Series: Nonconvex Optimization and Its Applications, Vol. 80
2005, XXII, 396 p., Hardcover
ISBN: 0-387-28155-X
About this book
This book is devoted to the recent progress on the turnpike
theory. The turnpike property was discovered by Paul A.
Samuelson, who applied it to problems in mathematical economics
in 1949. These properties were studied for optimal trajectories
of models of economic dynamics determined by convex processes. In
this monograph the author, a leading expert in modern turnpike
theory, presents a number of results concerning the turnpike
properties in the calculus of variations and optimal control
which were obtained in the last ten years. These results show
that the turnpike properties form a general phenomenon which
holds for various classes of variational problems and optimal
control problems. The book should help to correct the
misapprehension that turnpike properties are only special
features of some narrow classes of convex problems of
mathematical economics.
Table of contents
Preface.- Introduction.- Infinite Horizon Variational Problems.-
Extremals of Nonautonomous Problems.- Extremals of Autonomous
Problems.- Infinite Horizon Autonomous Problems.- Turnpike for
Autonomous Problems.- Linear Periodic Control Systems.- Linear
Systems with Nonperiodic Integrands.- Discrete-Time Control
Systems.- Control Problems in Hilbert Spaces.- A Class of
Differential Inclusions.- Convex Processes.- A Dynamic Zero-Sum
Game.- Comments.- References.- Index.
2005, Approx. 700 p., Hardcover
ISBN: 3-540-25994-5
Due: December 2, 2005
About this book
Exploratory data analysis (EDA) is about detecting and describing
patterns, trends, and relations in data, motivated by certain
purposes of investigation. As something relevant is detected in
data, new questions arise, causing specific parts to be viewed in
more detail. So EDA has a significant appeal: it involves
hypothesis generation rather than mere hypothesis testing.
The authors describe in detail and systemize approaches,
techniques, and methods for exploring spatial and temporal data
in particular. They start by developing a general view of data
structures and characteristics and then build on top of this a
general task typology, distinguishing between elementary and
synoptic tasks. This typology is then applied to the description
of existing approaches and technologies, resulting not just in
recommendations for choosing methods but in a set of generic
procedures for data exploration.
Professionals practicing analysis will profit from tested
solutions ? illustrated in many examples ? for reuse in the
catalogue of techniques presented. Students and researchers will
appreciate the detailed description and classification of
exploration techniques, which are not limited to spatial data
only. In addition, the general principles and approaches
described will be useful for designers of new methods for EDA.
Table of contents
Introduction.- Data.- Tasks.- Tools.- General Principles.-
Conclusion.- Appendices, References.
Series: Probability and its Applications
2006, Approx. 400 p., Hardcover
ISBN: 3-540-28328-5
Due: December 2, 2005
About this book
The Malliavin calculus (or stochastic calculus of variations) is
an infinite-dimensional differential calculus on a Gaussian space.
Originally, it was developed to provide a probabilistic proof to
Hormander's "sum of squares" theorem, but it has found
a wide range of applications in stochastic analysis. This
monograph presents the main features of the Malliavin calculus
and discusses in detail its main applications. The author begins
by developing the analysis on the Wiener space, and then uses
this to establish the regularity of probability laws and to prove
Hormander's theorem. The regularity of the law of stochastic
partial differential equations driven by a space-time white noise
is also studied. The subsequent chapters develop the connection
of the Malliavin with the anticipating stochastic calculus,
studying anticipating stochastic differential equations and the
Markov property of solutions to stochastic differential equations
with boundary conditions.
The second edition of this monograph includes recent applications
of the Malliavin calculus in finance and a chapter devoted to the
stochastic calculus with respect to the fractional Brownian
motion.
Written for:
Researchers in stochastic analysis, mathematicians with a
background in probability theory who wish to learn Malliavin
calculus and their main applications
Keywords:
Anticipating stochastic calculus
Gaussian processes
Girsanov theorem
MSC (2000): 60H07, 60H10, 60H15, 60-02
Malliavin Calculus
Markov processes
Skorohod integral
Stochastic differential equations
Stochastic partial differential equations
1st ed. 1995. 2nd printing, 2005, XXVI, 622 p., Hardcover
ISBN: 1-4020-4215-9
About this book
This handbook covers a wealth of topics from number theory,
special attention being given to estimates and inequalities. As a
rule, the most important results are presented, together with
their refinements, extensions or generalisations. These may be
applied to other aspects of number theory, or to a wide range of
mathematical disciplines. Cross-references provide new insight
into fundamental research.
Audience: This is an indispensable reference work for specialists
in number theory and other mathematicians who need access to some
of these results in their own fields of research.
Table of contents
Preface. Basic Symbols. Basic Notations. I. Euler's phi-function.
II. The arithmetical function d(n), its generalizations and its
analogues. III. Sum-of-divisors function, generalizations,
analogues; Perfect numbers and related problems. IV. P, p, B,
beta and related functions. V. omega(n), Omega(n) and related
functions. VI. Function mu; k-free and k-full numbers. VII.
Functions pi(x), psi(x), theta(x), and the sequence of prime
numbers. VIII. Primes in arithmetic progressions and other
sequences. IX. Additive and diophantine problems involving primes.
X. Exponential sums. XI. Character sums. XII. Binomial
coefficients, consecutive integers and related problems. XIII.
Estimates involving finite groups and semi-simple rings. XIV.
Partitions. XV. Congruences, residues and primitive roots. XVI.
Additive and multiplicative functions. Index of authors.
Series: Graduate Texts in Mathematics, Vol. 158
2006, Approx. 330 p. 25 illus., Hardcover
ISBN: 0-387-27677-7
About this textbook
Intended for graduate courses or for independent study, this book
presents the basic theory of fields. The first part begins with a
discussion of polynomials over a ring, the division algorithm,
irreducibility, field extensions, and embeddings. The second part
is devoted to Galois theory. The third part of the book treats
the theory of binomials. The book concludes with a chapter on
families of binomials ? the Kummer theory.
This new edition has been completely rewritten in order to
improve the pedagogy and to make the text more accessible to
graduate students. The exercises have also been improved and a
new chapter on ordered fields has been included.
Table of contents
Preface.- Preliminaries.- Polynomials.- Field Extensions.-
Algebraic Independence.- Separability.- Galois Theory I.- Galois
Theory II.- A Field Extension as a Vector Space.- Finite Fields I:
Basic Properties.- Finite Fields II: Additional Properties.- The
Roots of Unity.- Cyclic Extensions.- Solvable Extensions.-
Binomials.- Families of Binomials.- Mobius Inversion.- References.-
Index of Symbols.- Index.
Series: Lecture Notes in Mathematics, Vol. 1872
2006, Approx. 260 p., Softcover
ISBN: 3-540-29162-8
Due: December 2, 2005
About this book
This volume introduces some basic mathematical models for cell
cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives
an overview of the modeling of the cell division cycle. Chapter 2
describes how tumor secretes growth factors to form new blood
vessels in its vicinity, which provide it with nutrients it needs
in order to grow. Chapter 3 explores the process that enables the
tumor to invade the neighboring tissue. Chapter 4 models the
interaction between a tumor and the immune system. Chapter 5 is
concerned with chemotherapy; it uses concepts from control theory
to minimize obstacles arising from drug resistance and from cell
cycle dynamics. Finally, Chapter 6 reviews mathematical results
for various cancer models.
Table of contents
Modeling the Cell Division Cycle (B. Aguda).- Angiogenesis - A
Biochemical/Mathematical Prospective (H. A. Levine and M. Nilsen-Hamilton).-
Spatio-Temporal Models of the uPA System and Tissue Invasion (G.
Lolas).- Mathematical Modeling of Spatio-Temporal Phenomena in
Tumor Immunology (M. Chaplain and A. Matzavinos).- Control Theory
Approach to Cancer Chemotherapy: Benefiting from Phase Dependence
and Overcoming Drug Resistance (M. Kimmel and A. Swierniak).-
Cancer Models and their Mathematical Analysis (A. Friedman).