Download or read book Introduction to Algebraic Independence Theory written by Yuri V. Nesterenko and published by Springer. This book was released on 2003-07-01 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
Download or read book Introduction to Algebraic Independence Theory written by Yuri V. Nesterenko and published by . This book was released on 2014-01-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Independence written by I︠U︡riĭ Valentinovich Nesterenko and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the notes of a course of lectures given by at the Tata Institute of Fundamental Research in 1998. It deals with several important results and methods in transcendental number theory. First, the classical result of Lindemann-Weierstrass and its applications are dealt with. Subsequently, Siegel's theory of $E$-functions is developed systematically, culminating in Shidlovskii's theorem on the algebraic independence of the values of the $E$-functions satisfying a system of differential equations at certain algebraic values. Proof of the Gelfond-Schneider Theorem is given based on the method of interpolation determinants introduced in 1992 by M. Laurent. The author's famous result in 1996 on the algebraic independence of the values of the Ramanujan functions is the main theme of the reminder of the book. After deriving several beautiful consequences of his result, the author develops the algebraic material necessary for the proof. The two important technical tools in the proof are Philippon's criterion for algebraic independence and zero bound for Ramanujan functions. The proofs of these are covered in detail. The author also presents a direct method, without using any criterion for algebraic independence as that of Philippon, by which one can obtain lower bounds for transcendence degree of finitely generated field $\mathbb Q(\omega_1,\ldots,\omega_m)$. This is a contribution towards Schanuel's conjecture. The book is self-contained and the proofs are clear and lucid. A brief history of the topics is also given. Some sections intersect with Chapters 3 and 10 of Introduction to Algebraic Independence Theory, Lecture Notes in Mathematics, Springer, 1752, edited by Yu. V. Nesterenko and P. Philippon.
Download or read book Set Theory An Introduction To Independence Proofs written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.
Download or read book Algebraic Independence of the Values at Algebraic Points of a Class of Functions Considered by Mahler written by N. Ch Wass and published by . This book was released on 1990 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1,\... m)(\*)\cr} TABLE/EQUATION ENDS)for b $\geq$ 2, a$\sb{\rm ij}$(z), b$\sb{\rm j}$(z) in K(z). Suppose finally that $\alpha\in\kappa$ is such that 0 $
Download or read book An Introduction to Commutative Algebra written by Huishi Li and published by World Scientific. This book was released on 2004 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Contains many examples and problems (with hints) - Provides a good introduction for beginners in algebraic number theory and algebraic geometry
Download or read book Simplicial Complexes of Graphs written by Jakob Jonsson and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.
Download or read book Zeta Functions of Groups and Rings written by Marcus du Sautoy and published by Springer Science & Business Media. This book was released on 2008 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.
Download or read book Stochastic Calculus for Fractional Brownian Motion and Related Processes written by Yuliya Mishura and published by Springer Science & Business Media. This book was released on 2008-01-02 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.
Download or read book Introduction to Modern Number Theory written by Yu. I. Manin and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.
Download or read book Axiom of Choice written by Horst Herrlich and published by Springer. This book was released on 2006-07-21 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. It is shunned by some, used indiscriminately by others. This treatise shows paradigmatically that disasters happen without AC and they happen with AC. Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
Download or read book Random Times and Enlargements of Filtrations in a Brownian Setting written by Roger Mansuy and published by Springer Science & Business Media. This book was released on 2006-02-10 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: In November 2004, M. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York. These notes follow the contents of that course, covering expansion of filtration formulae; BDG inequalities up to any random time; martingales that vanish on the zero set of Brownian motion; the Azéma-Emery martingales and chaos representation; the filtration of truncated Brownian motion; attempts to characterize the Brownian filtration. The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the progressive kind. It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of Brownian motion.
Download or read book Combinatorial Stochastic Processes written by Jim Pitman and published by Springer. This book was released on 2006-07-21 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
Download or read book Laplacian Eigenvectors of Graphs written by Türker Biyikoglu and published by Springer. This book was released on 2007-07-07 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, and graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. Eigenvectors of graph Laplacians may seem a surprising topic for a book, but the authors show that there are subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs.
Download or read book Stability of Nonautonomous Differential Equations written by Luis Barreira and published by Springer. This book was released on 2007-09-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Download or read book Entropy Methods for the Boltzmann Equation written by Fraydoun Rezakhanlou and published by Springer. This book was released on 2007-12-22 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring updated versions of two research courses held at the Centre Émile Borel in Paris in 2001, this book describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields. It also discusses four conjectures for the kinetic behavior of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Download or read book Parameter Estimation in Stochastic Differential Equations written by Jaya P. N. Bishwal and published by Springer. This book was released on 2007-09-26 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.
