Engel, Klaus-Jochen, Nagel, Rainer
A Short Course on Operator Semigroups
Series: Universitext
2006, Approx. 250 p. 3 illus., Hardcover
ISBN: 0-387-31341-9
About this textbook
The book offers a direct and up-to-date introduction to the
theory of one-parameter semigroups of linear operators on Banach
spaces. It contains the fundamental results of the theory such as
the Hille-Yoshida generation theorem, the bounded perturbation
theorem, and the Trotter-Kato approximation theorem, but also
treats the spectral theory of semigroups and its consequences for
the qualitative behavior.
The book is intended for students and researchers who want to
become acquainted with the concept of semigroups in order to work
with it in fields like partial and functional differential
equations, stochastic processes, infinite dimensional control
theory, or dynamical systems coming from physics or biology.
Written for:
graduate students, professors
Table of contents
Preface.- Introduction.- Semigroups, Generators, and Resolvents.-
Perturbation of Semigroups.- Approximation of Semigroups.-
Spectral Theory and Asymptotics for Semigroups.- Positive
Semigroups.- Appendix.- References.- Selected References to
Recent Research.- List of Symbols and Abbreviations.- Index.
Flum, J., Grohe, M.
Parameterized Complexity Theory
Series: Texts in Theoretical Computer Science. An EATCS Series
2006, XIV, 493 p. 51 illus., Hardcover
ISBN: 3-540-29952-1
About this book
Parameterized complexity theory is a recent branch of
computational complexity theory that provides a framework for a
refined analysis of hard algorithmic problems. The central notion
of the theory, fixed-parameter tractability, has led to the
development of various new algorithmic techniques and a whole new
theory of intractability.
This book is a state-of-the-art introduction into both
algorithmic techniques for fixed-parameter tractability and the
structural theory of parameterized complexity classes, and it
presents detailed proofs of recent advanced results that have not
appeared in book form before. Several chapters each are devoted
to intractability, algorithmic techniques for designing fixed-parameter
tractable algorithms, and bounded fixed-parameter tractability
and subexponential time complexity. The treatment is
comprehensive, and the reader is supported with exercises, notes,
a detailed index, and some background on complexity theory and
logic.
The book will be of interest to computer scientists,
mathematicians and graduate students engaged with algorithms and
problem complexity.
Written for:
Researchers, lecturers, graduate students
Table of contents
Fixed-Parameter Tractability.- Reductions and Parameterized
Intractability.- The Class W[P].- Logic and Complexity.- Two
Fundamental Hierarchies.- The First Level of the Hierarchies.-
The W-Hierarchy.- The A- Hierarchy.- Kernelization and Linear
Programming Techniques.- The Automata-Theoretic Approach.- Tree
Width.- Planarity and Bounded Local Tree Width.- Homomorphisms
and Embeddings.- Parameterized Counting Problems.- Bounded Fixed-Parameter
Tractability.- Subexponential Fixed-Parameter Tractability.-
Appendix, Background from Complexity Theory.- References.-
Notation.- Index.
Kabanov, Yuri; Lipster, Robert; Stoyanov, Jordan (Eds.)
From Stochastic Calculus to Mathematical Finance
The Shiryaev Festschrift
2006, XXXVIII, 634 p. 15 illus., Hardcover
ISBN: 3-540-30782-6
About this book
Dedicated to the eminent Russian mathematician Albert Shiryaev on
the occasion of his 70th birthday, the Festschrift is a
collection of papers, including several surveys, written by his
former students, co-authors and colleagues. These reflect the
wide range of scientific interests of the teacher and his Moscow
school. The topics range from the disorder problems to stochastic
calculus and their applications to mathematical economics and
finance. A full biobibliography of Shiryaev’s works is included.
The book represents the modern state of art of many aspects of a
quickly maturing theory and will be an essential source and
reading for researchers in this area. The diversity of the topics
and the comprehensive style of the papers make the book amenable
and attractive for PhD students and young researchers.
Written for:
Researchers and graduate students
Table of contents
Lutkepohl, Helmut
New Introduction to Multiple Time Series Analysis
2006, XXII, 764 p. 49 illus., Softcover
ISBN: 3-540-26239-3
About this textbook
This reference work and graduate level textbook considers a wide
range of models and methods for analyzing and forecasting
multiple time series. The models covered include vector
autoregressive, cointegrated, vector autoregressive moving
average, multivariate ARCH and periodic processes as well as
dynamic simultaneous equations and state space models. Least
squares, maximum likelihood, and Bayesian methods are considered
for estimating these models. Different procedures for model
selection and model specification are treated and a wide range of
tests and criteria for model checking are introduced. Causality
analysis, impulse response analysis and innovation accounting are
presented as tools for structural analysis.
The book is accessible to graduate students in business and
economics. In addition, multiple time series courses in other
fields such as statistics and engineering may be based on it.
Applied researchers involved in analyzing multiple time series
may benefit from the book as it provides the background and tools
for their tasks. It bridges the gap to the difficult technical
literature on the topic.
Written for:
Graduate students, researchers
Table of contents
Introduction.- Finite Order Vector Autoregressive Processes:
Stable Vector Autoregressive Processes.- Estimation of Vector
Autoregressive Processes.- VAR Order Selection and Checking the
Model Adequacy.- VAR Processes with Parameter Constraints.
Cointegrated Processes: Vector Error Correction Models.-
Estimation of Vector Error Correction Models.- Specification of
VECMs. Structural and Conditional Models: Structural VARs and
VECMs.- Systems of Dynamic Simultaneous Equations. Infinite Order
Vector Autoregressive Processes: Vector Autoregressive Moving
Average Processes.- Estimation of VARMA Models.- Specification
and Checking the Adequacy of VARMA.- Cointegrated VARMA Processes.-
Fitting Finite Order VAR Models to Infinite Order Processes. Time
Series Topics: Multivariate ARCH and GARCH Models.- Periodic VAR
Processes and Intervention Models.- State Space Models.
Appendices: Vectors and Matrices.- Multivariate Normal and
Related Distributions.- Stochastic Convergence and Asymptotic
Distributions.- Evaluating Properties of Estimators and Test
Statistics by Simulation and Resampling Techniques.
Nebe, Gabriele, Rains, Eric M., Sloane, Neil J. A.
Self-Dual Codes and Invariant Theory
Series: Algorithms and Computation in Mathematics, Vol. 17
2006, XXVII, 430 p. 10 illus., Hardcover
ISBN: 3-540-30729-X
About this book
One of the most remarkable and beautiful theorems in coding
theory is Gleason's 1970 theorem about the weight enumerators of
self-dual codes and their connections with invariant theory. In
the past 35 years there have been hundreds of papers written
about generalizations and applications of this theorem to
different types of codes. This self-contained book develops a new
theory which is powerful enough to include all the earlier
generalizations.
It is also in part an encyclopedia that gives a very extensive
list of the different types of self-dual codes and their
properties, including tables of the best codes that are presently
known. Besides self-dual codes, the book also discusses two
closely-related subjects, lattices and modular forms, and quantum
error-correcting codes.
This book, written by the leading experts in the subject, has no
equivalent in the literature and will be of great interest to
mathematicians, communication theorists, computer scientists and
physicists.
Written for:
Mathematicians, communication theorists, computer scientists and
physicists
Table of contents
Preface.- 1 The Type of a Self-Dual Code.- 2 Weight Enumerators
and Important Types.- 3 Closed Codes.- 4 The Category Quad.- 5
The Main Theorems.- 6 Real and Complex Clifford Groups.- 7
Classical Self-Dual Codes.- 8 Further Examples of Self-Dual Codes.-
9 Lattices.- 10 Maximal Isotropic Codes and Lattices.- 11
Extremal and Optimal Codes.- 12 Enumeration of Self-Dual Codes.-
13 Quantum Codes.- Bibliography.- Index