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Winner of the 2009 Japan Statistical Association Publication Prize. The Akaike information criterion (AIC) derived as an estimator of the Kullback-Leibler information discrepancy provides a useful tool for evaluating statistical models, and numerous successful applications of the AIC have been reported in various fields of natural sciences, social sciences and engineering. One of the main objectives of this book is to provide comprehensive explanations of the concepts and derivations of the AIC and related criteria, including Schwarz’s Bayesian information criterion (BIC), together with a wide range of practical examples of model selection and evaluation criteria. A secondary objective is to provide a theoretical basis for the analysis and extension of information criteria via a statistical functional approach. A generalized information criterion (GIC) and a bootstrap information criterion are presented, which provide unified tools for modeling and model evaluation for a diverse range of models, including various types of nonlinear models and model estimation procedures such as robust estimation, the maximum penalized likelihood method and a Bayesian approach. Sadanori Konishi is Professor of Faculty of Mathematics at Kyushu University. His primary research interests are in multivariate analysis, statistical learning, pattern recognition and nonlinear statistical modeling. He is the editor of the Bulletin of Informatics and Cybernetics and is co-author of several Japanese books. He was awarded the Japan Statistical Society Prize in 2004 and is a Fellow of the American Statistical Association. Genshiro Kitagawa is Director-General of the Institute of Statistical Mathematics and Professor of Statistical Science at the Graduate University for Advanced Study. His primary interests are in time series analysis, non-Gaussian nonlinear filtering and statistical modeling. He is the executive editor of the Annals of the Institute of Statistical Mathematics, co-author of Smoothness Priors Analysis of Time Series, Akaike Information Criterion Statistics, and several Japanese books. He was awarded the Japan Statistical Society Prize in 1997 and Ishikawa Prize in 1999, and is a Fellow of the American Statistical Association.
Stochastic analysis. --- Information modeling. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Modeling, Information --- System analysis --- Analysis, Stochastic --- Stochastic processes
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Conventional calculus is too hard and too complex. Students are forced to learn too many theorems and proofs. In Free Calculus, the author suggests a direct approach to the two fundamental concepts of calculus - differentiation and integration - using two inequalities. Regular calculus is condensed into a single concise chapter. This makes the teaching of physics in step with the calculus teaching.
Calculus. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal
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Function Theory in the Unit Ball of Cn. From the reviews: "…The book is easy on the reader. The prerequisites are minimal—just the standard graduate introduction to real analysis, complex analysis (one variable), and functional analysis. This presentation is unhurried and the author does most of the work. …certainly a valuable reference book, and (even though there are no exercises) could be used as a text in advanced courses." R. Rochberg in Bulletin of the London Mathematical Society. "…an excellent introduction to one of the most active research fields of complex analysis. …As the author emphasizes, the principal ideas can be presented clearly and explicitly in the ball, specific theorems can be quickly proved. …Mathematics lives in the book: main ideas of theorems and proofs, essential features of the subjects, lines of further developments, problems and conjectures are continually underlined. …Numerous examples throw light on the results as well as on the difficulties." C. Andreian Cazacu in Zentralblatt für Mathematik.
Holomorphic functions. --- Unit ball. --- Applied Mathematics --- Engineering & Applied Sciences --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Global analysis (Mathematics) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Global analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis
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This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. From the reviews: The aim of this interesting new contribution to the series Readings in Mathematics is an attempt to restore the historical order in the presentation of basic mathematical analysis...such a historical approach can provide a very fruitful and interesting approach to mathematical analysis. - Jean Mawhin, Zentralblatt The authors include a large number of once-traditional subjects which have now vanished from the analysis curriculum, at least in the standard American courses. Thus we find continued fractions, elliptic integrals, the Euler-MacLaurin summation formula, etc., most of which are found only in more compendious works. Many of the exercises are inspired by original papers, with the bibliographic references sometimes given. The work is very well illustrated. The book is definitely an analysis text, rather than a history, but a great deal of reliable historical material is included. For those seeking an alternative to the traditional approach, it seems to me to be of great interest. - Thomas Archibald, Mathematical Reviews The authors...have assembled an impressive array of annotated results, quotations, tables, charts, figures and drawings, many copied from original documents....they write with great enthusiasm and with evident affection for both analysis and history. - John Troutman, American Mathematical Monthly.
Mathematics. --- Functions of real variables. --- History. --- Real Functions. --- History of Mathematical Sciences. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Didactics of mathematics --- Annals --- Auxiliary sciences of history --- Real variables --- Functions of complex variables
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After the pioneering work on complex dynamics by Fatou and Julia in the early 20th century, Noel Baker went on to lay the foundations of transcendental complex dynamics. As one of the leading exponents of transcendental dynamics, he showed how developments in complex analysis such as Nevanlinna theory could be applied. His work has inspired many others to take up this increasingly active subject, and will continue to do so. Presenting papers by researchers in transcendental dynamics and complex analysis, this book is written in honour of Noel Baker. The papers describe the state of the art in this subject, with new results on completely invariant domains, wandering domains, the exponential parameter space, and normal families. The inclusion of comprehensive survey articles on dimensions of Julia sets, buried components of Julia sets, Baker domains, Fatou components of functions of small growth, and ergodic theory of transcendental meromorphic functions means this is essential reading for students and researchers in complex dynamics and complex analysis.
Functions of complex variables. --- Differentiable dynamical systems. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Complex variables --- Elliptic functions --- Functions of real variables
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Andrzej Mostowski was one of the leading 20th century logicians. This volume examines his legacy, devoted both to his scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and person. It includes the bibliography of Mostowski's writings.
Logic, Symbolic and mathematical. --- Mathematical analysis --- Logicians --- Mathematicians --- Scientists --- Philosophers --- 517.1 Mathematical analysis --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Foundations. --- Mostowski, Andrzej. --- Mostowski, A.
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The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Most of the results derived from this time were derived using methods which would be found unacceptable today, and as a result, when one looks back to the theory of series prior to Cauchy without reconstructing internal motivations and the conceptual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a magician or diviner rather than the penetrating and complex work of great mathematicians. This monograph not only describes the entire complex of 17th and 18th century procedures and results concerning series, but it also reconstructs the implicit and explicit principles upon which they are based, draws attention to the underlying philosophy, highlights competing approaches, and investigates the mathematical context where the theory originated. The aim here is to improve the understanding of the framework of 17th and 18th century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some sense, to a unified theory that has come down to us today. Giovanni Ferraro is Professor of Mathematics and History of Mathematics at University of Molise.
Series --- Mathematics --- History --- Math --- Science --- Algebra --- Processes, Infinite --- Sequences (Mathematics) --- Sequences (Mathematics). --- Mathematics. --- Global analysis (Mathematics). --- History of Mathematical Sciences. --- Sequences, Series, Summability. --- Real Functions. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical sequences --- Numerical sequences --- History. --- Functions of real variables. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Real variables --- Annals --- Auxiliary sciences of history
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In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of certain developments in the field during the decades since the book first appeared. From reviews of the 2nd Edition: "..the new edition of Professor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work." - Nigel Hitchin, Bulletin of the London Mathematical Society "Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material." - Daniel M. Burns, Jr., Mathematical Reviews.
Complex manifolds. --- Differentiable manifolds. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Differential manifolds --- Manifolds (Mathematics) --- Analytic spaces --- Global analysis (Mathematics). --- Global analysis. --- Analysis. --- Global Analysis and Analysis on Manifolds. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Manifolds (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Geometry, Differential --- Topology
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Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject.
Algebras, Linear. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology --- Mathematical physics. --- Algebra. --- Mathematical Methods in Physics. --- Physical mathematics --- Physics --- Mathematics --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics
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This book presents recent results concerning the global existence in time, the large-time behaviour, decays of solutions and the existence of global attractors for some nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations arising from physics, mechanics and material science, such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. To keep the book as self-contained as possible, the first chapter introduces to the needed results and tools from functional analysis, Sobolev spaces, differential and integral inequa
Differential equations, Partial. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories --- Partial differential equations --- Global analysis (Mathematics). --- Differential equations, partial. --- Operator theory. --- Analysis. --- Partial Differential Equations. --- Operator Theory. --- Functional analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- 517.1 Mathematical analysis --- Mathematical analysis
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