Series: Applied Mathematical Sciences, Vol. 141
2011, XII, 419 p., Hardcover
ISBN: 978-1-4419-7894-3
Due: April 29, 2011
This volume is intended to carry on the program, initiated in Topology, Geometry, and Gauge Fields: Foundations (Springer, 2010), of exploring the interrelations between particle physics and topology that arise from their shared notion of a gauge field. The text begins with a synopsis of the geometrical background assumed of the reader (manifolds, Lie groups, bundles, connections, etc.). There follows a lengthy, and somewhat informal discussion of a number of the most basic of the classical gauge theories arising in physics, including classical electromagnetic theory and Dirac monopoles, the Klein-Gordon and Dirac equations and SU(2) Yang-Mills-Higgs theory. The real purpose here is to witness such things as spacetime manifolds, spinor structures, de Rham cohomology, and Chern classes arise of their own accord in meaningful physics. All of these are then developed rigorously in the remaining chapters. With the precise definitions in hand, one can, for example, fully identify magnetic charge and instanton number with the Chern numbers of the bundles on which the charge and instanton live, and uncover the obstruction to the existence of a spinor structure in the form of the second Stiefel-Whitney class. This second edition of the book includes, in an Appendix, a much expanded sketch of Seiberg-Witten gauge theory, including a brief discussion of its origins in physics and its implications for topology. To provide the reader with the opportunity to pause en route and join in the fun, there are 228 exercises, each an integral part of the development and each located at precisely the point at which it can be solved with optimal benefit.
gNaberfs goal is not to teach a sterile course on geometry and topology, but rather to enable us to see the subject in action, through gauge theory.h (SIAM Review)
gThe presentation c is enriched by detailed discussions about the physical interpretations of connections, their curvatures and characteristic classes. I particularly enjoyed Chapter 2 where many fundamental physical examples are discussed at great length in a reader friendly fashion. No detail is left to the readerfs imagination or interpretation. I am not aware of another source where these very important examples and ideas are presented at a level accessible to beginners.h (Mathematical Reviews)
2011, XVI, 236 p., Hardcover
ISBN: 978-1-4419-9475-2
Due: April 29, 2011
Almost Periodic Stochastic Processes is among the few published books that is entirely devoted to almost periodic stochastic processes and their applications. The topics treated range from existence, uniqueness, boundedness, and stability of solutions, to stochastic difference and differential equations. Motivated by the studies of the natural fluctuations in nature, this work aims to lay the foundations for a theory on almost periodic stochastic processes and their applications.
This book is divided in to eight chapters and offers useful bibliographical notes at the end of each chapter. Highlights of this monograph include the introduction of the concept of p-th mean almost periodicity for stochastic processes and applications to various equations. The book offers some original results on the boundedness, stability, and existence of p-th mean almost periodic solutions to (non)autonomous first and/or second order stochastic differential equations, stochastic partial differential equations, stochastic functional differential equations with delay, and stochastic difference equations. Various illustrative examples are also discussed throughout the book.
The results provided in the book will be of particular use to those conducting research in the field of stochastic processing including engineers, economists, and statisticians with backgrounds in functional analysis and stochastic analysis. Advanced graduate students with backgrounds in real analysis, measure theory, and basic probability, may also find the material in this book quite useful and engaging.
Keywords â exponential dichotomy - p-mean almost periodic process - stochastic difference equations - stochastic differential equations - stochastic functional differential equations with delay
Related subjects â Analysis - Dynamical Systems & Differential Equations - Probability Theory and Stochastic Processes
Preface.-1. Banach and Hilbert Spaces.-2. Bounded and Unbounded Linear Operators.- 3.An Introduction to Stochastic Differential Equations.-4. P-th Mean Almost Periodic Random Functions.-5. Existence Results for Some Stochastic Differential Equations.-6. Existence Results for Some Partial Stochastic Differential Equations.-7.Existence Results for Some Second-Order Stochastic Differential Equations.-8. Mean Almost Periodic Random Sequences and Their Applications to Stochastic Difference Equations.-References.-Index.
2011, VIII, 171 p. 22 illus., Hardcover
ISBN: 978-1-4419-8272-8
Due: May 29, 2011
Gravitation, electromagnetics and the two types of nuclear forces constitute the four fundamental forces of nature which regulate our everyday life. Amazingly, they are all described by a single idea of the 19th century proposed by Bernhard Riemann, and with the exception of gravitation, these ideas have been since confirmed by high energy experiments and cosmological observations. Geometry of the Fundamental Interactions - On Riemann's Legacy to High Energy Physics and Cosmology is a mathematical narrative of how we have come to agree on such a complex plot of nature, starting with the basic geometrical concepts and ending with hints on the perspective for cosmology.
This book originated from lectures given for several years to a mixed audience of mathematicians, physicists, astronomers, engineers, philosophers and sociologists seeking to understand the basics of those interactions and how the concept of Riemann curvature came to occupy such a central position in physics. The author takes on the challenge of making the path toward understanding both accessible and interesting to a wide audience.
Content Level â Research
Keywords â Minkowski's space time - Newton's space-time - Yang-Mills theory - coordinate symmetries - fiber bundles - noether's theorem - nonlinear scalar fields - search for unified field theories - three gauge interactions - vector and spinor fields
Related subjects â Algebra - Geometry & Topology - Particle and Nuclear Physics - Theoretical, Mathematical & Computational Physics
The Fundamental Interactions.- The Physical Manifold.- Symmetry.- The Algebra of Observables.- Geometry of Space-Times.- Scalar Fields.- Vector, Tensor, and Spinor Fields.- Noether's Theorem.- Bundles and Connections.- Gauge Field Theory.- Gravitation.
Series: Abel Symposia, Vol. 6
2011, 198 p. 1 illus. in color., Hardcover
ISBN: 978-3-642-19491-7
Due: May 2011
.The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field.
This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Soderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions.
The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.
Content Level â Research
Keywords â algebraic geometry - combinatorics - commutative algebra
Related subjects â Algebra
The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two: M.Boij, G.Floystad.- Koszul Cycles: W.Bruns, A.Conca, T.Romer.- Boij-Soderberg Theory: D.Eisenbud, F.-O.Schreyer.- Powers of Componentwise Linear Ideals: J.Herzog, T.Hibi, H.Ohsugi.- Modules With 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A.: J.Kamnitzer, C.Sadanand.- Realization Spaces for Tropical Fans: E.Katz, S.Payne.- A Relation Between Symmetric Polynomials and the Algebra of Classes, Motivated by Equivariant Schubert Calculus: D.Laksov.- Theory and Applications of Lattice Point Methods for Binomial Ideals: E.Miller.- Equations Defining Secant Varieties: Geometry and Computation: J.Sidman, P. Vermeire.
Series: Progress in Probability, Vol. 64
1st Edition., 2011, XXVI, 325 p., Hardcover
ISBN: 978-3-0346-0243-3
Due: June 30, 2011
These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg, Austria) between June 29th and July 5th, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'.
Content Level â Research
Related subjects â Probability Theory and Stochastic Processes
Preface.- Programme of the Workshop on gBoundariesh.- Programme of the
Alp-Workshop 2009.- Publications of D.I. Cartwright.- Publications of M.A.
Picardello.- Publications of V.A. Kaimonvich.- M.J. Dunwoody, An Inaccessible
Graph.- J. Parkinson and B. Schapira, A Local Limit Theorem for Random
Walks on the Chambers of A2 Buildings.- A. Erschler, On Continuity of Range,
Entropy and Drift for Random Walks on Groups.- Y. Guivarcfh and C.R.E.
Raja, Polynomial Growth, Recurrence and Ergodicity for Random Walks on
Locally Compact Groups and Homogeneous Spaces.- M. Bjorklund, Ergodic Theorems
for Homogeneous Dilations.- A. Gnedin, Boundaries from Inhomogeneous Bernoulli
Trials.- P.E.T. Jorgensen and E.P.J. Pearse, Resistance Boundaries of Infinite
Networks.- M. Arnaudon and A. Thalmaier, Brownian Motion and Negative Curvature.-
R.K. Wojciechowski, Stochastically Incomplete Manifolds and Graphs.- S.
Haeseler and M. Keller, Generalized Solutions and Spectrum for Dirichlet
Forms on Graphs.- R. Froese, D. Hasler and W. Spitzer, A Geometric Approach
to Absolutely Continuous Spectrum for Discrete Schrodinger Operators.-
A. Bendikov, B. Bobikau and C. Pittet, Some Spectral and Geometric Aspects
of Countable Groups.- P. Muller and P. Stollmann, Percolation Hamiltonians.-
T.S. Turova, Survey of Scalings for the Largest Connected Component in
Inhomogeneous Random Graphs.- D. DfAngeli, A. Donno and T. Nagnibeda,
Partition Functions of the Ising Model on Some Self-similar Schreier Graphs.-
I. Krasovsky, Aspects of Toeplitz Determinants.