Highlights new developments in the main directions of Clifford analysis
Offers new perspectives and outlines current trends for researchers
interested in or working on these topics
Theoretical contributions were written by leading experts in the field, while
contributions of an expository nature were written for persons working in
these areas and are easily accessible for non-specialists
Commemorates the work of Paul Dirac
This book, intended to commemorate the work of Paul Dirac, highlights new developments in
the main directions of Clifford analysis. Just as complex analysis is based on the algebra of the
complex numbers, Clifford analysis is based on the geometric Clifford algebras. Many methods
and theorems from complex analysis generalize to higher dimensions in various ways.
However, many new features emerge in the process, and much of this work is still in its
infancy. Some of the leading mathematicians working in this field have contributed to this book
in conjunction with “Clifford Analysis and Related Topics: a conference in honor of Paul A.M.
Dirac,” which was held at Florida State University, Tallahassee, on December 15-17, 2014. The
content reflects talks given at the conference, as well as contributions from mathematicians
who were invited but were unable to attend. Hence much of the mathematics presented here
is not only highly topical, but also cannot be found elsewhere in print. Given its scope, the
book will be of interest to mathematicians and physicists working in these areas, as well as
students seeking to catch up on the latest developments.
1st ed. 2018, VII, 152 p.
Hardcover
ISBN 978-3-030-00047-9
Softcover
ISBN 978-3-030-13080-0
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
Other renditions
Offers contributions from broad areas related to quantum mysteries including
working experimental and theoretical physicists, mathematicians, quantum
information scientists, and philosophers
Discusses the boundaries of our current understanding of the quantum world
including non-locality, complementarity, and uncertainty
Includes new mathematical ideas that approach quantum foundations
including operator algebras, category theory, topos theory, and quantum
information theory
This volume contains papers based on presentations at the “Nagoya Winter Workshop 2015:
Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in
March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and
confusions, and have encouraged innovations in mathematical languages to describe, analyze,
and delineate this wonderland. Both ontological and epistemological questions about quantum
reality and measurement have been placed in the center of the mysteries explored originally by
Bohr, Heisenberg, Einstein, and Schrodinger. This volume describes how those traditional
problems are nowadays explored from the most advanced perspectives. It includes new
research results in quantum information theory, quantum measurement theory, information
thermodynamics, operator algebraic and category theoretical foundations of quantum theory,
and the interplay between experimental and theoretical investigations on the uncertainty
principle. This book is suitable for a broad audience of mathematicians, theoretical and
experimental physicists, and philosophers of science.
1st ed. 2018, VIII, 396 p.
30 illus., 16 illus. in color.
Hardcover
ISBN 978-981-13-2486-4
Softcover
ISBN 978-981-13-4783-2
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
The first book on this topic
Includes a full literature review on the homogenization of various boundaryvalue problems, spectral
problems, variational inequalities, optimal control problems in thick junctions
Provides a complete and unified presentation of the topic and recent results
of the authors
Presents approximation techniques for solutions to semilinear elliptic and
parabolic problems with various alternating nonlinear Robin boundary
conditions
This book presents asymptotic methods for boundary-value problems (linear and semilinear,
elliptic and parabolic) in so-called thick multi-level junctions. These complicated structures
appear in a large variety of applications.A concise and readable introduction to the topic, the
book provides a full review of the literature as well as a presentation of results of the authors,
including the homogenization of boundary-value problems in thick multi-level junctions with
non-Lipschitz boundaries, and the construction of approximations for solutions to semilinear
problems. Including end-of-chapter conclusions discussing the results and their physical
interpretations, this book will be of interest to researchers and graduate students in asymptotic
analysis and applied mathematics as well as to physicists, chemists and engineers interested in
processes such as heat and mass transfer
1st ed. 2019, VIII, 105 p. 7 illus., 2 illus. in color.
Softcover
ISBN 978-3-030-35536-4
Product category : Brief
Series : SpringerBriefs in Mathematics
A Brief Introduction to Statistical Mechanics and the Second Law of
Thermodynamics
Provides a novel, but accurate introduction to statistical mechanics
Using simple geometry and algebra, without high level mathematics and
calculus
Introduces the more easily understood, statistical explanation of entropy
before connecting it to the more abstract thermodynamic definition
Illustrates entropy changes for common examples in terms of the
astronomical numbers involved
This book provides a complete and accurate atomic level statistical mechanical explanation of
entropy and the second law of thermodynamics. It assumes only a basic knowledge of
mechanics and requires no knowledge of calculus. The treatment uses primarily geometric
arguments and college level algebra. Quantitative examples are given at each stage to buttress
physical understanding. This text is of benefit to undergraduate and graduate students, as well
as educators and researchers in the physical sciences (whether or not they have taken a
thermodynamics course) who want to understand or teach the atomic/molecular origins of
entropy and the second law. It is particularly aimed at those who, due to insufficient
mathematical background or because of their area of study, are not going to take a traditional
statistical mechanics course
1st ed. 2019, IX, 63 p. 20 illus.
Softcover
ISBN 978-3-030-35459-6
Product category : Brief
Series : SpringerBriefs in Physics
The final book in Israel Gelfand's internationally renowned correspondence
course
Focuses on geometric constructions and includes over 400 figures in order to
develop students' geometrical intuition
Contains a large number of exercises with answers, as well as problems
suggested for further study
This text is the fifth and final in the series of educational books written by Israel Gelfand with
his colleagues for high school students. These books cover the basics of mathematics in a
clear and simple format ? the style Gelfand was known for internationally. Gelfand prepared
these materials so as to be suitable for independent studies, thus allowing students to learn
and practice the material at their own pace without a class. Geometry takes a different
approach to presenting basic geometry for high-school students and others new to the subject.
Rather than following the traditional axiomatic method that emphasizes formulae and logical
deduction, it focuses on geometric constructions. Illustrations and problems are abundant
throughout, and readers are encouraged to draw figures and “move” them in the plane,
allowing them to develop and enhance their geometrical vision, imagination, and creativity.
Chapters are structured so that only certain operations and the instruments to perform these
operations are available for drawing objects and figures on the plane. This structure
corresponds to presenting, sequentially, projective, affine, symplectic, and Euclidean geometries,
all the while ensuring students have the necessary tools to follow along. Geometry is suitable
for a large audience, which includes not only high school geometry students, but also teachers
and anyone else interested in improving their geometrical vision and intuition, skills useful in
many professions. Similarly, experienced mathematicians can appreciate the book’s unique way
of presenting plane geometry in a simple form while adhering to its depth and rigor. “Gelfand
was a great mathematician and also a great teacher. The book provides an atypical view of
geometry. Gelfand gets to the intuitive core of geometry, to the phenomena of shapes and how
they move in the plane, leading us to a better understanding of what coordinate geometry and
axiomatic geometry seek to describe.
1st ed. 2020, XXI, 420 p. 467 illus.
Softcover
ISBN 978-1-0716-0297-3
Product category : Undergraduate textbook
Nominated as an outstanding PhD thesis by the Department of Physics at
Kyoto University
Presents for the first time a novel type of topological phase transition in
disordered systems
Explores the development of a renormalization group technique for driven
disordered systems
This book investigates phase transitions and critical phenomena in disordered systems driven
out of equilibrium. First, the author derives a dimensional reduction property that relates the
long-distance physics of driven disordered systems to that of lower dimensional pure systems.
By combining this property with a modern renormalization group technique, the critical
behavior of random field spin models driven at a uniform velocity is subsequently investigated.
The highlight of this book is that the driven random field XY model is shown to exhibit the
Kosterlitz?Thouless transition in three dimensions. This is the first example of topological phase
transitions in which the competition between quenched disorder and nonequilibrium driving
plays a crucial role. The book also includes a pedagogical review of a renormalizaion group
technique for disordered systems.
1st ed. 2019, XIII, 156 p.
38 illus., 27 illus. in color.
Hardcover
ISBN 978-981-13-6170-8
Softcover
ISBN 978-981-13-6173-9
Product category : Monograph
Series : Springer Theses
Three levels of exposition in this book oriented towards different categories of
readers ranging from graduate students and PhD students to professional researchers
Based on lectures given at Mekhmat (Department of Mechanics and
Mathematics of Moscow State University), one of the top mathematical
departments worldwide, with its rich traditions of teaching functional analysis
Extensive additional information is presented in complementary sections and
exercises provided with detailed hints or references
This book is based on lectures given at "Mekhmat", the Department of Mechanics and
Mathematics at Moscow State University, one of the top mathematical departments worldwide,
with a rich tradition of teaching functional analysis. Featuring an advanced course on real and
functional analysis, the book presents not only core material traditionally included in university
courses of different levels, but also a survey of the most important results of a more subtle
nature, which cannot be consideredbasic but which are useful for applications. Further, it
includes several hundred exercises of varying difficulty with tips and references. The book is
intended for graduate and PhD students studying real and functionalanalysis as well as
mathematicians and physicists whose research is related to functionalanalysis
1st ed. 2020, XVI, 586 p.
Printed book
Hardcover
ISBN 978-3-030-38218-6
Product category : Graduate/advanced undergraduate textbook
Series : Moscow Lectures