Series: Theoretical and Mathematical Physics
2012, 2012, X, 750 p. 45 illus., 3 in color.
Hardcover
ISBN 978-3-642-29496-9
Due: July 31, 2012
.Provides a self-contained pedagogical introduction to string theory
Authored by leading researchers in the field
Suitable as graduate textbook for courses and for self-study
The purpose of this book is to thoroughly prepare the reader for research in string theory. It is intended as a textbook in the sense that, starting from the basics, the material is presented in a pedagogical and self-contained fashion. The emphasis is on the world-sheet perspective of closed strings and of open strings ending on D-branes, where two-dimensional conformal field theory is the main tool. Compactifications of string theory, with and without fluxes, and string dualities are also discussed from the space-time point of view, i.e. in geometric language. End-of-chapter references have been added to guide the reader intending to pursue further studies or to start research in the topics covered by this book.
The Classical Bosonic String.- The Quantized Bosonic String.- Introduction to Conformal Field Theory.- Parametrization Ghosts and BRST Quantization.- String Perturbation Theory and One-Loop Amplitudes.- The Classical Fermionic String.- The Quantized Fermionic String.- Superstrings.- Toroidal Compactifications ? 10-Dimensional Heterotic String.- Conformal Field Theory II: Lattices and Kac-Moody Algebras.- Conformal Field Theory III: Superconformal Field Theory.- Covariant Vertex Operators, BRST and Covariant Lattices.- String Compactifications.- CFTs for Type II and Heterotic String Vacua.- String Scattering Amplitudes and Low Energy Effective Field Theory.- Compactifications of the Type II Superstring With D-branes and Fluxes.- String Dualities and M-theory.
Series: Universitext
2012, 2012, XVIII, 550 p. 3 illus.
Softcover version
ISBN 978-1-4471-4095-5
Due: July 31, 2012
An easily accessible overview of elementary, analytic and algebraic number theory in one book
A wide variety of exercises that not only directly illustrate the theory but target problems that are rarely covered in existing literature
Includes a number of topics that are not covered in existing undergraduate texts for example counting integer points close to smooth curves
Number theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding.
Classical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Mobius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included.
Topics in Multiplicative Number Theory introduces offers a comprehensive introduction into these topics with an emphasis on analytic number theory. Since it requires very little technical expertise it will appeal to a wide target group including upper level undergraduates, doctoral and masters level students.
Basic Tools.- Bezout and Gauss.- Prime Numbers.- Arithmetic Functions.- Integer Points Close to Smooth Curves.- Exponential Sums.- Algebraic Number Fields.
Series: Universitext
2012, 2012, VI, 178 p.
Softcover Information
Softcover
ISBN 978-1-4614-3893-9
Due: July 31, 2012
.Presents an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level
One of the few textbooks to bridge the gap between the available elementary texts and high level texts
Includes many non-trivial applications of the theory and interesting exercises
This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary.
In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.
Preface.- 1 Normed Vector Spaces.- 2 Differentiation.- 3 Mean value theorems.- 4 Higher derivatives and differentials.- 5 Taylor theorems and applications.- 6 Hilbert spaces.- 7 Convex functions.- 8 The inverse and implicit mapping theorems.- 9 Vector fields.- 10 The flow of a vector field.- 11 The calculus of variations: an introduction.- Bibliography.- Index
Series: Developments in Mathematics, Vol. 27
2012, 2012, XXIV, 340 p.
Hardcover
ISBN 978-1-4614-4035-2
Due: July 31, 2012
Discusses the progress of fractional calculus as a tool in the study of
dynamical systems
Presents solutions to the various classes of Darboux problems for hyperbolic differential equations
Addresses a wide audience of specialists including mathematicians, engineers, biologists, and physicists?
During the last decade, there has been an explosion of interest in fractional dynamics as it was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media. Fractional calculus generalizes integrals and derivatives to non-integer orders and has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. This book is addressed to a wide audience of researchers working with fractional dynamics, including mathematicians, engineers, biologists, and physicists. This timely publication may also be suitable for a graduate level seminar for students studying differential equations.
Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. In this book, problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. An historical introduction to fractional calculus will be of general interest to a wide range of researchers. Chapter one contains some preliminary background results. The second Chapter is devoted to fractional order partial functional differential equations. Chapter three is concerned with functional partial differential inclusions, while in the fourth chapter, we consider functional impulsive partial hyperbolic differential equations. Chapter five is concerned with impulsive partial hyperbolic functional differential inclusions. Implicit partial hyperbolic differential equations are considered in Chapter six, and finally in Chapter seven, Riemann-Liouville fractional order integral equations are considered. Each chapter concludes with a section devoted to notes and bibliographical remarks. The work is self-contained but also contains questions and directions for further research.
Preface.- 1. Preliminary Background.- 2. Partial Hyperbolic Functional Differential Equations.- 3. Partial Hyperbolic Functional Differential Inclusio
ns.- 4. Impulsive Partial Hyperbolic Functional Differential Equations.- 5. Impulsive Partial Hyperbolic Functional Differential Inclusions.- 6. Implicit Partial Hyperbolic Functional Differential Equations.- 7. Fractional Order Riemann-Liouville Integral Equations.- References.- Index.
Series: The IMA Volumes in Mathematics and its Applications, Vol. 155
2012, 2012, XV, 695 p. 104 illus., 62 in color.
Hardcover
ISBN 978-1-4614-3996-7
Due: August 31, 2012
This volume developed from a Workshop on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding which was held at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, from June 1-5, 2010. The subject matter ranged widely from observational data to theoretical mechanics, and reflected the broad scope of the workshop. In both the prepared presentations and in the informal discussions, the workshop engaged exchanges across disciplines and invited a lively interaction between modelers and observers.
The articles in this volume were invited and fully refereed. They provide a representative if necessarily incomplete account of the field of natural locomotion during a period of rapid growth and expansion. The papers presented at the workshop, and the contributions to the present volume, can be roughly divided into those pertaining to swimming on the scale of marine organisms, swimming of microorganisms at low Reynolds numbers, animal flight, and sliding and other related examples of locomotion.
Content Level ≫ Research
Keywords ≫ Insect flight - Natural locomotion - fluid dynamics in nature - model of fish schooling - newtonian dynamics of insect flight
Related subjects ≫ Applications - Classical Continuum Physics - Computational Science & Engineering