Part of Lecture Notes in Logic
Publication planned for: May 2017
availability: Not yet published - available from May 2017
format: Hardback
isbn: 9781107014527
Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.
Contains original results which use methods from finite model theory to show the interaction between graph theory and computational complexity
Includes a wealth of new results, not previously published
Provides a reference for future research in this area
1. Introduction
Part I. The Basic Theory:
2. Background from graph theory and logic
3. Descriptive complexity
4. Treelike decompositions
5. Definable decompositions
6. Graphs of bounded tree width
7. Ordered treelike decompositions
8. 3-Connected components
9. Graphs embeddable in a surface
Part II. Definable Decompositions of Graphs with Excluded Minors:
10. Quasi-4-connected components
11. K5-minor free graphs
12. Completions of pre-decompositions
13. Almost planar graphs
14. Almost planar completions
15. Almost embeddable graphs
16. Decompositions of almost embeddable graphs
17. Graphs with excluded minors
18. Bits and pieces
Appendix. Robertson and Seymour's version of the local structure theorem
References
Symbol index
Index.
***
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: January 2018
availability: Not yet published - available from January 2018
format: Hardback
isbn: 9781107162624
This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.
Traces the theory of Banach spaces from its origins to the present day
Proves all the results from scratch
Highlights how classical and harmonic analysis, and probability, interact with the theory of Banach spaces
Preface
1. Euclidean sections
2. Separable Banach spaces without the approximation property
3. Gaussian processes
4. Reflexive subspaces of L1
5. The method of selectors. Examples of its use
6. The Pisier space of almost surely continuous functions. Applications
Appendix. News in the theory of infinite-dimensional Banach spaces in the past twenty years G. Godefroy
An update on some problems in high dimensional convex geometry and related probabilistic results O. Guedon
A few updates and pointers G. Pisier
On the mesh condition for Sidon sets L. Rodriguez-Piazza
Bibliography
Author index
Notation index
Subject index.
August 15, 2017
Reference - 300 Pages - 180 B/W Illustrations
ISBN 9781138053816
Several books are available on the subject of wavelet theory and applications but (to the best of the author’s knowledge) there is no book in which partial as well as fractional order differential equations occurring in physical problems has been studied
The solution and analysis of real physical models through modelling of differential equations is the main attention of this book
The target readers are post graduates and researchers as well as scientists and engineers
It is particularly suitable for research in the direction of applications of wavelet method and fractional differential equations
It may be included in the curriculum of most science and engineering students all over the world
Summary
The main focus of the book is to implement wavelet based transform methods for solving the problem of fractional order partial differential equations arising in modelling real physical phenomena. This book explores the analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.
Numerous Analytical and Numerical Methods. Numerical Solution of Partial Differential Equations by Haar Wavelet Method. Numerical Solution of System of Partial Differential Equations. Numerical Solution of Fractional Differential Equations by Haar Wavelet Method. Application of Legendre Wavelet Methods for Numerical Solution of Fractional Differential Equations. Application of Chebyshev Wavelet Methods for Numerical Simulation of Fractional Differential Equations. Application of Hermite Wavelet Method for Numerical Simulation of Fractional Differential Equations. Implementation of Petrov-Galerkin Method for Solving Fractional Differential Equations.
Zurich Lectures in Advanced Mathematics
ISBN print 978-3-03719-173-6,
March 2017, 160 pages, softcover, 17.0 x 24.0 cm.
A classical topic in Mathematical Finance is the theory of portfolio optimization. Robert Merton's work from the early seventies had enormous impact on academic research as well as on the paradigms guiding practitioners.
One of the ramifications of this topic is the analysis of (small) proportional transaction costs, such as a Tobin tax. The lecture notes present some striking recent results of the asymptotic dependence of the relevant quantities when transaction costs tend to zero.
An appealing feature of the consideration of transaction costs is that it allows for the first time to reconcile the no arbitrage paradigm with the use of non-semimartingale models, such as fractional Brownian motion. This leads to the culminating theorem of the present lectures which roughly reads as follows: for a fractional Brownian motion stock price model we always find a shadow price process for given transaction costs. This process is a semimartingale and can therefore be dealt with using the usual machinery of mathematical finance.
Keywords: Portfolio optimization, transaction costs, shadow price, semimartingale, fractional Brownian motion
EMS Series of Lectures in Mathematics
ISBN print 978-3-03719-172-9
March 2017, 138 pages, softcover, 17 x 24 cm.
This book deals with PDE models for chemotaxis (the movement of biological cells or organisms in response of chemical gradients) and hydrodynamics (viscous, homogeneous, and incompressible fluid filling the entire space). The underlying Keller?Segel equations (chemotaxis), Navier?Stokes equations (hydrodynamics), and their numerous modifications and combinations are treated in the context of inhomogeneous spaces of Besov?Sobolev type paying special attention to mapping properties of related nonlinearities. Further models are considered, including (deterministic) Fokker?Planck equations and chemotaxis Navier?Stokes equations.
These notes are addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of Besov-Sobolev type and interested in mathematical biology and physics.
Keywords: Function spaces of Besov?Sobolev type, chemotaxis, hydrodynamics, heat equations, Keller?Segel equations, Navier?Stokes equations
9781421422671
paperback 344pp
"In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."?Albert Einstein
The year was 1915, and the young mathematician Emmy Noether had just settled into Gottingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity. Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy. Knowing of her expertise in invariance theory, they requested Noether’s help. To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries?one of the most important pieces of mathematical reasoning ever developed.
Noether’s "first" and "second" theorem was published in 1918. The first theorem relates symmetries under global spacetime transformations to the conservation of energy and momentum, and symmetry under global gauge transformations to charge conservation. In continuum mechanics and field theories, these conservation laws are expressed as equations of continuity. The second theorem, an extension of the first, allows transformations with local gauge invariance, and the equations of continuity acquire the covariant derivative characteristic of coupled matter-field systems. General relativity, it turns out, exhibits local gauge invariance. Noether’s theorem also laid the foundation for later generations to apply local gauge invariance to theories of elementary particle interactions.