Series: Lecture Notes in Mathematics , Vol. 1907
2007, Approx. 220 p., Softcover
ISBN: 978-3-540-71224-4
About this book
Although, bifurcation theory of equations with autonomous and
periodic time dependence is a major object of research in the
study of dynamical systems since decades, the notion of a
nonautonomous bifurcation is not yet established. In this book,
two different approaches are developed which are based on special
definitions of local attractivity and repulsivity. It is shown
that these notions lead to nonautonomous Morse decompositions,
which are useful to describe the global asymptotic behavior of
systems on compact phase spaces. Furthermore, methods from the
qualitative theory for linear and nonlinear systems are derived,
and nonautonomous counterparts of the classical one-dimensional
autonomous bifurcation patterns are developed.
Table of contents
Introduction.- Preliminaries.- Notions of Attractivity
Repulsivity, Bifurcation and Transition.- Nonautonomous Morse
Decompositions.- Linear Systems.- Nonlinear Systems.-
Bifurcations in Dimension One.- Bifurcations of Asymptotically
Autonomous Systems.- Appendix.- Bibliography
Series: Information Security and Cryptography
2007, Approx. 380 p., Hardcover
ISBN: 978-3-540-49243-6
About this textbook
Due to the rapid growth of digital communication and electronic
data exchange, information security has become a crucial issue in
industry, business, and administration. Modern cryptography
provides essential techniques for securing information and
protecting data.
In the first part, this book covers the key concepts of
cryptography on an undergraduate level, from encryption and
digital signatures to cryptographic protocols. Essential
techniques are demonstrated in protocols for key exchange, user
identification, electronic elections and digital cash. In the
second part, more advanced topics are addressed, such as the bit
security of one-way functions and computationally perfect
pseudorandom bit generators. The security of cryptographic
schemes is a central topic. Typical examples of provably secure
encryption and signature schemes and their security proofs are
given. Though particular attention is given to the mathematical
foundations, no special background in mathematics is presumed.
The necessary algebra, number theory and probability theory are
included in the appendix. Each chapter closes with a collection
of exercises.
The second edition contains corrections, revisions and new
material, including a complete description of the AES, an
extended section on cryptographic hash functions, a new section
on random oracle proofs, and a new section on public-key
encryption schemes that are provably secure against adaptively-chosen-ciphertext
attacks.
Table of contents
Introduction.- Symmetric-Key Encryption.- Public-Key Cryptography.-
Cryptographic Protocols.- Probabilistic Algorithms.- One-Way
Functions and the Basic Assumptions.- Bit Security of One-Way
Functions.- One-Way Functions and Pseudorandomness.- Provably
Secure Encryption.- Provably Secure Digital Signatures.- Algebra
and Number Theory.- Probabilities and Information Theory.-
References.- Index
Series: Lecture Notes in Mathematics
Subseries: Ecole d'Ete Probabilit.Saint-Flour , Vol. 1897
2007, VIII, 145 p., Softcover
ISBN: 978-3-540-48510-0
About this book
Levy processes, i.e. processes in continuous time with stationary
and independent increments, are named after Paul Levy, who made
the connection with infinitely divisible distributions and
described their structure. They form a flexible class of models,
which have been applied to the study of storage processes,
insurance risk, queues, turbulence, laser cooling, ... and of
course finance, where the feature that they include examples
having "heavy tails" is particularly important. Their
sample path behaviour poses a variety of difficult and
fascinating problems. Such problems, and also some related
distributional problems, are addressed in detail in these notes
that reflect the content of the course given by R. Doney in St.
Flour in 2005.
Table of contents
1.Introduction to Levy processes.- 2.Subordinators.- 3.Local
times and excursions.- 4.Ladder processes and the Wiener-Hopf
factorisation.- 5.Further Wiener-Hopf developments.- 6.Creeping
and related questions.- 7.Spitzer’s Condition.- 8.Levy
processes conditioned to stay positive.- 9.Spectrally negative L´evy
processes.- 10.Small
Series: International Mathematical Series , Vol. 5
Volume package Mathematical Problems from Applied Logic
2007, XXX, 354 p., Hardcover
ISBN: 978-0-387-69244-9
About this book
"Mathematical Problems from Applied Logic II" presents
chapters from selected, world renowned, logicians. Important
topics of logic are discussed from the point of view of their
further development in light of requirements arising from their
successful application in areas such as Computer Science and AI
language. Fields covered include: logic of provability,
applications of computability theory to biology, psychology,
physics, chemistry, economics, and other basic sciences;
computability theory and computable models; logic and space-time
geometry; hybrid systems; logic and region-based theory of space.
Table of contents
On Two Models of Provability: Provability Logic, Logic of Proofs.-
Directions for Computability Theory Beyond Pure Mathematical:
Motivations, Directions, Progress So Far And How One Might Go
From Here.- Computability and Computable Models: Preliminaries,
Bounds for Computable Models, Structure Complexity of Computable
Models, Isomorphism Problem, Classes of Computable Models and
Index Sets.- First-order Logic Foundation of Relativity Theories:
Introduction (Logic and Spacetime Geometry), More Concrete
Introduction (Foundation of Spacetime), Intriguing Features of GR
Spacetimes (Challenges for the Logician), A FOL Axiom System of
SR Extended with Accelerated Observers, One Step toward GR (Effect
of Gravitation on Clocks), Questions, Suggestions for Future
Research.- Beyond Hybrid Systems: Digital Programs, Continuous
Plants and Controllers, Hybrid Systems, Discretization,
Continualization, Methodology.- Region-Based Theory of Space:
Algebras of Regions, Representation Theory, and Logics:
Historical Excursion in the Region-Based Theory of Space,
Algebras of Regions, Models, and Representation Theory, Region-Based
Propositional Modal Logics of Space.
2007, Approx. 380 p., Softcover
ISBN: 978-0-387-70784-6
About this textbook
The authors present tools and concepts of multivariate data
analysis by means of exercises and their solutions. The first
part is devoted to graphical techniques. The second part deals
with multivariate random variables and presents the derivation of
estimators and tests for various practical situations. The last
part introduces a wide variety of exercises in applied
multivariate data analysis. The book demonstrates the application
of simple calculus and basic multivariate methods in real life
situations. It contains altogether 234 solved exercises which can
assist a university teacher in setting up a modern multivariate
analysis course. All computer-based exercises are available in
the R or XploRe languages. The corresponding libraries are
downloadable from the Springer link web pages and from the author’s
home pages.
Table of contents
Comparison of batches.- A short excursion into matrix algebra.-
Moving to higher dimensions.- Multivariate distributions.- Theory
of the multinormal.- Theory of estimation.- Hypothesis testing.-
Decomposition of data matrices by factors.- Principal components
analysis.- Factor analysis.- Cluster analysis.- Discriminate
analysis.- Correspondence analysis.- Canonical correlation
analysis.- Multidimensional scaling.- Conjoint measurement
analysis.- Applications in finance.- Highly interactive,
computationally intensive techniques.
Series: Undergraduate Texts in Mathematics
2007, Approx. 345 p., 65 illus., Hardcover
ISBN: 978-0-387-69315-6
About this textbook
Intended for an honors calculus course or for an introduction to
analysis, this is an ideal text for undergraduate majors since it
covers rigorous analysis, computational dexterity, and a breadth
of applications. The book contains many remarkable features: *
complete avoidance of /epsilon-/delta arguments by using
sequences instead * definition of the integral as the area under
the graph, while area is defined for every subset of the plane *
complete avoidance of complex numbers * heavy emphasis on
computational problems * applications from many parts of
analysis, e.g. convex conjugates, Cantor set, continued
fractions, Bessel functions, the zeta functions, and many more *
344 problems with solutions in the back of the book.
Table of contents
The Set of Real Numbers.- Continuity.- Differentiation.-
Integration.- Applications.- Solutions.- References.- Index.
Series: Lecture Notes in Mathematics , Vol. 1898
2007, XIV, 283 p., Softcover
ISBN: 978-3-540-71128-5
About this book
The present volume is self-contained and introduces to the
treatment of linear and nonlinear (quasi-linear) abstract
evolution equations by methods from the theory of strongly
continuous semigroups. The theoretical part is accessible to
graduate students with basic knowledge in functional analysis.
Only some examples require more specialized knowledge from the
spectral theory of linear, self-adjoint operators in Hilbert
spaces. Particular stress is on equations of the hyperbolic type
since considerably less often treated in the literature. Also,
evolution equations from fundamental physics need to be
compatible with the theory of special relativity and therefore
are of hyperbolic type. Throughout, detailed applications are
given to hyperbolic partial differential equations occurring in
problems of current theoretical physics, in particular to
Hermitian hyperbolic systems. This volume is thus also of
interest to readers from theoretical physics.
Table of contents
Preface- 1.Conventions.- 2.Mathematical Introduction.-3.Prerequisites.-
4.Strongly Continuous Semigroups.- 5.Examples of Generators of
Strongly Continuous Semigroups.- 6.Intertwining Relations,
Operator Homomorphisms.- 7.Examples of Constrained Systems.- 8.Kernels,
Chains, and Evolution Operators.- 9.The Linear Evolution Equation.-10
Examples of Linear Evolution Equations.-11.The Quasi-Linear
Evolution Equation.-12.Examples of Quasi-Linear Evolution
Equations.- 13.Appendix.- References.- Index of Notation.- Index
of Terminology.