctor of Mathematical Sciences (1994) degrees from the Hungarian Academy of Sciences. He is the author of more than 100 research papers and currently he is professor and Canada Research Chair of mathematics at the University of Calgary. About the book: This multipurpose book can serve as a textbook for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Finally, the forty-some selected research problems offer a great chance to use the book as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. The text is centered around four major and by now classical problems in discrete geometry. The first is the problem of densest sphere packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the approximately 50 years old illumination conjecture of V. Boltyanski and H. Hadwiger. The third topic is on covering by planks and cylinders with emphases on the affine invariant version of Tarski's plank problem, which was raised by T. Bang more than 50 years ago. The fourth topic is centered around the Kneser-Poulsen Conjecture, which also is approximately 50 years old. All four topics witnessed very recent breakthrough results, explaining their major role in this book Nota de contenido: Classical Topics Revisited -- Sphere Packings -- Finite Packings by Translates of Convex Bodies -- Coverings by Homothetic Bodies - Illumination and Related Topics -- Coverings by Planks and Cylinders -- On the Volume of Finite Arrangements of Spheres -- Ball-Polyhedra as Intersections of Congruent Balls -- Selected Proofs -- Selected Proofs on Sphere Packings -- Selected Proofs on Finite Packings of Translates of Convex Bodies -- Selected Proofs on Illumination and Related Topics -- Selected Proofs on Coverings by Planks and Cylinders -- Selected Proofs on the Kneser–Poulsen Conjecture -- Selected Proofs on Ball-Polyhedra En línea: http://dx.doi.org/10.1007/978-1-4419-0600-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33576 Classical Topics in Discrete Geometry [documento electrónico] / Károly Bezdek ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XIV, 166p : online resource. - (CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, ISSN 1613-5237) .
ISBN : 978-1-4419-0600-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Clasificación: 51 Matemáticas Resumen: About the author: Karoly Bezdek received his Dr.rer.nat.(1980) and Habilitation (1997) degrees in mathematics from the Eötvös Loránd University, in Budapest and his Candidate of Mathematical Sciences (1985) and Doctor of Mathematical Sciences (1994) degrees from the Hungarian Academy of Sciences. He is the author of more than 100 research papers and currently he is professor and Canada Research Chair of mathematics at the University of Calgary. About the book: This multipurpose book can serve as a textbook for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Finally, the forty-some selected research problems offer a great chance to use the book as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. The text is centered around four major and by now classical problems in discrete geometry. The first is the problem of densest sphere packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the approximately 50 years old illumination conjecture of V. Boltyanski and H. Hadwiger. The third topic is on covering by planks and cylinders with emphases on the affine invariant version of Tarski's plank problem, which was raised by T. Bang more than 50 years ago. The fourth topic is centered around the Kneser-Poulsen Conjecture, which also is approximately 50 years old. All four topics witnessed very recent breakthrough results, explaining their major role in this book Nota de contenido: Classical Topics Revisited -- Sphere Packings -- Finite Packings by Translates of Convex Bodies -- Coverings by Homothetic Bodies - Illumination and Related Topics -- Coverings by Planks and Cylinders -- On the Volume of Finite Arrangements of Spheres -- Ball-Polyhedra as Intersections of Congruent Balls -- Selected Proofs -- Selected Proofs on Sphere Packings -- Selected Proofs on Finite Packings of Translates of Convex Bodies -- Selected Proofs on Illumination and Related Topics -- Selected Proofs on Coverings by Planks and Cylinders -- Selected Proofs on the Kneser–Poulsen Conjecture -- Selected Proofs on Ball-Polyhedra En línea: http://dx.doi.org/10.1007/978-1-4419-0600-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33576 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Discrete Geometry and Optimization / SpringerLink (Online service) ; Károly Bezdek ; Antoine Deza ; Yinyu Ye (2013)
Título : Discrete Geometry and Optimization Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Károly Bezdek ; Antoine Deza ; Yinyu Ye Editorial: Heidelberg : Springer International Publishing Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Fields Institute Communications, ISSN 1069-5265 num. 69 Número de páginas: X, 336 p Il.: online resource ISBN/ISSN/DL: 978-3-319-00200-2 Idioma : Inglés (eng) Palabras clave: Mathematics Convex geometry Discrete Operations research Management science Mathematical optimization and Geometry Optimization Research, Science Clasificación: 51 Matemáticas Resumen: Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects. The purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to further stimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas. The inspiring Fejes Tóth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified this approach. While these fields have recently witnessed a lot of activity and successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial time algorithm for linear optimization is one of the most important unsolved problems at the beginning of the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections between different approaches, and features novel results and state-of-the-art surveys as well as open problems Nota de contenido: Preface -- Discrete Geometry in Minkowski Spaces (Alonso, Martini, and Spirova) -- Engineering Branch-and-Cut Algorithms for the Equicut Program (Anjos, Liers, Pardella, and Schmutzer) -- An Approach to the Dodecahedral Conjecture Based on Bounds for Spherical Codes (Anstreicher) -- On Minimal Tilings with Convex Cells Each Containing a Unit Ball (Bezdek) -- On Volumes of Permutation Polytopes (Burggraf, De Loera, and Omar) -- Monotone Paths in Planar Convex Subdivisions and Polytopes (Dumitrescu, Rote, and Toth).- Complexity of the Positive Semidefinite Matrix Completion Problem with a Rank Constraint (Eisenberg-Nagy, Laurent, and Varvitsiotis) -- The Strong Dodecahedral Conjecture and Fejes Toth's Conjecture on Sphere Packings with Kissing Number Twelve (Hales) -- Solving Nuclear Norm Regularized and Semidefinite Matrix Least Squares Problems with Linear Equality Constraints (Jiang, Sun, and Toh) -- Techniques for Submodular Maximization (Lee) -- A Further Generalization of the Colourful Caratheodory theorem (Meunier, Deza) -- Expected Crossing Numbers (Mohar, Stephen) -- EL-Labelings and Canonical Spanning Trees for Subword Complexes (Pilaud, Stump) -- Bandwidth, Vertex Separators, and Eigenvalue Optimization (Rendl, Lisser, and Piacentini) -- Exploiting Symmetries in Polyhedral Computations (Schurmann) -- Conditions for Correct Sensor Network Localization Using SDP Relaxation (Shamsi, Taheri, Zhu, and Ye) -- A Primal-Dual Smooth Perceptron-von Neumann Algorithm (Soheili, Pena) -- Open Problems (Bezdek, Deza, and Ye). En línea: http://dx.doi.org/10.1007/978-3-319-00200-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32455 Discrete Geometry and Optimization [documento electrónico] / SpringerLink (Online service) ; Károly Bezdek ; Antoine Deza ; Yinyu Ye . - Heidelberg : Springer International Publishing : Imprint: Springer, 2013 . - X, 336 p : online resource. - (Fields Institute Communications, ISSN 1069-5265; 69) .
ISBN : 978-3-319-00200-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Convex geometry Discrete Operations research Management science Mathematical optimization and Geometry Optimization Research, Science Clasificación: 51 Matemáticas Resumen: Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects. The purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to further stimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas. The inspiring Fejes Tóth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified this approach. While these fields have recently witnessed a lot of activity and successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial time algorithm for linear optimization is one of the most important unsolved problems at the beginning of the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections between different approaches, and features novel results and state-of-the-art surveys as well as open problems Nota de contenido: Preface -- Discrete Geometry in Minkowski Spaces (Alonso, Martini, and Spirova) -- Engineering Branch-and-Cut Algorithms for the Equicut Program (Anjos, Liers, Pardella, and Schmutzer) -- An Approach to the Dodecahedral Conjecture Based on Bounds for Spherical Codes (Anstreicher) -- On Minimal Tilings with Convex Cells Each Containing a Unit Ball (Bezdek) -- On Volumes of Permutation Polytopes (Burggraf, De Loera, and Omar) -- Monotone Paths in Planar Convex Subdivisions and Polytopes (Dumitrescu, Rote, and Toth).- Complexity of the Positive Semidefinite Matrix Completion Problem with a Rank Constraint (Eisenberg-Nagy, Laurent, and Varvitsiotis) -- The Strong Dodecahedral Conjecture and Fejes Toth's Conjecture on Sphere Packings with Kissing Number Twelve (Hales) -- Solving Nuclear Norm Regularized and Semidefinite Matrix Least Squares Problems with Linear Equality Constraints (Jiang, Sun, and Toh) -- Techniques for Submodular Maximization (Lee) -- A Further Generalization of the Colourful Caratheodory theorem (Meunier, Deza) -- Expected Crossing Numbers (Mohar, Stephen) -- EL-Labelings and Canonical Spanning Trees for Subword Complexes (Pilaud, Stump) -- Bandwidth, Vertex Separators, and Eigenvalue Optimization (Rendl, Lisser, and Piacentini) -- Exploiting Symmetries in Polyhedral Computations (Schurmann) -- Conditions for Correct Sensor Network Localization Using SDP Relaxation (Shamsi, Taheri, Zhu, and Ye) -- A Primal-Dual Smooth Perceptron-von Neumann Algorithm (Soheili, Pena) -- Open Problems (Bezdek, Deza, and Ye). En línea: http://dx.doi.org/10.1007/978-3-319-00200-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32455 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
Título : Lectures on Sphere Arrangements – the Discrete Geometric Side Tipo de documento: documento electrónico Autores: Károly Bezdek ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Fields Institute Monographs, ISSN 1069-5273 num. 32 Número de páginas: XII, 175 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-8118-8 Idioma : Inglés (eng) Palabras clave: Mathematics Convex geometry Discrete Polytopes and Geometry Clasificación: 51 Matemáticas Resumen: This monograph gives a short introduction to parts of modern discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains 30 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course. The core of this book is based on three lectures given by the author at the Fields Institute during the thematic program on Discrete Geometry and Applications and contains four basic topics. The first two deal with active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics as well as to some other important research areas such as that on coverings by planks (with close ties to geometric analysis). The fourth basic topic is discussed under covering balls by cylinders. Nota de contenido: 1. Unit Sphere Packings -- 2. Proofs on Unit Sphere Packings -- 3. Contractions of Sphere Arrangements -- 4. Proofs on Contractions of Sphere Arrangements -- 5. Ball-Polyhedra and Spindle Convex Bodies -- 6. Proofs on Ball-Polyhedra and Spindle Convex Bodies -- 7. Coverings by Cylinders -- 8. Proofs on Coverings by Cylinders -- 9. Research Problems - an Overview -- Glossary -- References En línea: http://dx.doi.org/10.1007/978-1-4614-8118-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32378 Lectures on Sphere Arrangements – the Discrete Geometric Side [documento electrónico] / Károly Bezdek ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XII, 175 p : online resource. - (Fields Institute Monographs, ISSN 1069-5273; 32) .
ISBN : 978-1-4614-8118-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Convex geometry Discrete Polytopes and Geometry Clasificación: 51 Matemáticas Resumen: This monograph gives a short introduction to parts of modern discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains 30 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course. The core of this book is based on three lectures given by the author at the Fields Institute during the thematic program on Discrete Geometry and Applications and contains four basic topics. The first two deal with active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics as well as to some other important research areas such as that on coverings by planks (with close ties to geometric analysis). The fourth basic topic is discussed under covering balls by cylinders. Nota de contenido: 1. Unit Sphere Packings -- 2. Proofs on Unit Sphere Packings -- 3. Contractions of Sphere Arrangements -- 4. Proofs on Contractions of Sphere Arrangements -- 5. Ball-Polyhedra and Spindle Convex Bodies -- 6. Proofs on Ball-Polyhedra and Spindle Convex Bodies -- 7. Coverings by Cylinders -- 8. Proofs on Coverings by Cylinders -- 9. Research Problems - an Overview -- Glossary -- References En línea: http://dx.doi.org/10.1007/978-1-4614-8118-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32378 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
