Hardcover
ISBN 978-981-13-2885-5
Discusses major topics in real and complex analysis
Includes the essential analysis that is needed for the study of functional
analysis
Presents applications of complex analysis to analytic number theory
Features over 800 step-by-step, fully solved examples
Is useful to undergraduate students of mathematics and engineering
This is the second volume of the two-volume book on real and complex analysis. This volume
is an introduction to the theory of holomorphic functions. Multivalued functions and branches
have been dealt carefully with the application of the machinery of complex measures and
power series. Intended for undergraduate students of mathematics and engineering, it covers
the essential analysis that is needed for the study of functional analysis, developing the
concepts rigorously with sufficient detail and with minimum prior knowledge of the
fundamentals of advanced calculus required. Divided into four chapters, it discusses
holomorphic functions and harmonic functions, Schwarz reflection principle, infinite product and
the Riemann mapping theorem, analytic continuation, monodromy theorem, prime number
theorem, and Picard’s little theorem. Further, it includes extensive exercises and their solutions
with each concept. The book examines several useful theorems in the realm of real and
complex analysis, most of which are the work of great mathematicians of the 19th and 20th
centuries.
Hardcover
ISBN 978-981-13-3031-5
The first book presenting the Periodic Unfolding Method in detail, written by
the three mathematicians who developed it
Significantly clarifies and simplifies the approach of homogenization for
partial differential problems
Contains detailed theory, as well as numerous and varied examples of
applications
This is the first book on thesubject of the periodic unfolding method (originally called
"eclatement periodique" in French), which was originally developed to clarify and simplify many
questions arising in the homogenization of PDE's. It has since led to the solution of some open
problems. Written by the three mathematicians who developed the method, the book presents
both the theory as well as numerous examples of applications for partial differential problems
with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains
(Part II), and in domains with small holes generating a strange term (Part IV). The method
applies to the case of multiple microscopic scales (with finitely many distinct scales) which is
connected to partial unfolding (also useful for evolution problems). This is discussed in the
framework of oscillating boundaries (Part III). A detailed example of its application to linear
elasticity is presented in the case of thin elastic plates (Part V). Lastly, a complete
determination of correctors for the model problem in Part I is obtained (Part VI). This book can
be used as a graduate textbook to introduce the theory of homogenization of partial
differential problems, and is also a must for researchers interested in this field.
Hardcover
ISBN 978-3-030-01592-3
High-quality articles written by leading experts, including several ICM
speakers, the 2014 Fields medalist Martin Hairer and the 2018 Henri
Poincare Prize laureate Percy Deift
Presents developments in the field of deterministic and stochastic dynamical
systems from the combined points of view of mathematical analysis,
computational mathematics and control theory
Unique and new emphasis on the fruitful interplay between analytic problems
and tools from algebraic combinatorics
The Abel Symposia volume at hand contains a collection of high-quality articles written by the
world’s leading experts, and addressing all mathematicians interested in advances in
deterministic and stochastic dynamical systems, numerical analysis, and control theory. In
recent years we have witnessed a remarkable convergence between individual mathematical
disciplines that approach deterministic and stochastic dynamical systems from mathematical
analysis, computational mathematics and control theoretical perspectives. Breakthrough
developments in these fields now provide a common mathematical framework for attacking
many different problems related to differential geometry, analysis and algorithms for stochastic
and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-
19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic
differential equations, control theory, numerical analysis, algebra and random processes
presented and discussed the current state of the art in these diverse fields. The current Abel
Symposia volume may serve as a point of departure for exploring these related but diverse
fields of research, as well as an indicator of important current and future developments in
modern mathematics.
Hardcover
ISBN 978-3-030-01958-7
Presents recent mathematical methods for optimal control problems and
their applications
Provides rigorous mathematical results
Offers several hints on numerical methods and on the construction of efficient
algorithms
This work presents recent mathematical methods in the area of optimal control with a
particular emphasis on the computational aspects and applications. Optimal control theory
concerns the determination of control strategies for complex dynamical systems, in order to
optimize some measure of their performance. Started in the 60's under the pressure of the
"space race" between the US and the former USSR, the field now has a far wider scope, and
embraces a variety of areas ranging from process control to traffic flow optimization,
renewable resources exploitation and management of financial markets. These emerging
applications require more and more efficient numerical methods for their solution, a very
difficult task due the huge number of variables. The chapters of this volume give an up-to-date
presentation of several recent methods in this area including fast dynamic programming
algorithms, model predictive control and max-plus techniques.This book is addressed to
researchers, graduate students and applied scientists working in the area of control problems,
differential games and their applications.
Hardcover
ISBN 978-3-030-01586-2
Includes a broad range of related topics and applications in microlocal
analysis
Provides a range of topics from foundational material to advanced researchlevel
papers
Addresses new research applications, including symplectic geometry and
topological field theory
This book presents contributions from two workshops in algebraic and analytic microlocal
analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand
on mini-courses and talks ranging from foundational material to advanced research-level
papers, and new applications in symplectic geometry, mathematical physics, partial differential
equations, and complex analysis are discussed in detail. Topics include Procesi bundles and
symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex
manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Khler metrics, and
partial Bergman kernels. This volume is a valuable resource for graduate students and
researchers in mathematics interested in understanding microlocal analysis and learning about
recent research in the area.
Hardcover
ISBN 978-3-030-01601-2
Investigates the mathematics of collective phenomena emerging from
quantum theory at observable scales
Highlights fruitful connections to functional analysis, spectral theory,
statistical mechanics, and variational calculus
Presents technical details in an accessible way to advanced graduate students
Based on the workshop of the same name, this proceedings volume presents selected research
investigating the mathematics of collective phenomena emerging from quantum theory at
observable scales. Featured contributions from leading scientists provide a thorough overview
of current and active research. Methods from functional analysis, spectral theory,
renormalization group theory, and variational calculus are used to prove rigorous results in
quantum physics. Topics include superconductivity and mathematical aspects of the BCS theory,
the Jellium model and Bose-Einstein condensation, among others. Presenting technical details
in an accessible way, this book serves as an introduction to research for advanced graduate
students and is suitable for specialists in mathematical physics. The workshop “Macroscopic
Limits of Quantum Systems” was held over three days in the spring of 2017 at the Technical
University of Munich. The conference celebrated the achievements of Herbert Spohn and his
reception of the Max Planck Medal
Hardcover
ISBN 978-3-030-02824-4
Discusses both theory and applications
Features mathematical methods and models in applications to important
problems of science and engineering
Includes high-quality, peer-reviewed contributed chapters, which present
various new methods and results, reviews of up to date research and open
directions and problems for future research
Serves as a source of inspiration for a broad spectrum of researchers and
research students in mathematics and its applications in other subjects
This book highlights the latest advances in stochastic processes, probability theory,
mathematical statistics, engineering mathematics and algebraic structures, focusing on
mathematical models, structures, concepts, problems and computational methods and
algorithms important in modern technology, engineering and natural sciences applications. It
comprises selected, high-quality, refereed contributions from various large research
communities in modern stochastic processes, algebraic structures and their interplay and
applications. The chapters cover both theory and applications, illustrated by numerous figures,
schemes, algorithms, tables and research results to help readers understand the material and
develop new mathematical methods, concepts and computing applications in the future.
Presenting new methods and results, reviews of cutting-edge research, and open problems and
directions for future research, the book serves as a source of inspiration for a broad spectrum
of researchers and research students in probability theory and mathematical statistics, applied
algebraic structures, applied mathematics and other areas of mathematics and applications of
mathematics. The book is based on selected contributions presented at the International
Conference on “Stochastic Processes and Algebraic Structures ? From Theory Towards
Applications” (SPAS2017) to mark Professor Dmitrii Silvestrov’s 70th birthday and his 50 years
of fruitful service to mathematics, education and international cooperation, which was held at
Malardalen University in Vasteras and Stockholm University, Sweden, in October 2017.