Geometr A Y Luz
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Information Geometry
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Author : Nihat Ay
language : en
Publisher: Springer
Release Date : 2017-08-25
Information Geometry written by Nihat Ay and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-25 with Mathematics categories.
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.
Algebra And Trigonometry With Analytic Geometry
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Author : Walter Fleming
language : en
Publisher: Pearson Educación
Release Date : 1989
Algebra And Trigonometry With Analytic Geometry written by Walter Fleming and has been published by Pearson Educación this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Perspectives In Dynamical Systems I Applications
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Author : Jan Awrejcewicz
language : en
Publisher: Springer Nature
Release Date :
Perspectives In Dynamical Systems I Applications written by Jan Awrejcewicz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Geometric Properties For Parabolic And Elliptic Pde S
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Author : Rolando Magnanini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-27
Geometric Properties For Parabolic And Elliptic Pde S written by Rolando Magnanini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-27 with Mathematics categories.
The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name a few. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulating future developments and perspectives in this very active area of research.
Algebraic Geometry And Arithmetic Curves
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Author : Qing Liu
language : en
Publisher: Oxford University Press
Release Date : 2006-06-29
Algebraic Geometry And Arithmetic Curves written by Qing Liu and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-29 with Mathematics categories.
This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.
Cubic Bipolar Fuzzy Ordered Weighted Geometric Aggregation Operators And Their Application Using Internal And External Cubic Bipolar Fuzzy Data
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Author : Muhammad Riaz
language : en
Publisher: Infinite Study
Release Date :
Cubic Bipolar Fuzzy Ordered Weighted Geometric Aggregation Operators And Their Application Using Internal And External Cubic Bipolar Fuzzy Data written by Muhammad Riaz and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In the present study, we discuss the concept of internal cubic bipolar fuzzy (ICBF) sets and external cubic bipolar fuzzy (ECBF) sets.We also discuss some properties of ICBF-sets and ECBF-sets under both P-Order and R-Order. We present examples and counterexamples to support our concepts. Furthermore, we see the importance of ICBF-sets and EBCF-sets in multiple attribute decision making. We proposed two cubic bipolar fuzzy ordered weighted geometric aggregation operators, including, P-CBFOWG operator and R-CBFOWG operator to aggregate cubic bipolar fuzzy information with both perspectives, i.e., ICBF data and ECBF data. Finally, we present a multiple attribute decision making problem to examine the useability and capability of these operators and a comparison between ICBF information and ECBF information.
Calculus And Analytic Geometry
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Author : Abraham Schwartz
language : en
Publisher:
Release Date : 1967
Calculus And Analytic Geometry written by Abraham Schwartz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Calculus categories.
The Physics Of Foraging
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Author : Gandhimohan. M. Viswanathan
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-02
The Physics Of Foraging written by Gandhimohan. M. Viswanathan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-02 with Science categories.
Do the movements of animals, including humans, follow patterns that can be described quantitatively by simple laws of motion? If so, then why? These questions have attracted the attention of scientists in many disciplines, and stimulated debates ranging from ecological matters to queries such as 'how can there be free will if one follows a law of motion?' This is the first book on this rapidly evolving subject, introducing random searches and foraging in a way that can be understood by readers without a previous background on the subject. It reviews theory as well as experiment, addresses open problems and perspectives, and discusses applications ranging from the colonization of Madagascar by Austronesians to the diffusion of genetically modified crops. The book will interest physicists working in the field of anomalous diffusion and movement ecology as well as ecologists already familiar with the concepts and methods of statistical physics.
Discovering Geometry
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Author : Michael Serra
language : en
Publisher:
Release Date : 2003-03-01
Discovering Geometry written by Michael Serra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-01 with Mathematics categories.
Geometric Algebra
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Author : Bertram Huppert
language : en
Publisher:
Release Date : 1970
Geometric Algebra written by Bertram Huppert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Algebraic fields categories.