Series: Lecture Notes in Mathematics , Vol. 1981
2009, Approx. 165 p., Softcover
ISBN: 978-3-642-03063-5
Due: September 2009
The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups. The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups.
This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups.
1 On Commutative Algebra.- 2 On Blocks.- 3 On Essential Algebras.- 4 On Hecke Algebras.- 5 On the Determination of the Rouquier Blocks.- A Clifford Theory and Schur Elements for Generic Hecke Algebras
Series: Interdisciplinary Applied Mathematics , Vol. 35
2010, Approx. 400 p., Hardcover
ISBN: 978-0-387-87707-5
Due: March 2010
This book is motivated by a perceived need for an overview of how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience.
The book arose out of several courses that the authors have taught including a graduate course in computational neuroscience with students from psychology, mathematics, computer science, physics and neuroscience backgrounds.
The book begins with bio-physics of the cell membrane and from this introduces compartmental models, continuum limits and cable theory and active ion channels.
Prior to the work on active channels, all equations are linear and in theory completely solvable in closed form.
Introductory material.- Dendrites.- Dynamics.- Voltage-gated channels.- Action potentials.- Synaptic channels.- Noise.- Networks.- Neuro oscillators.- Firing rate models.- Spatially distributed networks.
Series: Problem Books in Mathematics
2009, Approx. 170 p. 85 illus., Hardcover
ISBN: 978-1-4419-1095-0
Due: October 2009
This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to master solution techniques. The theoretical part is rigorous and with important details presented with care. Hints are provided to help the reader restore the arguments to their full rigor. Many examples from physics are intended to keep the book intuitive and to illustrate the applied nature of the subject. The book is useful for a higher-level undergraduate course and for self-study.
Preface.- Hyperbolic Equations. Method of Characteristics.- The Fourier Method.- Distributions and Greenfs Functions.- Fundamental Solutions and Greenfs Functions in Higher Dimensions.- Classification of the Second-Order Equations.- References.- Index
Series: Mathematics Education Library , Vol. 47
2009, Approx. 130 p. 35 illus., Hardcover
ISBN: 978-0-387-98131-4
Due: January 2010
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade though high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the Editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level.
This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.
Introduction.- The Longitudinal Study.- Methodology.- Representations as a Tool for Building Arguments.- Building Towers: Justifications Leading to Proof Making.- Making Pizzas: Reasoning by Cases and recursion.- Responding to Ankur's Challenge: Co-construction of Argument Leading to Proof.- Co-construction of Proof.- The Case of Stephanie.- Representations and Connections.- Pizzas, Block Towers, and Binomials.- Generalizing from Pizzas, Towers, Binomial Expansion, and Pascal's Triangle.- Extending and Generalizing the Isomorphism: Towers, Pizzas, Pascal's Triangle, and the Taxicab Problem.- College Students Building Towers and Making Pizzas.- Comparing the Problem Solving of College Students with Longitudinal Study Students.- Conclusions and Suggestions for Practice.
Series: Operator Theory: Advances and Applications , Vol. 194
2010, Approx. 260 p., Hardcover
ISBN: 978-3-7643-8997-0
Due: November 2009
This book gives a complete exposition of the theory of tauberian operators from the very basic results to the most recent advances making emphasis in its applications to Banach space theory.
After describing the origins of the subject in the study of summability of series, it presents the general theory for tauberian operators on abstract Banach spaces.
The main sources of examples of tauberian operators are described in detail, including the case of operators on spaces of integrable functions.
Graduate students and researchers interested in Banach spaces and operator theory
Tauberian operator
factorization
semigroup