Series: Springer Series in Statistics
2006, XVI, 496 p., Hardcover.
ISBN: 0-387-32909-9
Due: August 2006
About this book
Many important statistical topics involve finite mixture models.
The area of potential applications extends beyond simple data
analysis to regression analysis and to non-linear time series
analysis using Markov switching models.
Recent years have seen the emergence of powerful computational
tools for dealing with these models which combine a Bayesian
approach with recent Monte simulation techniques based on Markov
chains. This book reviews these techniques and covers the most
recent advances in the field, among them bridge sampling
techniques and reversible jump Markov chain Monte Carlo methods.
Table of contents
Finite mixture modelling.- Statistical inference for a finite
mixture model with known number of components.- Practical
bayesian inference for a finite mixture model with known number
of components.- Statistical inference for finite mixture models
under model specification uncertainty.- Computational tools for
Bayesian inference for finite mixture models under model
specification uncertainty.- Finite mixture models with normal
components.- Data analysis based on finite mixtures.- Finite
mixtures of regression models.- Finite mixture models with non-normal
components.- Finite Markov mixture modelling.- Statistical
inference for Markov switching models.- Non-linear time series
analysis based on Markov switching models.- Switching state space
models.
2006, Approx. 535 p., 40 illus., Hardcover.
ISBN: 3-540-20441-5
Due: August 2, 2006
About this book
The cultural historian Theodore Merz called it the great book
with seven seals, the mathematician Leopold Kronecker, "the
book of all books" : already one century after their
publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) had
acquired an almost mythical reputation. It had served throughout
the XIX th century and beyond as an ideal of exposition in
matters of notation, problems and methods; as a model of
organisation and theory building; and of course as a source of
mathematical inspiration. Various readings of the Disquisitiones
Arithmeticae have left their mark on developments as different as
Galois's theory of algebraic equations, Lucas's primality tests,
and Dedekind's theory of ideals.
The present volume revisits successive periods in the reception
of the Disquisitiones: it studies which parts were taken up and
when, which themes were further explored. It also focuses on how
specific mathematicians reacted to Gauss's book: Dirichlet and
Hermite, Kummer and Genocchi, Dedekind and Zolotarev, Dickson and
Emmy Noether, among others. An astounding variety of research
programmes in the theory of numbers can be traced back to it.
The 18 authors - mathematicians, historians, philosophers - who
have collaborated on this volume contribute in-depth studies on
the various aspects of the bicentennial voyage of this
mathematical text through history, and the way that the number
theory we know today came into being.
Written for:
Researchers and students interested in the history of
mathematics, number theory, Gauss.
Table of contents
I. A Book’s History. ? C. Goldstein, N. Schappacher. II.
Algebraic Equations, Quadratic Forms, Higher Congruences: Key
Mathematical Techniques of the Disquistiones. - O. Neumann: The
Disquisitiones Arithmeticae and the Theory of Equations.- H.M.
Edwards: Composition of Binary Quadratic Forms and the
Foundations of Mathematics.- D. Fenster, J. Schwermer:
Composition of Quadratic Forms: An Algebraic Perspective.- G.
Frei: Gauss’s Unpublished Section Eight: On the Way to Function
Fields over a Finite Field.- III. The German Reception of the
Disquisitiones Arithmeticae: Institutions and Ideas. ? H. Pieper:
A Network of Scientific Philanthropy: Humboldt’s Relations with
Number Theorists.- J. Ferreiros: The Rise of Pure Mathematics as
Arithmetic after Gauss.- IV. Complex Numbers and Complex
Functions in Arithmetic.- R. Bolling: From Reciprocity Laws to
Ideal Numbers: An (Un)Known 1844 Manuscript by E.E. Kummer.- C.
Houzel: Elliptic Functions and Arithmetic. V. Numbers as Model
Objects of Mathematics.- J. Boniface: The Concept of Number from
Gauss to Kronecker.- B. Petri, N. Schappacher: On Arithmetization.
VI. Number Theory in France in the Second Half of the Nineteenth
Century.- C. Goldstein: Hermitian Forms of Reading the
Disquisitiones Arithmeticae.- A.-M. Decaillot: Number Theory at
the Association francaise pour l’avancement des sciences.- VII.
Spotlighting Some Later Reactions.- A. Brigaglia: An Overview on
Italian Arithmeitc after the Disquistiones Arithmeticae. P.
Piazza: Zolotarev’s Theory of Algebraic Numbers.- D. Fenster:
Gauss Goes West: The Reception of the Disquistiones Arithmeticae
in the USA. VIII. Gauss’s Theorem in the Long Run: Three Case
Studies.- J. Schwermer: Reduction Theory of Quadratic Forms:
Toward Raumliche Anschauung in Minkowski’s Early Work.- S. J.
Patterson: Gauss Sums.- F. Lemmermeyer: The Principal Genus
Theorem.- List of Illustrations.- Index.- Author’s Addresses.
2006, Approx. 195 p., Hardcover.
ISBN: 1-4020-5035-6
Due: August 2006
About this book
If you have not heard about cohomology, this book may be suited
for you. Fundamental notions in cohomology for examples,
functors, representable functors, Yoneda embedding, drived
functors, spectral sequences, derived categories are explained in
elementary fashion. Applications to sheaf cohomology is given.
Also cohomological aspects of D-modules and of the computation of
zeta functions of the Weierstrass family are provided.
Written for:
Undergraduate students who are interested in grasping the
fundamental notions used in Algebraic Geometry and Algebraic
Analysis. Even mature mathematicians may enjoy observing the
interplay among Category Theory, Sheaf Cohomology, Zeta
Invariants and D-Modules.
Table of contents
Preface; 1. Category.- Derived Functors.- Spectral Sequences.-
Derived Categories.- Cohomological Aspects of Algebraic Geometry
and Algebraic Analysis.- References.- Epilogue.- Index.
2007, Approx. 250 p., Hardcover.
ISBN: 0-387-33883-7
Due: September 2006
About this book
Cryptographic solutions using software methods can be used for
those security applications where data traffic is not too large
and low encryption rate is tolerable. On the other hand, hardware
methods offer high-speed solutions making them highly suitable
for applications where data traffic is fast and large data is
required to be encrypted in real time. VLSI (also known as ASIC),
and FPGAs (Field Programmable Gate Arrays) are two alternatives
for implementing cryptographic algorithms in hardware. FPGAs
offer several benefits for cryptographic algorithm
implementations over VLSI as they offer high flexibility. Due to
its reconfigurable property, keys can be changed rapidly.
Moreover, basic primitives in most cryptographic algorithms can
efficiently be implemented in FPGAs.
Since the invention of the Data Encryption Standard (DES), some
40 years ago, a considerable amount of cryptographic algorithm
implementation literature has been produced both, for software
and hardware platforms. Unfortunately, virtually there exists no
book explaining how the main cryptographic algorithms can be
implemented on reconfigurable hardware devices.
This book will cover the study of computational methods, computer
arithmetic algorithms, and design improvement techniques needed
to implement efficient cryptographic algorithms in FPGA
reconfigurable hardware platforms. The concepts and techniques to
be reviewed in this book will make special emphasis on the
practical aspects of reconfigurable hardware design, explaining
the basic mathematics related and giving a comprehensive
description of state-of-the-art implementation techniques. Thus,
the main goal of this monograph is to show how high-speed
cryptographic algorithms implementations can be achieved on
reconfigurable hardware devices without posing prohibited high
requirements for hardware resources.
Written for:
Professionals in technical areas related to Computer Engineering
and networks in network security, graduate students in Computer
Engineering and Communications
Table of contents
Introduction.- A Brief Introduction to Modern Cyptography.-
Reconfigurable Hardware Technology.- Mathematical Background.-
Prime Finite Field Arithmetic.- Binary Finite Field Arithmetic.-
Reconfigurable Hardware Implementation of Hash Functions.-
General Guidelines for Implementing Block Ciphers in FPGAs.-
Architectural Designs for Advanced Encryption Standard.- Elliptic
Curve Cryptography.
Series: Universitext
2006, Approx. 450 p., Softcover.
ISBN: 3-540-34457-8
Due: August 2, 2006
About this textbook
This comprehensive two-volume textbook presents presents the
whole area of Partial Differential Equations - of the elliptic,
parabolic, and hyperbolic type - in two and several variables.
Special emphasis is put on the connection of PDEs and complex
variable methods.
In this first volume the following topics are treated:
Integration and differentiation on manifolds, Functional analytic
foundations, Brouwer's degree of mapping, Generalized analytic
functions, Potential theory and spherical harmonics, Linear
partial differential equations. While we solve the partial
differential equations via integral representations in this
volume, we shall present functional analytic solution methods in
the second volume.
This textbook can be chosen for a course over several semesters
on a medium level. Advanced readers may study each chapter
independently from the others.
Written for:
Advanced undergraduate and graduate students as well as
researchers in mathematics
Table of contents
Differentiation and Integration on Manifolds.- Foudations of
Functional Analysis.- Brouwer´s Degree of Mapping with Geometric
Applications.- Generalized Analytic Functions.- Potential Theory
and Spherical Harmonics.- Linear Partial Differential Equations
in Rn.
Series: Universitext
2006, Approx. 400 p., Softcover.
ISBN: 3-540-34461-6
Due: August 2, 2006
About this textbook
This comprehensive two-volume textbook presents presents the
whole area of Partial Differential Equations - of the elliptic,
parabolic, and hyperbolic type - in two and several variables.
Special emphasis is put on the connection of PDEs and complex
variable methods.
In this second volume we the following topics are treated:
Solvability of operator equations in Banach spaces, Linear
operators in Hilbert spaces and spectral theory, Schauder's
theory of linear elliptic differential equations, Weak solutions
of differential equations, Nonlinear partial differential
equations and characteristics, Nonlinear elliptic systems with
differential-geometric applications. While partial differential
equations are solved via integral representations in the
preceding volume, functional analytic methods are used in this
volume.
This textbook can be chosen for a course over several semesters
on a medium level. Advanced readers may study each chapter
independently from the others.
Table of contents
Operators in Banach Spaces.- Linear Operators in Hilbert Spaces.-
Linear Elliptic Differential Equations.- Weak Solutions of
Elliptic Differential Equations.- Nonlinear Partial Differential
Equations.- Nonlinear Elliptic Systems.