Series: Classics in Mathematics
Reprint of the 1st ed. Berlin Heidelberg New York 1987, 2007,
XIII, 592 p., Softcover
ISBN: 978-3-540-69843-2
Due: March 2007
About this book
This book gives the exposition of the inverse scattering method
and its applications to soliton theory. The main characteristic
feature of this book is the consistant Hamiltonian aproach to the
theory. The nonlinear Schrodinger equations (not the KdV
equations as usual) is considered as a main example, the
inverstigation of this equations forms the first part of the book.
The second part is devoted to such fundamental models as the sine-Gordon
equation, Heidenberg equation, Toda lattice, etc, the
classification of integrable models and the methods for
constructing their solutions.
Table of contents
Introduction.- The Nonlinear Schrodinger Equation (NS Model):
Zero Curvature Representation. The Riemann Problem. The
Hamiltonian Formulation.- General Theory of Integrable Evolution
Equations: Basic Examples and Their General Properties.
Fundamental Continuous Models. Fundamental Models on the Lattice.
Lie-Algebraic Approach to the Classification and Analysis of
Integrable Models.- Conclusion.- List of Symbols.- Index.
Series: Lecture Notes in Mathematics , Vol. 1903
2007, Approx. 155 p., Softcover
ISBN: 978-3-540-69573-8
Due: March 2, 2007
About this book
This volume contains a coherent point of view on various sharp
pointwise inequalities for analytic functions in a disk in terms
of the real part of the function on the boundary circle or in the
disk itself. Inequalities of this type are frequently used in the
theory of entire functions and in the analytic number theory.
Rich opportunities are anticipated to extend these inequalities
to analytic functions of several complex variables and solutions
of partial differential equations.
Table of contents
Preface.- Introduction.- Estimates for analytic functions bounded
with respect to their real part.- Estimates for analytic
functions with respect to the Lp-norm of Re f on the circle.-
Estimates for analytic functions by the best Lp-approximation of
Re f on the circle.- Estimates for directional derivatives of
harmonic functions.- Estimates for derivatives of analytic
functions.- Bohr's type real part estimates.- Estimates for the
increment of derivatives of analytic functions.- References.-
Index.- List of symbols.
2007, 21 illus., Softcover
ISBN: 978-0-8176-4546-5
Due: June 2007
About this textbook
The Math Problems Notebook is a collection of non-trivial,
unconventional problems requiring deep insight and imagination
nostalgic of those discussed at the Sunday Math Circles. These
circles are comprised of college students who have a common
passion for mathematics, and have become a place for
disseminating beautiful mathematics at an elementary level.
Following in the tradition of the math circles, the authors hope
to inspire further enjoyment of mathematics with their collection
of problems.
The problems cover many topics, including number theory, algebra,
combinatorics, geometry and analysis, of varying levels of
difficulty; beginning with simple exercises and following with
more difficult problems, challenging enough even for the
experienced problem solver. The introductory problems focus on
the basic methods and tools while the advanced problems aim to
develop problem solving techniques, intuition and to promote
further research in the area.
Undergraduates and teachers of advanced mathematics, as will as
the casual mathematician will mutually enjoy The Math Problems
Notebook.
Table of contents
Preface.- I. Problems.- Number Theory.- Algebra and Combinatorics.-
Geometry.- Analysis.- II. Solutions and Comments to the Problems.-
Number Theory Solutions.- lgebra and Combinatorics Solutions.-
Geometry Solutions.- Analysis Solutions.- Glossary.- Index.
Series: Operator Theory: Advances and Applications , Vol. 176
2007, Approx. 340 p., Hardcover
ISBN: 978-3-7643-8136-3
Due: April 2007
About this book
This volume contains six peer-refereed articles written on the
occasion of the workshop Operator theory, system theory and
scattering theory: multidimensional generalizations and related
topics, held at the Department of Mathematics of the Ben-Gurion
University of the Negev during the period June 26-July 1, 2005.
The papers present the newest developments in key directions of
current research in complex analysis and operator theory. Topics
considered include Schur analysis, hierarchical semiseparable
matrices, canonical forms for pairs of quaternionic matrices, the
theory of homogeneous operators, algebras of fractions of
continuous functions, and moment problems. Schur analysis in its
various aspects occupies more than half of the volume, and
moments problems have also an important place in the papers
presented here.
The volume will be of interest to a wide audience of pure and
applied mathematicians, electrical engineers and theoretical
physicists.
Table of contents
Editorial Introduction.- The Transformation of Schur in an
Indefinite Setting (D. Alpay, A. Dijksma, H. Langer).- A
Truncated Matricial Moment Problem on a Finite Interval (A.
Choque Rivero, Y. Dyukaerv, B. Fritzsche, B. Kirstein).- On the
Irreducibility of a Class of Homogeneous Operators (G. Misra, S.
Shyan Roy).- Canonical Forms for Quaternionic Matrix Pencils (L.
Rodman).- Algorithms to Solve Hierarchically Semi-separable
Systems (Z. Sheng, P. Dewilde, S. Chandrasekaran).- Unbounded
Normal Algebras and Spaces of Fractions (F.-H. Vasilescu).
Series: Texts in Applied Mathematics , Vol. 26
2007, Approx. 455 p., 89 illus., Hardcover
ISBN: 978-0-387-35763-8
Due: June 2007
About this textbook
This is a book about modelling, analysis and control of linear
time- invariant systems. The book uses what is called the
behavioral approach towards mathematical modelling. An essential
feature of using the behavioral approach is that it allows these
and similar concepts to be introduced in a representation-free
manner. Thus a system is viewed as a dynamical relation between
manifest and latent variables. The emphasis is on dynamical
systems that are represented by systems of linear constant
coefficients. The book contains numerous exercises, including
simulation problems, and examples, notably of mechanical systems
and electrical circuits.
Table of contents
Preface.- Dynamical Systems.- Introduction.- Models.- The
universum and the behavior.- Behavioral equations.- Latent
variables.- Dynamical systems.- The basic concept.- Latent
variables in dynamical systems.- Linearity and time-invariance.-
Dynamical behavioral equations.- Recapitulation .- Notes and
references.- Exercises.- Systems defined by Linear Differential
Equations.- Notation
2007, Approx. 420 p., Softcover
ISBN: 978-3-7643-8271-1
Due: August 2007
About this textbook
Complex analysis nowadays has higher-dimensional analoga: the
algebra of complex numbers is replaced then by the non-commutative
algebra of real quaternions or Clifford-algebras. During the last
30 years the so-called quaternionic and Clifford or hypercomplex
analysis successfully developed to a powerful theory with many
applications in analysis, engineering and mathematical physics.
This textbook introduces both to classical and higher-dimensional
results based on a uniform notion of holomorphy. Historical
remarks, lots of examples, figures and exercises accompany each
chapter.
Table of contents
Introduction.- I. Numbers.- Complex Numbers - Quaternions -
Clifford numbers.- II. Functions.- Topological Aspects -
Holomorphic Functions - Power Functions and Mobius
Transformations.- III. Integration und Integral Theorems -
Integral Theorems and -formulas - Teodorescu Transformation.- IV.
Series and Local Properties - Power Series- Orthogonal Series -
Elementary Functions.- Local Structure of Holomorphic Functions -
Special Functions.- Appendices.- Bibliography.- Index.