Addresses several important classes of nonlinear PDEs
Adapts as a textbook for advanced graduate courses in dissipative dynamics
Appeals to both mathematicians interested in synchronization theory as well
as physicists and engineers interested in mathematical background and
methods for the asymptotic analysis of infinite-dimensional dissipative systems
Uniquely presents synchronization theory in the infinite-dimensional case at the monograph level
Remains accessible to advanced students and scientific professionals without
deep knowledge of Sobolev theory and functional spaces
The main goal of this book is to systematically address the mathematical methods that are
applied in the study of synchronization of infinite-dimensional evolutionary dissipative or
partially dissipative systems. It bases its unique monograph presentation on both general and
abstract models and covers several important classes of coupled nonlinear deterministic and
stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts
readily to advanced graduate coursework in dissipative dynamics, requires some background
knowledge in evolutionary equations and introductory functional analysis as well as a basic
understanding of PDEs and the theory of random processes. Suitable for researchers in
synchronization theory, the book is also relevant to physicists and engineers interested in both
the mathematical background and the methods for the asymptotic analysis of coupled infinitedimensional
dissipative systems that arise in continuum mechanics.
Due 2020-08-14
1st ed. 2020, XVII, 329 p.
Hardcover
ISBN 978-3-030-47090-6
Product category : Monograph
Mathematics : Dynamical Systems and Ergodic Theory
Series : Applied Mathematical Sciences
Presents a new iterative technique for solving nonlinear equations
Substantially broadens the scope of Kantorovichfs theory for Newtonfs method
Intended for researchers and postgraduate students working on nonlinear equations
In this book the authors use a technique based on recurrence relations to study the
convergence of the Newton method under mild differentiability conditions on the first derivative
of the operator involved. The authorsf technique relies on the construction of a scalar
sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the
convergence of the method. The application is user-friendly and has certain advantages over
Kantorovichfs majorant principle. First, it allows generalizations to be made of the results
obtained under conditions of Newton-Kantorovich type and, second, it improves the results
obtained through majorizing sequences. In addition, the authors extend the application of
Newtonfs method in Banach spaces from the modification of the domain of starting points. As
a result, the scope of Kantorovichfs theory for Newtonfs method is substantially broadened.
Moreover, this technique can be applied to any iterative method. This book is chiefly intended
for researchers and (postgraduate) students working on nonlinear equations, as well as
scientists in general with an interest in numerical analysis.
Due 2020-08-18
1st ed. 2020, X, 152 p. 50
illus., 44 illus. in color.
Softcover
ISBN 978-3-030-48701-0
Product category : Monograph
Mathematics : Operator Theory
Series : Frontiers in Mathematics
Explains in detail direct and simple methods for solving direct and inverse
Sturm-Liouville and scattering problems on finite and infinite intervals
Includes a brief introduction to the notion and properties of transmutation operators
Formulates some of the most typical direct and inverse spectral and scattering problems
This book provides an introduction to the most recent developments in the theory and practice
of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal
approach for practical solving of direct and inverse spectral and scattering problems is
presented, based on the notion of transmutation (transformation) operators and their efficient
construction. Analytical representations for solutions of Sturm-Liouville equations as well as for
the integral kernels of the transmutation operators are derived in the form of functional series
revealing interesting special features and lending themselves to direct and simple numerical
solution of a wide variety of problems. The book is written for undergraduate and graduate
students, as well as for mathematicians, physicists and engineers interested in direct and
inverse spectral problems.
Due 2020-08-18
1st ed. 2020, X, 158 p.
Softcover
ISBN 978-3-030-47848-3
Product category : Monograph
Mathematics : Analysis
Series : Frontiers in Mathematics
Presents a way of solving PDEs with very little theory
Provides required background knowledge in the appendix
Appeals to students and researchers alike
This book presents a concise introduction to a unified Hilbert space approach to the
mathematical modellingof physical phenomena which has been developed over recent years by
Picard and his co-workers. The main focus is on time-dependent partial differential equations
with a particular structure in the Hilbert space setting that ensures well-posedness and
causality, two essential properties of any reasonable model in mathematical physics or
engineering.However, the application of the theory to other types of equations is also
demonstrated. By means of illustrative examples, from the straightforward to the more
complex, the authors show that many of the classical models in mathematical physics as well
as more recent models of novel materials and interactions are covered, or can be restructured
to be covered, by this unified Hilbert space approach. The reader should require only a basic
foundation in the theory of Hilbert spaces and operators therein. For convenience, however,
some of the more technical background requirements are covered in detail in two appendices
The theory is kept as elementary as possible, making the material suitable for a senior
undergraduate or masterfs level course. In addition, researchers in a variety of fields whose
work involves partial differential equations and applied operator theory will also greatly benefit
from this approach to structuring their mathematical models in order that the general theory
can be applied to ensure the essential properties of well-posedness and causality.
Due 2020-08-18
1st ed. 2020, X, 130 p.
Softcover
ISBN 978-3-030-47332-7
Product category : Monograph
Mathematics : Partial Differential Equations
Series : Frontiers in Mathematics
Illuminates the mathematical theory behind modern geometry processing
Offers a uniquely accessible entry-point that is suitable for students and professionals alike
Builds the mathematical theory behind modern applications in medical
imaging, computer vision, robotics, and machine learning
Includes exercises throughout that are suitable for class use or independent study
This textbook offers an introduction to differential geometry designed for readers interested in
modern geometry processing. Working from basic undergraduate prerequisites, the authors
develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian
geometry follow, culminating in the theory that underpins manifold optimization techniques.
Students and professionals working in computer vision, robotics, and machine learning will
appreciate this pathway into the mathematical concepts behind many modern applications.
Starting with the matrix exponential, the text begins with an introduction to Lie groups and
group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the
construction of manifolds from gluing data is particularly relevant to the reconstruction of
surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second
part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds
encompass Riemannian metrics, geodesics, and curvature. Topics that follow include
submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter
highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the
machinery needed to generalize important optimization techniques to Riemannian manifolds.
Exercises are included throughout, along with optional sections that delve into more theoretical
topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely
accessible perspective on differential geometry for those interested in the theory behind
modern computing applications. Equally suited to classroom use or independent study, the text
will appeal to students and professionals alike; only a background in calculus and linear
algebra is assumed
Due 2020-08-04
1st ed. 2020, X, 739 p. 33
illus., 32 illus. in color.
Hardcover
ISBN 978-3-030-46039-6
Product category : Graduate/advanced undergraduate textbook
Mathematics : Differential Geometry
Series : Geometry and Computing
Explores the advanced mathematical theory behind modern geometry processing
Offers a uniquely accessible approach that is suitable for students and professionals alike
Augments core topics in advanced differential geometry with analytic and algebraic perspectives
Includes exercises throughout that are suitable for class use or independent study
This textbook explores advanced topics in differential geometry, chosen for their particular
relevance to modern geometry processing. Analytic and algebraic perspectives augment core
topics, with the authors taking care to motivate each new concept. Whether working toward
theoretical or applied questions, readers will appreciate this accessible exploration of the
mathematical concepts behind many modern applications. Beginning with an in-depth study of
tensors and differential forms, the authors go on to explore a selection of topics that showcase
these tools. An analytic theme unites the early chapters, which cover distributions, integration
on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An
exploration of bundles follows, from definitions to connections and curvature in vector bundles,
culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford
algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as
a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second
Course captures the mathematical theory needed for advanced study in differential geometry
with a view to furthering geometry processing capabilities. Suited to classroom use or
independent study, the text will appeal to students and professionals alike. A first course in
differential geometry is assumed; the authorsf companion volume Differential Geometry and Lie
Groups: A Computational Perspective provides the ideal preparation.
Due 2020-08-16
1st ed. 2020, XX, 560 p. 32 illus. in color.
Hardcover
ISBN 978-3-030-46046-4
Product category : Graduate/advanced undergraduate textbook
Mathematics : Differential Geometry
Series : Geometry and Computing
Perspectives of the Work of GianCarlo Ghirardi
Bears witness to the broad scientific legacy of GianCarlo Ghirardi
Provides the history, philosophical implications and current status of collapse models
Surveys experimental as well as theoretical work on wave function collapse
This book is a tribute to the scientific legacy of GianCarlo Ghirardi, who was one of the most
influential scientists in the field of modern foundations of quantum theory. In this appraisal,
contributions from friends, collaborators and colleagues reflect the influence of his world of
thoughts on theory, experiments and philosophy, while also offeringprospectsfor future
research in the foundations of quantum physics. The themes of the contributions revolve
around the physical reality of thewave function and its notorious collapse, randomness,
relativity and experiments.
Due 2020-11-06
1st ed. 2020, IX, 427 p. 45
illus., 38 illus. in color.
Hardcover
ISBN 978-3-030-46776-0
Product category : Monograph
Physics : Quantum Physics
Series : Fundamental Theories of Physics