Series: Springer Undergraduate Mathematics Series
2012, 2012, XII, 356 p.
Softcover, ISBN 978-1-4471-2729-1
Due: March 31, 2012
The theory of abelian groups is introduced in an understandable and concrete way using only basic linear algebra
In an analogous way, the similarity of matrices over a field is treated including the Jordan Normal Form
Computational techniques are stressed to get students ‘on board’
At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S. Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to the decomposition of such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part 2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a simpler matrix with only few non-vanishing entries: the Jordan form.
The reader is assumed to be familiar with elementary properties of rings and fields. Also a knowledge of abstract linear algebra including vector spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but from a more general standpoint: the role of vector spaces is widened to modules commutative rings.
Based on a lecture course taught by the author for over thirty years, the book emphasises computational techniques and features numerous worked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second- and third-year undergraduate students, while the later chapters, which cover closely related areas suitable for further study, e.g., field extensions, endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced student . The book can therefore bridge the gap between linear algebra and higher algebra.
Part 1. Finitely generated abelian groups.- Matrices with integer entries: the Smith normal form.- Basic theory of additive abelian groups.- Decomposition of finitely generated modules.- Part 2. Similarity of square matrices over a field.- Equivalence of matrices over where is a field.- modules: similarity of matrices over a field .- Canonical forms and similarity classes of square matrices over a field.- Answers to selected exercises.?
2012, 2012, XIII, 502 p.
Hardcover, ISBN 978-3-642-25587-8
Due: March 31, 2012
do Carmo is one of the outstanding differential geometers of his time
M.do Carmo in one of the pioneers of modern mathematics in Brazil
M. do Carmo is well-known to many students who have used his excellent and popular textbooks
This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.
Preface.- A Summary of the Scientific Activities of Manfredo P. do Carmo.- Summary of thePapers in this Volume by Manfredo P. do Carmo.- Contributions.- Complete List of Publications of Manfredo P. do Carmo.- List of D.Sc. Students of Manfredo P. do Carmo.
Series: Operator Theory: Advances and Applications, Vol. 220
2012, 2012, 350 p.
Hardcover, ISBN 978-3-0348-0345-8
Due: March 30, 2012
This volume contains twenty-one solicited articles by speakers at the IWOTA 2009 workshop, ranging from expository surveys to original research papers, each carefully refereed. The contributions reflect recent developments in operator theory and its applications. Consistent with the topics of recent IWOTA meetings, IWOTA 2009 was designed as a comprehensive, inclusive conference covering all aspects of theoretical and applied operator theory, ranging from classical analysis, differential and integral equations, complex and harmonic analysis to mathematical physics, mathematical systems and control theory, signal processing and numerical analysis. The conference brought together international experts for a week-long stay at Hotel Real de Minas, in an atmosphere conducive to fruitful professional interactions. These Proceedings reflect the high quality of the papers presented at the conference.
Content Level ≫ Research
Keywords ≫ Toeplitz operators - factorization problems - hypercomplex operator theory - singe and multivariable operator theory
Related subjects ≫ Analysis - Dynamical Systems & Differential Equations
Series: Progress in Mathematics, Vol. 298
2012, 2012, VIII, 240 p.
Hardcover, ISBN 978-3-0348-0350-2
Due: March 31, 2012
Award winning monograph of the 2011 Ferran Sunyer i Balaguer Prize competition
Contains basic material on intersection cohomology, modular cycles and automorphic forms from the classical and adelic points of view
Contains topics of interest for geometers and number theorists interested in locally symmetric spaces and automorphic forms
In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adelic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.
Chapter 1. Introduction.- Chapter 2. Review of Chains and Cochains.- Chapter 3. Review of Intersection Homology and Cohomology.- Chapter 4. Review of Arithmetic Quotients.- Chapter 5. Generalities on Hilbert Modular Forms and Varieties.- Chapter 6. Automorphic vector bundles and local systems.- Chapter 7. The automorphic description of intersection cohomology.- Chapter 8. Hilbert Modular Forms with Coefficients in a Hecke Module.- Chapter 9. Explicit construction of cycles.- Chapter 10. The full version of Theorem 1.3.- Chapter 11. Eisenstein Series with Coefficients in Intersection Homology.- Appendix A. Proof of Proposition 2.4.- Appendix B. Recollections on Orbifolds.- Appendix C. Basic adelic facts.- Appendix D. Fourier expansions of Hilbert modular forms.- Appendix E. Review of Prime Degree Base Change for GL2.- Bibliography.
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Series: Lecture Notes in Mathematics, Vol. 2046
Subseries: Seminaire de Probabilites
2012, 2012, X, 438 p. 17 illus., 10 in color.
Softcover, ISBN 978-3-642-27460-2
Due: March 31, 2012
As usual, some of the contributions to this 44th Seminaire de Probabilites were presented during the Journees de Probabilites held in Dijon in June 2010. The remainder were spontaneous submissions or were solicited by the editors. The traditional and historical themes of the Seminaire are covered, such as stochastic calculus, local times and excursions, and martingales. Some subjects already touched on in the previous volumes are still here: free probability, rough paths, limit theorems for general processes (here fractional Brownian motion and polymers), and large deviations.
Lastly, this volume explores new topics, including variable length Markov chains and peacocks. We hope that the whole volume is a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France.
Context trees, variable length Markov chains and dynamical sources.- Martingale property of generalized stochastic exponentials.- Some classes of proper integrals and generalized Ornstein-Uhlenbeck processes.- Martingale representations for diffusion processes and backward stochastic differential equations.- Quadratic Semimartingale BSDEs Under an Exponential Moments Condition.- The derivative of the intersection local time of Brownian motion through Wiener chaos.- On the occupation times of Brownian excursions and Brownian loops.- Discrete approximation to solution flows of Tanaka’s SDE related to Walsh Brownian motion.- Spectral Distribution of the Free unitary Brownian motion: another approach.- Another failure in the analogy between Gaussian and semicircle laws.- Global solutions to rough differential equations with unbounded vector fields.- Asymptotic behavior of oscillatory fractional processes.- Time inversion property for rotation invariant self-similar diffusion processes.- On Peacocks: a general introduction to two articles.- Some examples of peacocks in a Markovian set-up.- Peacocks obtained by normalisation; strong and very strong peacocks.- Branching Brownian motion: Almost sure growth along scaled paths.- On the delocalized phase of the random pinning model.- Large deviations for Gaussian stationary processes and semi-classical analysis.- Girsanov theory under a finite entropy condition.
Series: Lecture Notes in Mathematics, Vol. 2048
Subseries: C.I.M.E. Foundation Subseries
2012, 2012, XII, 332 p. 46 illus. in color.
Softcover, ISBN 978-3-642-27892-1
Due: April 30, 2012
The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010. Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a friendly introduction to, and an updated account of, some of the most active trends in current research.
1 On some recent advances on stabilization for hyperbolic equations.- 2 Notes on the Control of the Liouville Equation.- 3 Some questions of control in ?uid mechanics.- 4 Carleman estimates and some applications to control theory.- 5 The Wave Equation: Control and Numerics