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Título : Solving the Pell Equation Tipo de documento: documento electrónico Autores: Jacobson, Michael J ; SpringerLink (Online service) ; Williams, Hugh C Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Colección: CMS Books in Mathematics, ISSN 1613-5237 Número de páginas: XX, 495 p Il.: online resource ISBN/ISSN/DL: 978-0-387-84923-2 Idioma : Inglés ( eng)Palabras clave: Mathematics Number theory Ecotoxicology Theory Clasificación: 51 Matemáticas Resumen: Pell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks and recreational books concerning elementary number theory, but usually not in much depth. This book provides a modern and deeper approach to the problem of solving the Pell equation. The main component of this will be computational techniques, but in the process of deriving these it will be necessary to develop the corresponding theory. One objective of this book is to provide a less intimidating introduction for senior undergraduates and others with the same level of preparedness to the delights of algebraic number theory through the medium of a mathematical object that has fascinated people since the time of Archimedes. To achieve this, this work is made accessible to anyone with some knowledge of elementary number theory and abstract algebra. Many references and notes are provided for those who wish to follow up on various topics, and the authors also describe some rather surprising applications to cryptography. The intended audience is number theorists, both professional and amateur, and students, but we wish to emphasize that this is not intended to be a textbook; its focus is much too narrow for that. It could, however be used as supplementary reading for students enrolled in a second course in number theory Nota de contenido: Early History of the Pell Equation -- Continued Fractions -- Quadratic Number Fields -- Ideals and Continued Fractions -- Some Special Pell Equations -- The Ideal Class Group -- The Analytic Class Number Formula -- Some Additional Analytic Results -- Some Computational Techniques -- (f, p) Representations of -ideals -- Compact Representations -- The Subexponential Method -- Applications to Cryptography -- Unconditional Verification of the Regulator and the Class Number -- Principal Ideal Testing in -- Conclusion En línea: http://dx.doi.org/10.1007/978-0-387-84923-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33891 Solving the Pell Equation [documento electrónico] / Jacobson, Michael J ; SpringerLink (Online service) ; Williams, Hugh C . - New York, NY : Springer New York, 2009 . - XX, 495 p : online resource. - (CMS Books in Mathematics, ISSN 1613-5237) .ISBN: 978-0-387-84923-2

Idioma : Inglés (eng)

Palabras clave: Mathematics Number theory Ecotoxicology Theory Clasificación: 51 Matemáticas Resumen: Pell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks and recreational books concerning elementary number theory, but usually not in much depth. This book provides a modern and deeper approach to the problem of solving the Pell equation. The main component of this will be computational techniques, but in the process of deriving these it will be necessary to develop the corresponding theory. One objective of this book is to provide a less intimidating introduction for senior undergraduates and others with the same level of preparedness to the delights of algebraic number theory through the medium of a mathematical object that has fascinated people since the time of Archimedes. To achieve this, this work is made accessible to anyone with some knowledge of elementary number theory and abstract algebra. Many references and notes are provided for those who wish to follow up on various topics, and the authors also describe some rather surprising applications to cryptography. The intended audience is number theorists, both professional and amateur, and students, but we wish to emphasize that this is not intended to be a textbook; its focus is much too narrow for that. It could, however be used as supplementary reading for students enrolled in a second course in number theory Nota de contenido: Early History of the Pell Equation -- Continued Fractions -- Quadratic Number Fields -- Ideals and Continued Fractions -- Some Special Pell Equations -- The Ideal Class Group -- The Analytic Class Number Formula -- Some Additional Analytic Results -- Some Computational Techniques -- (f, p) Representations of -ideals -- Compact Representations -- The Subexponential Method -- Applications to Cryptography -- Unconditional Verification of the Regulator and the Class Number -- Principal Ideal Testing in -- Conclusion En línea: http://dx.doi.org/10.1007/978-0-387-84923-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33891 ## Ejemplares

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Título : Statistical Analysis of Environmental Space-Time Processes Tipo de documento: documento electrónico Autores: Le, Nhu D ; SpringerLink (Online service) ; Zidek, James V Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Springer Series in Statistics, ISSN 0172-7397 Número de páginas: XVI, 342 p Il.: online resource ISBN/ISSN/DL: 978-0-387-35429-3 Idioma : Inglés ( eng)Palabras clave: Environment Earth sciences Epidemiology Statistics Ecotoxicology Environmental Monitoring/Analysis Sciences, general Statistical Theory and Methods Clasificación: 51 Matemáticas Resumen: This book provides a broad introduction to the fascinating subject of environmental space-time processes; addressing the role of uncertainty. Within that context, it covers a spectrum of technical matters from measurement to environmental epidemiology to risk assessment. It showcases non-stationary vector-valued processes, while treating stationarity as a special case. The contents reflect the authors’ cumulative knowledge gained over many years of consulting and research collaboration. In particular, with members of their research group, they developed within a hierarchical Bayesian framework, the new statistical approaches presented in the book for analyzing, modeling, and monitoring environmental spatio-temporal processes. Furthermore they indicate new directions for development. This book contains technical and non-technical material and it is written for statistical scientists as well as consultants, subject area researchers and students in related fields. Novel chapters present the authors’ hierarchical Bayesian approaches to spatially interpolating environmental processes designing networks to monitor environmental processes multivariate extreme value theory incorporating risk assessment. In addition, they present a comprehensive and critical survey of other approaches, highlighting deficiencies that their method seeks to overcome. Special sections marked by an asterisk provide rigorous development for readers with a strong technical background. Alternatively readers can go straight to the tutorials supplied in chapter 14 and learn how to apply the free, downloadable modeling and design software that the authors and their research partners have developed. Nhu Le is a Senior Scientist in Cancer Control Research and a former Director of the Occupational Oncology Research Program at the British Columbia Cancer Agency (BCCA). An Adjunct Professor of Statistics at the University of British Columbia since 1992, he also teaches graduate courses and supervises graduate students. He is heavily involved in epidemiological research and the impact environmental and occupational factors have on cancer development. He has published over 100 peer-reviewed research articles in statistical- and subject-area journals. He received his Ph.D. in statistics from the University of Washington in Seattle. Jim Zidek is a Professor Emeritus and Founding Head of the Department of Statistics at the University of British Columbia. He has served on a number of scientific advisory committees, most notably on the United States’ EPA’s Clean Air Scientific Advisory Committees Ozone Panel. His scientific interests lie equally in environmetrics (the subject of this book) and in the theory of decision analysis (particularly, the compilation of expert opinion). His work has been published extensively and he has been invited to give numerous presentations. He received his Ph.D. from Stanford University and his honors include Fellowships in the Royal Society of Canada, the American Statistical Association (ASA), and the Institute of Mathematical Statistics. He has earned the Distinguished Achievement Medal in Environmental Statistics of the ASA and the Gold Medal of the Statistical Society of Canada Nota de contenido: Environmental Processes -- First Encounters -- Case Study -- Uncertainty -- Measurement -- Modeling -- Space-Time Modeling -- Covariances -- Spatial Prediction: Classical Approaches -- Bayesian Kriging -- Hierarchical Bayesian Kriging -- Design and Risk Assessment -- Multivariate Modeling*** -- Environmental Network Design -- Extremes -- Implementation -- Risk Assessment -- A Tutorial in R -- Appendices -- References En línea: http://dx.doi.org/10.1007/0-387-35429-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34817 Statistical Analysis of Environmental Space-Time Processes [documento electrónico] / Le, Nhu D ; SpringerLink (Online service) ; Zidek, James V . - New York, NY : Springer New York, 2006 . - XVI, 342 p : online resource. - (Springer Series in Statistics, ISSN 0172-7397) .ISBN: 978-0-387-35429-3

Idioma : Inglés (eng)

Palabras clave: Environment Earth sciences Epidemiology Statistics Ecotoxicology Environmental Monitoring/Analysis Sciences, general Statistical Theory and Methods Clasificación: 51 Matemáticas Resumen: This book provides a broad introduction to the fascinating subject of environmental space-time processes; addressing the role of uncertainty. Within that context, it covers a spectrum of technical matters from measurement to environmental epidemiology to risk assessment. It showcases non-stationary vector-valued processes, while treating stationarity as a special case. The contents reflect the authors’ cumulative knowledge gained over many years of consulting and research collaboration. In particular, with members of their research group, they developed within a hierarchical Bayesian framework, the new statistical approaches presented in the book for analyzing, modeling, and monitoring environmental spatio-temporal processes. Furthermore they indicate new directions for development. This book contains technical and non-technical material and it is written for statistical scientists as well as consultants, subject area researchers and students in related fields. Novel chapters present the authors’ hierarchical Bayesian approaches to spatially interpolating environmental processes designing networks to monitor environmental processes multivariate extreme value theory incorporating risk assessment. In addition, they present a comprehensive and critical survey of other approaches, highlighting deficiencies that their method seeks to overcome. Special sections marked by an asterisk provide rigorous development for readers with a strong technical background. Alternatively readers can go straight to the tutorials supplied in chapter 14 and learn how to apply the free, downloadable modeling and design software that the authors and their research partners have developed. Nhu Le is a Senior Scientist in Cancer Control Research and a former Director of the Occupational Oncology Research Program at the British Columbia Cancer Agency (BCCA). An Adjunct Professor of Statistics at the University of British Columbia since 1992, he also teaches graduate courses and supervises graduate students. He is heavily involved in epidemiological research and the impact environmental and occupational factors have on cancer development. He has published over 100 peer-reviewed research articles in statistical- and subject-area journals. He received his Ph.D. in statistics from the University of Washington in Seattle. Jim Zidek is a Professor Emeritus and Founding Head of the Department of Statistics at the University of British Columbia. He has served on a number of scientific advisory committees, most notably on the United States’ EPA’s Clean Air Scientific Advisory Committees Ozone Panel. His scientific interests lie equally in environmetrics (the subject of this book) and in the theory of decision analysis (particularly, the compilation of expert opinion). His work has been published extensively and he has been invited to give numerous presentations. He received his Ph.D. from Stanford University and his honors include Fellowships in the Royal Society of Canada, the American Statistical Association (ASA), and the Institute of Mathematical Statistics. He has earned the Distinguished Achievement Medal in Environmental Statistics of the ASA and the Gold Medal of the Statistical Society of Canada Nota de contenido: Environmental Processes -- First Encounters -- Case Study -- Uncertainty -- Measurement -- Modeling -- Space-Time Modeling -- Covariances -- Spatial Prediction: Classical Approaches -- Bayesian Kriging -- Hierarchical Bayesian Kriging -- Design and Risk Assessment -- Multivariate Modeling*** -- Environmental Network Design -- Extremes -- Implementation -- Risk Assessment -- A Tutorial in R -- Appendices -- References En línea: http://dx.doi.org/10.1007/0-387-35429-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34817 ## Ejemplares

Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar