Taschner, Rudolf
The Continuum
A Constructive Approach to Basic Concepts of Real Analysis
2005. xi, 136 pp. Hardc.
ISBN: 3-8348-0040-6 - Sofort lieferbar
In this small text the basic theory of the continuum, including
the elements of metric space theory and continuity is developed
within the system of intuitionistic mathematics in the sense of L.E.J.
Brouwer and H. Weyl. The main features are proofs of the famous
theorems of Brouwer concerning the continuity of all functions
that are defined on "whole" intervals, the uniform
continuity of all functions that are defined on compact
intervals, and the uniform convergence of all pointwise
converging sequences of functions defined on compact intervals.
The constructive approach is interesting both in itself and as a
contrast to, for example, the formal axiomatic one.
Introduction and Historical Remarks - Real Numbers - Metric
Spaces - Continuous Functions
- Advanced Undergraduate / Graduate Students in Mathematics
- Lecturers in Mathematics (Real Analysis)
- Academic Logicians, Mathematicians, Philosophers
- Interested Teachers in Mathematics
Rudolf Taschner is Professor of Mathematics at the "Institute
for Analysis and Scientific Computing", Technical University
Vienna, Austria. In his recent book "Der Zahlen gigantische
Schatten" (Vieweg 2004) he describes how intensively numbers
penetrate the aspects of our life, and how far the "shadows
of numbers" reach.
Table of contents
edited by Herbert Heyer (University of Tubingen, Germany), Takeshi Hirai (Kyoto University, Japan), Takeshi Kawazoe (Keio University, Japan) & Kimiaki Saito (Meijo University, Japan)
INFINITE DIMENSIONAL HARMONIC ANALYSIS III
Proceedings of the Third German-Japanese Symposium University of
Tubingen, Germany 15 - 20 September 2003
This volume contains contributions on recent results in
infinite dimensional harmonic analysis and its applications to
probability theory. Some papers deal with purely analytic topics
such as Frobenius reciprocity, diffeomorphism groups, equivariant
fibrations and Harish?Chandra modules. Several other papers touch
upon stochastic processes, in particular Levy processes. The
majority of the contributions emphasize on the algebraic-topological
aspects of the theory by choosing configuration spaces, locally
compact groups and hypergroups as their basic structures. The
volume provides a useful survey of innovative work pertaining to
a highly actual section of modern analysis in its pure and
applied shapings.
Contents:
Recent Developments on Harmonic Forms and L2-Betti Numbers of
Infinite Configuration Spaces with Poisson Measures (S Albeverio
& A Daletsukii)
Une Reciprocite de Frobenius (H Fujiwara)
Markov Property of Monotone Levy Processes (U Franz & N
Muraki)
Geometric Properties of the Set of Extensions of a Stochastic
Matrix (R Gohm)
Heat Kernel Analysis on Infinite Dimensional Groups (M Gordina)
On Infinite Divisibility and Embedding of Probability Measures on
a Locally Compact Abelian Group (H Heyer & G Pap)
White Noise Analysis, Filtering Equation and the Index Theorem
for Families (R Leandre)
Admissible White Noise Operators and Their Quantum White Noise
Derivatives (U C Ji & N Obata)
PDE Approach to Invariant and Gibbs Measures with Applications (M
Rockner)
An Infinite Dimensional Laplacian Acting on Multiple Wiener
Integrals by Some Levy Process (K Saito)
Levy Processes on Deformations of Hopf Algebras (M Schurmann)
An Application of the Method of Moments in Random Matrix Theory (M
Stolz)
and other papers
Readership: Researchers in the fields of probability and
statistics and mathematical physics.
368pp Pub. date: Nov 2005
ISBN 981-256-593-0
edited by Eusebius J Doedel (Concordia University, Canada), Gabor Domokos (Budapest University
of Technology and Economics, Hungary) & Ioannis G Kevrekidis (Princeton
University, USA)
MODELING AND COMPUTATIONS IN DYNAMICAL SYSTEMS
Dedicated to John von Neumann
The Hungarian born mathematical genius, John von Neumann, was
undoubtedly one of the greatest and most influential scientific
minds of the 20th century. Von Neumann made fundamental
contributions to Computing and he had a keen interest in
Dynamical Systems, specifically Hydrodynamic Turbulence. This
book, offering a state-of-the-art collection of papers in
computational dynamical systems, is dedicated to the memory of
von Neumann. Including contributions from J E Marsden, P J
Holmes, M Shub, A Iserles, M Dellnitz and J Guckenheimer, this
book offers a unique combination of theoretical and applied
research in areas such as geometric integration, neural networks,
linear programming, dynamical astronomy, chemical reaction
models, structural and fluid mechanics.
Contents:
Transport in Dynamical Astronomy and Multibody Problems (M
Dellnitz et al.)
A Brief Survey on the Numerical Dynamics for Functional
Differential Equations (B M Garay)
Bifurcations and Continuous Transitions of Attractors in
Autonomous and Nonautonomous Systems (P E Kloeden & S
Siegmund)
A Survey of Methods for Computing (Un)Stable Manifolds of Vector
Fields (B Krauskopf et al.)
Commutators of Skew-Symmetric Matrices (A M Bloch & A Iserles)
Simple Neural Networks That Optimize Decisions (E Brown et al.)
Newton Flow and Interior Point Methods in Linear Programming (J-P
Dedieu & M Shub)
Numerical Continuation of Branch Points of Equilibria and
Periodic Orbits (E J Doedel et al.)
Coarse-Grained Observation of Discretized Maps (G Domokos)
Multiple Helical Perversions of Finite, Intristically Curved Rods
(G Domokos & T J Healey)
Bifurcations of Stable Sets in Noninvertible Planar Maps (J P
England et al.)
Multiparametric Bifurcations in an Enzyme-Catalyzed Reaction
Model (E Freire et al.)
Straightforward Computation of Spatial Equilibria of
Geometrically Exact Cosserat Rods (T J Healey & P G Mehta)
Multiparameter Parallel Search Branch Switching (M E Henderson)
Equation-Free, Effective Computation for Discrete Systems: A Time
Stepper Based Approach (J Moller et al.)
Model Reduction for Fluids, Using Balanced Proper Orthogonal
Decomposition (C W Rowley)
Bifurcation Tracking Algorithms and Software for Large Scale
Applications (A G Salinger et al.)
An Algorithm for Finding Invariant Algebraic Curves of a Given
Degree for Polynomial Planar Vector Fields (G Swirszcz)
Readership: Graduate students and scientists interested in
applied and computational mathematics, dynamical systems,
mechanics and related areas.
360pp (approx.) Pub. date: Scheduled Winter 2005
ISBN 981-256-596-5
edited by Alberto Facchini (Universita di Padova, Italy), Kent Fuller (University of Iowa, USA), Claus
M Ringel (Universitat Bielefeld, Germany) & Catarina Santa-Clara (Universidade
de Lisboa, Portugal)
ALGEBRAS, RINGS AND THEIR REPRESENTATIONS
Proceedings of the International Conference Lisbon, Portugal 14 -
18 July 2003
Surveying the most influential developments in the field, this
proceedings reviews the latest research on algebras and their
representations, commutative and non-commutative rings, modules,
conformal algebras, and torsion theories.
The volume collects stimulating discussions from world-renowned
names including Tsit-Yuen Lam, Larry Levy, Barbara Osofsky, and
Patrick Smith.
Contents:
Krull Monoids and Their Application in Module Theory (A Facchini)
Infinite Progenerator Sums (A Facchini & L S Levy)
Quadratic Algebras of Skew Type (E Jespers & J Okninski)
Representation Type of Commutative Noetherian Rings (Introduction)
(L Klingler & L S Levy)
Corner Ring Theory: A Generalization of Peirce Decompositions (T-Y
Lam)
Quasideterminants and Right Roots of Polynomials Over Division
Rings (B L Osofsky)
Injective Dimension Relative to a Torsion Theory (P F Smith)
and other papers
Readership: Algebraists, mathematicians interested in the
connections between algebra and other fields, and graduate
students interested in algebra.
350pp (approx.) Pub. date: Scheduled Spring 2006
ISBN 981-256-598-1
by Doug Hensley (Texas A&M University, USA)
CONTINUED FRACTIONS
The Euclidean algorithm is one of the oldest in mathematics,
while the study of continued fractions as tools of approximation
goes back at least to Euler and Legendre. While our understanding
of continued fractions and related methods for simultaneous
diophantine approximation has burgeoned over the course of the
past decade and more, many of the results have not been brought
together in book form. Continued fractions have been studied from
the perspective of number theory, complex analysis, ergodic
theory, dynamic processes, analysis of algorithms, and even
theoretical physics, which has further complicated the situation.
This book places special emphasis on continued fraction Cantor
sets and the Hausdorff dimension, algorithms and analysis of
algorithms, and multi-dimensional algorithms for simultaneous
diophantine approximation. Extensive, attractive computer-generated
graphics are presented, and the underlying algorithms are
discussed and made available.
Contents:
Generalizations of the gcd and the Euclidean Algorithm
Continued Fractions with Small Partial Quotients
Ergodic Theory
Complex Continued Fractions
Multi-Dimensional Diophantine Approximation
Powers of an Algebraic Integer
Marshall Hallfs Theorem
Functional-Analytic Techniques
The Generating Function Method
Conformal Iterated Function Systems
Convergence of Continued Fractions
Readership: Graduate students and researchers in pure and applied
mathematics.
250pp (approx.) Pub. date: Scheduled Spring 2006
ISBN 981-256-477-2