Series: Problem Books in Mathematics
2012, XIV, 392 p.
Hardcover, ISBN 978-1-4614-3687-4
Due: June 30, 2012
Provides more than 1500 exercises and problems for professors using GTM 95 as a course text
While book can be used along with GTM 95, it is self-contained
Cover traditional areas of probability theory, as well as recent developements
Author is a well-known expert in the field, and an experienced writer
Problems in Probability comprises one of the most comprehensive, nearly encyclopedic, collections of problems and exercises in probability theory. Albert Shiryaev has skillfully created, collected, and compiled the exercises in this text over the course of many years while working on topics which interested him the most. A substantial number of the exercises resulted from diverse sources such as textbooks, lecture notes, exercise manuals, monographs, and discussions that took place during special seminars for graduate and undergraduate students. Many problems contain helpful hints and other relevant comments and a portion of the material covers some important applications from optimal control and mathematical finance. Readers of diverse backgrounds?from students to researchers?will find a great deal of value in this book and can treat the work as an exercise manual, a handbook, or as a supplementary text to a course in probability theory, control, and mathematical finance.
The problems and exercises in this book vary in nature and degree of difficulty. Some problems are meant to test the readerfs basic understanding, others are of medium-to-high degrees of difficulty and require more creative thinking. Other problems are meant to develop additional theoretical concepts and tools or to familiarize the reader with various facts that are not necessarily covered in mainstream texts. Additional problems are related to the passage from random walk to Brownian motions and Brownian bridges. The appendix contains a summary of the main results, notation and terminology that are used throughout the book. It also contains additional material from combinatorics, potential theory and Markov chains?subjects that are not covered in the book, but are nevertheless needed for many of the exercises included here.
Preface.- 1. Elementary Probability Theory.- 2. Mathematical Foundations of Probability Theory.- 3. Convergence of Probability Measures.- 4. Independent Random Variables.- 5. Stationary Random Sequences in Strict Sense.- 6. Stationary Random Sequences in Broad Sense.- 7. Martingales.- 8. Markov Chains.- Appendix.- References.
Series: Operator Theory: Advances and Applications, Vol. 223
Subseries: Linear Operators and Linear Systems
2012, 2012, Approx. 230 p.
Hardcover, ISBN 978-3-0348-0398-4
Due: May 29, 2012
Starts with elementary known results and progresses to advanced topics of current research
Introductory textbook for a course on infinite dimensional linear systems
Lecture notes include many worked-out examples and exercises
First textbook on infinite-dimensional port-Hamiltonian systems ?
This book gives a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results and further progresses smoothly to advanced topics of current research.
Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This approach leads to easily verifiable conditions for well-posedness and stability.
The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.
1 Introduction.- 2 State Space Representation.-3 Controllability of Finite-Dimensional Systems.- 4 Stabilizability of Finite-Dimensional Systems.- 5 Strongly Continuous Semigroups.- 6 Contraction and Unitary Semigroups.- 7 Homogeneous Port-Hamiltonian Systems.- 8 Stability.- 9 Stability of Port-Hamiltonian Systems.- 10 Inhomogeneous Abstract Differential Equations and Stabilization.- 11 Boundary Control Systems.- 12 Transfer Functions.- 13 Well-posedness.- A Integration and Hardy spaces.- Bibliography.- Index.?
Series: Lecture Notes in Mathematics, Vol. 2049
2012, 2012, X, 158 p. 12 illus., 6 in color.
Softcover, ISBN 978-3-642-28284-3
Due: May 31, 2012
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain.
From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, and coefficient identification, and to introduce relevant solving methods for each case.
1 Parameter identification in a parabolic-elliptic degenerate problem.- 2 Existence for diffusion degenerate problems.- 3 Existence for nonautonomous parabolic-elliptic degenerate diffusion Equations.- 4 Parameter identification in a parabolic-elliptic degenerate problem.
Series: Progress in Mathematics, Vol. 299
2012, 2012, 450 p.
Hardcover, ISBN 978-3-0348-0404-2
Due: June 29, 2012
Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This has been the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis.
By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value.
On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations.
Content Level ā Research
Keywords ā Tamari lattice - associahedron - associativity - polytope - poset
Related subjects ā Algebra - Geometry & Topology - Number Theory and Discrete Mathematics
Series: Operator Theory: Advances and Applications, Vol. 222
2012, 2012, XX, 300 p.
Hardcover, ISBN 978-3-0348-0410-3
Due: June 29, 2012
This volume is dedicated to Bill Helton on the occasion of his sixty fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty odd years. These include interpolation, Szego limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization.
The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, as well as a source book for seminars.
Preface.- Inroduction (an overview of the contents of the book, from the perspective of Helton's landmark contributions).- Biographical Note and List of Publications of J.W. Helton.- Bounded Analytic Interpolation and H-infinity Control.- Linear Matrix Inequalities and Matrix Convexity.- Optimization and Realization in the Free *-algebra.- Automatic Verification of Matrix Inequalities.- Non-commutative Algebraic Geometry.- Non-Commutative Differential Geometry and Probability.- Modern Trends in Robust Control.- Challenges of Mathematical Biology.- Mathematical Programming and Computer Science.
Series: Progress in Mathematics, Vol. 300
2012, 2012, VIII, 351 p. 89 illus.
Hardcover, ISBN 978-0-8176-8333-7
Due: June 30, 2012
Provides a comprehensive overview of an emerging area at the boundary among many fields of mathematics??
Includes high-quality papers from a conference on Multiple Dirichlet Series? with contributions by international experts in their respective fields?
Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions.
Preface.- Introduction: Multiple Dirichlet Series.- A Crystal Description for Symplectic Multiple Dirichlet Series.- Metaplectic Whittaker Functions and Crystals of Type B.- Metaplectic Ice.- Littelmann patterns and Weyl Group Multiple Dirichlet Series of Type D.- Toroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series.- Natural Boundaries and Integral Moments of L-functions.- A Trace Formula of Special Values of Automorphic L-functions.- The Adjoint L-function of SU(2,1).- Symplectic Ice.- On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III.- A Pseudo Twin-Prime Theorem.- Principal Series Representations of Metaplectic Groups over Local Fields.- Two-Dimensional Adelic Analysis and Cuspidal Automorphic Representations of GL(2).?