Series: Lecture Notes in Mathematics, Vol. 2201
1st ed. 2017, X, 115 p.
Softcover
ISBN 978-3-319-65806-3
* - Provides the first self-contained introduction to the field for nonexperts,
accessible to masters and Ph.D. students starting the subject.
* - Helpful for researchers working in high energy physics who want to
gain a solid background in the mathematical tools they use.
* - Collects recent results on nearly Kahler geometry in signature,
which will be of interest to mathematicians who are working in this
direction and/or who want to obtain an overview of the field.
Developing and providing an overview of recent results on nearly Kahler geometry on
pseudo-Riemannian manifolds, this monograph emphasizes the differences with the
classical Riemannian geometry setting. The focal objects of the text are related to special
holonomy and Killing spinors and have applications in high energy physics, such as
supergravity and string theory. Before starting into the field, a self-contained introduction
to the subject is given, aimed at students with a solid background in differential geometry.
The book will therefore be accessible to masters and Ph.D. students who are beginning
work on nearly Kahler geometry in pseudo-Riemannian signature, and also to non-experts
interested in gaining an overview of the subject. Moreover, a number of results and
techniques are provided which will be helpful for differential geometers as well as for high
energy physicists interested in the mathematical background of the geometric objects
they need.
Series: Graduate Texts in Mathematics, Vol. 278
2nd ed. 2017, IX, 398 p.
Hardcover
ISBN 978-3-319-64628-2
* Provides a foundation for further study in partial differential equations
* Completely self-contained text equips readers with the fundamentals
of graduate real analysis
* New edition extensively revised and updated
* Supplies frequent opportunities to practice techniques
This first year graduate text is a comprehensive resource in real analysis based on
a modern treatment of measure and integration. Presented in a definitive and selfcontained
manner, it features a natural progression of concepts from simple to difficult.
Several innovative topics are featured, including differentiation of measures, elements
of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the
area formula, Sobolev functions and applications to harmonic functions. Together, the
selection of topics forms a sound foundation in real analysis that is particularly suited to
students going on to further study in partial differential equations.
This second edition of Modern Real Analysis contains many substantial improvements,
including the addition of problems for practicing techniques, and an entirely new section
devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate
students with an understanding of advanced c
alculus, the text will also appeal to more experienced mathematicians as a useful
reference.
Series: Lecture Notes in Mathematics, Vol. 2190
1st ed. 2017, X, 95 p. 18 illus., 9 illus. in color.
Softcover
ISBN 978-3-319-64667-1
* Provides a very affordable approach to the homogenization theory
* Gives a complete vision - from theory to numerics - of consequences
of strong oscillations in transport phenomena Contains several
applications from environment questions to Iter plasmas
This book presents the classical results of the two-scale convergence theory and
explains * using several figures * why it works. It then shows how to use this theory
to homogenize ordinary differential equations with oscillating coefficients as well as
oscillatory singularly perturbed ordinary differential equations. In addition, it explores the
homogenization of hyperbolic partial differential equations with oscillating coefficients
and linear oscillatory singularly perturbed hyperbolic partial differential equations.
Further, it introduces readers to the two-scale numerical methods that can be built from
the previous approaches to solve oscillatory singularly perturbed transport equations
(ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book
appeals to masterfs and PhD students interested in homogenization and numerics, as well
as to the Iter community.
Series: Lecture Notes in Mathematics, Vol. 2195
1st ed. 2017, X, 165 p.
Softcover
ISBN 978-3-319-65836-0
* - Offers a new point of view on geometric complex analysis
* - Collects together notes in several very active areas of research
* - Includes expository presentations and numerous applications
The central theme of this reference book is the metric geometry of complex analysis in
several variables. Bridging a gap in the current literature, the text focuses on the fine
behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical
systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of
research. The modern points of view expressed in these notes, collected here for the first
time, will be of interest to academics working in the fields of several complex variables
and metric geometry. The different topics are treated coherently and include expository
presentations of the relevant tools, techniques and objects, which will be particularly
useful for graduate and PhD students specializing in the area.
Series: Lecture Notes in Mathematics, Vol. 2196
1st ed. 2017, XIII, 158 p. 12 illus. in color.
Softcover
ISBN 978-3-319-65465-2
* Presents important results in solving nonlinear reaction-diffusion equations
* Chapters contain ideas for further theoretical generalizations and
examples for real world applications
* Includes applications to pattern formation, ecology and population dynamics
This book presents several fundamental results in solving nonlinear reaction-diffusion
equations and systems using symmetry-based methods. Reaction-diffusion systems are
fundamental modeling tools for mathematical biology with applications to ecology,
population dynamics, pattern formation, morphogenesis, enzymatic reactions and
chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems,
which are relevant for biological applications, from the symmetry point of view, providing
rigorous definitions and constructive algorithms to search for conditional symmetry
(a nontrivial generalization of the well-known Lie symmetry) of nonlinear reactiondiffusion
systems. In order to present applications to population dynamics, it focuses
mainly on two- and three-component diffusive Lotka-Volterra systems. While it is
primarily a valuable guide for researchers working with reaction-diffusion systems and
those developing the theoretical aspects of conditional symmetry conception, parts of the
book can also be used in masterfs level mathematical biology courses.