2006, XXIII, 822 p., Hardcover
ISBN: 1-4020-4544-1
About this book
This volume presents a comprehensive introduction into rigorous
geometrical dynamics of complex systems of various natures. By
"complex systems", in this book are meant high-dimensional
nonlinear systems, which can be (but not necessarily are)
adaptive. This monograph proposes a unified geometrical approach
to dynamics of complex systems of various kinds: engineering,
physical, biophysical, psychophysical, sociophysical,
econophysical, etc. As their names suggest, all these multi-input
multi-output (MIMO) systems have something in common: the
underlying physics. Using sophisticated machinery composed of
differential geometry, topology and path integrals, this book
proposes a unified approach to complex dynamics ? of predictive
power much greater than the currently popular "soft-science"
approach to complex systems. The main objective of this book is
to show that high-dimensional nonlinear systems in "real
life" can be modeled and analyzed using rigorous
mathematics, which enables their complete predictability and
controllability, as if they were linear systems.
The book has two chapters and an appendix. The first chapter
develops the geometrical machinery in both an intuitive and
rigorous manner. The second chapter applies this geometrical
machinery to a number of examples of complex systems, including
mechanical, physical, control, biomechanical, robotic,
neurodynamical and psycho-social-economical systems. The appendix
gives all the necessary background for comprehensive reading of
this book.
Written for:
Researchers and students of complex systems (in engineering,
mathematics, physics, chemistry, biology, psychology, sociology,
economics and medicine), working both in industry and academia
Table of contents
Series: Mathematics and Its Applications, Vol. 582
2006, XVIII, 524 p., Hardcover
ISBN: 0-387-27730-7
About this textbook
This book is a revised and expanded edition of a successful
graduate and reference text. The material in the book is designed
for a standard graduate course on probability theory, including
some important applications. This new edition contains a detailed
treatment of the core area of probability, and both structural
and limit results are presented in full detail. Compared to the
first edition, the material and presentation are better
highlighted with several (small and large) alterations made to
each chapter. Key features of the book include:
- Indicating the need for abstract theory even in applications
and showing the inadequacy of existing results for certain
apparently simple real-world problems
- Attempting to deal with the existence problems for various
classes of random families that figure in the main results of the
subject
- Providing a treatment of conditional expectations and of
conditional probabilities that is more complete than in other
existing textbooks
Since this is a textbook, essentially all proofs are given in
complete detail (even at the risk of repetition), and some key
results are given multiple proofs when each argument has
something to contribute.
Written for:
Graduate students and researchers interested in probability
theory
Table of contents
Preface to Second Edition.- Preface to First Edition.- List of
Symbols.- PART I. FOUNDATIONS.- 1. Background Material and
Preliminaries.- 2. Independence and Strong Convergence.- 3.
Conditioning and Some Dependence Classes.- PART II. ANALYTICAL
THEORY.- 4. Probability Distributions and Characteristic
Functions.- 5. Weak Limit Laws.- PART III. APPLICATIONS.- 6.
Stopping Times, Martingales, and Convergences.- 7. Limit Laws for
Some Dependent Sequences.- 8. A Glimpse of Stochastic Processes.-
References.- Author Index.- Subject Index.
2006, X, 284 p. 135 illus., Hardcover
ISBN: 3-540-29545-3
About this book
This book presents models and algorithms for complex scheduling
problems. Besides resource-constrained project scheduling
problems with applications also job-shop problems with flexible
machines, transportation or limited buffers are discussed.
Discrete optimization methods like linear and integer
programming, constraint propagation techniques, shortest path and
network flow algorithms, branch-and-bound methods, local search
and genetic algorithms, and dynamic programming are presented.
They are used in exact or heuristic procedures to solve the
introduced complex scheduling problems. Furthermore, methods for
calculating lower bounds are described. Most algorithms are
formulated in detail and illustrated with examples.
Written for:
Researchers, graduate students
Table of contents
2006, XVI, 368 p. 5 illus., Hardcover
ISBN: 0-387-29851-7
About this textbook
Undergraduate courses in mathematics are commonly of two types.
On the one hand are courses in subjects - such as linear algebra
or real analysis - with which it is considered that every student
of mathematics should be acquainted. On the other hand are
courses given by lecturers in their own areas of specialization,
which are intended to serve as a preparation for research. But
after taking courses of only these two types, students might not
perceive the sometimes surprising interrelationships and
analogies between different branches of mathematics, and students
who do not go on to become professional mathematicians might
never gain a clear understanding of the nature and extent of
mathematics. The two-volume Number Theory: An Introduction to
Mathematics attempts to provide such an understanding of the
nature and extent of mathematics. It is a modern introduction to
the theory of numbers, emphasizing its connections with other
branches of mathematics. Part A, which should be accessible to a
first-year undergraduate, deals with elementary number theory.
Part B is more advanced than the first and should give the reader
some idea of the scope of mathematics today. The connecting theme
is the theory of numbers. By exploring its many connections with
other branches, we may obtain a broad picture.
Written for:
Undergraduate students in mathematics and engineering
Table of contents
Preface.- The Expanding Universe of Numbers.- Divisibility.- More
on Divisibility.- Continued Fractions and their Uses.- Hadamardfs
Determinant Problem.- Henselfs P-Adic Numbers.- Notations.-
Axioms.- Index.
2006, Approx. 375 p. 5 illus., Hardcover
ISBN: 0-387-29853-3
About this textbook
Undergraduate courses in mathematics are commonly of two types.
On the one hand are courses in subjects - such as linear algebra
or real analysis - with which it is considered that every student
of mathematics should be acquainted. On the other hand are
courses given by lecturers in their own areas of specialization,
which are intended to serve as a preparation for research. But
after taking courses of only these two types, students might not
perceive the sometimes surprising interrelationships and
analogies between different branches of mathematics, and students
who do not go on to become professional mathematicians might
never gain a clear understanding of the nature and extent of
mathematics. The two-volume Number Theory: An Introduction to
Mathematics attempts to provide such an understanding of the
nature and extent of mathematics. It is a modern introduction to
the theory of numbers, emphasizing its connections with other
branches of mathematics. Part A, which should be accessible to a
first-year undergraduate, deals with elementary number theory.
Part B is more advanced than the first and should give the reader
some idea of the scope of mathematics today. The connecting theme
is the theory of numbers, at first sight one of the most abstruse
and irrelevant branches of mathematics. Yet by exploring its many
connections with other branches, we may obtain a broad picture.
Written for:
Undergraduate students in mathematics and engineering
Table of contents
The Arithmetic of Quadratic Forms.- The Geometry of Numbers.- The
Number of Prime Numbers.- A Character Study.- Uniform
Distribution and Ergodic Theory.- Elliptic Functions.-
Connections with Number Theory.- Notations.- Axioms.- Index.