1st ed. 2017, X, 98 p. 20 illus., 18 illus. in color.
Softcover
ISBN 978-3-319-65330-3
Series: SpringerBriefs in Statistics
* Explores the use of Structured Additive Distributional Regression
to the analysis of economic inequalityIntroduces both Structured
Additive Distributional Regression and inequality analysisOffers new
lines of reasoning for a critical reflection on conventional economic
theory
This book seeks new perspectives on the growing inequalities that our societies face,
putting forward Structured Additive Distributional Regression as a means of statistical
analysis that circumvents the common problem of analytical reduction to simple point
estimators. This new approach allows the observed discrepancy between the individuals’
realities and the abstract representation of those realities to be explicitly taken into
consideration using the arithmetic mean alone. In turn, the method is applied to the
question of economic inequality in Germany.
1st ed. 2017, XII, 256 p. 7 illus., 2 illus. in color.
Printed book
Hardcover
ISBN 978-4-431-56598-7
November 5, 2017
Series: Springer Monographs in Mathematics
* Is based on elementary calculus
* Provides direct proof of Carleman estimates
* Is one of the few monographs on the approach using Carleman estimates
This book is a self-contained account of the method based on Carleman estimates for
inverse problems of determining spatially varying functions of differential equations
of the hyperbolic type by non-overdetermining data of solutions. The formulation
is different from that of Dirichlet-to-Neumann maps and can often prove the global
uniqueness and Lipschitz stability even with a single measurement. These types of inverse
problems include coefficient inverse problems of determining physical parameters in
inhomogeneous media that appear in many applications related to electromagnetism,
elasticity, and related phenomena. Although the methodology was created in 1981 by
Bukhgeim and Klibanov, its comprehensive development has been accomplished only
recently. In spite of the wide applicability of the method, there are few monographs
focusing on combined accounts of Carleman estimates and applications to inverse
problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates,
the theory of which has been established within a very general framework, so that the
method using Carleman estimates for inverse problems is misunderstood as being
very difficult. The main purpose of the book is to provide an accessible approach to
the methodology. To accomplish that goal, the authors include a direct derivation of
Carleman estimates, the derivation being based essentially on elementary calculus
working flexibly for various equations. Because the inverse problem depends heavily on
respective equations, too general and abstract an approach may not be balanced. Thus
a direct and concrete means was chosen not only because it is friendly to readers but
also is much more relevant. By practical necessity, there is surely a wide range of inverse
problems and the method delineated here can solve them. The intention is for readers to
learn that method and then apply it to solving new inverse problems.
1st ed. 2017, X, 341 p. 6 illus.
Printed book
Hardcover
ISBN 978-3-319-65426-3
November 5, 2017
Series: Mathematical Physics Studies
* Inspires especially young researchers who will get a global picture
and technical tools at the same timeBridges different active areas of
research in mathematics and physics
* Written with a notable pedagogical effort
This monograph presents various ongoing approaches to the vast topic of quantization,
which is the process of forming a quantum mechanical system starting from a classical
one, and discusses their numerous fruitful interactions with mathematics.
The opening chapter introduces the various forms of quantization and their interactions
with each other and with mathematics.
A first approach to quantization, called deformation quantization, consists of viewing
the Planck constant as a small parameter. This approach provides a deformation of the
structure of the algebra of classical observables rather than a radical change in the nature
of the observables. When symmetries come into play, deformation quantization needs to
be merged with group actions, which is presented in chapter 2, by Simone Gutt.
The noncommutativity arising from quantization is the main concern of noncommutative
geometry. Allowing for the presence of symmetries requires working with principal fiber
bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the
topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras,
are the subject of chapter 4, by Nicolas Andruskiewitsch.
The purely algebraic approaches given in the previous chapters do not take the geometry
of space-time into account. For this purpose a special treatment using a more geometric
point of view is required.
1st ed. 2017, X, 194 p. 30 illus.
Printed book
Softcover
ISBN 978-3-319-68169-6
Series: Springer Undergraduate Mathematics Series
* Clear and rigorous exposition is supported by engaging examples
and exercises
* Provides a means to learn complex analysis as well as subtle
introduction to careful mathematical reasoning
* Topics purposefully apportioned into 21 lectures, providing a
suitable format for either independent study or lecture-based
teaching
At its core, this concise textbook presents standard material for a first course in complex
analysis at the advanced undergraduate level. This distinctive text will prove most
rewarding for students who have a genuine passion for mathematics as well as certain
mathematical maturity. Primarily aimed at undergraduates with working knowledge of
real analysis and metric spaces, this book can also be used to instruct a graduate course.
The text uses a conversational style with topics purposefully apportioned into 21 lectures,
providing a suitable format for either independent study or lecture-based teaching.
Instructors are invited to rearrange the order of topics according to their own vision. A
clear and rigorous exposition is supported by engaging examples and exercises unique
to each lecture; a large number of exercises contain useful calculation problems. Hints
are given for a selection of the more difficult exercises. This text furnishes the reader
with a means of learning complex analysis as well as a subtle introduction to careful
mathematical reasoning. To guarantee a student’s progression, more advanced topics are
spread out over several lectures.
This text is based on a one-semester (12 week) undergraduate course in complex analysis
that the author has taught at the Australian National University for over twenty years.
Most of the principal facts are deduced from Cauchy’s Independence of Homotopy
Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and
Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with
a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex
numbers and concludes with a proof of another major milestone, the Riemann Mapping
Theorem, which is rarely part of a one-semester undergraduate course.
1st ed. 2017, XI, 86 p. 30 illus.
Printed book
Softcover
ISBN 978-981-10-6786-0
November 5, 2017
Series: SpringerBriefs in Mathematics
* Highly recommendable as a comprehensive introduction to the
modern Nevanlinna theory
* The last chapter is closely related to Kodaira’s remarkable last paper
* Recently, this lecture note was cited as a reference to basic formulas
which cannot be found in other places
This book deals with the classical theory of Nevanlinna on the value distribution of
meromorphic functions of one complex variable, based on minimum prerequisites for
complex manifolds. The theory was extended to several variables by S. Kobayashi, T.
Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in
his course at The University of Tokyo in 1973 and gave an introductory account of this
development in the context of his final paper, contained in this book. The first three
chapters are devoted to holomorphic mappings from C to complex manifolds. In the
fourth chapter, holomorphic mappings between higher dimensional manifolds are
covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to
those who want to understand Kodaira's unique approach to basic questions on complex
manifolds.