Due 2019-09-10
1st ed. 2019, VIII, 470 p. 8 illus.
Hardcover
ISBN 978-3-030-22421-9
First book in decades to discuss a variety of proofs of Loewner's Theorem
May be used as a text for a specialized graduate analysis course
Acts as a starting point for discussing a variety of methods in analysis
This book provides an in depth discussion of Loewner’s theorem on the characterization of
matrix monotone functions. The author refers to the book as a ‘love poem,’ one that highlights
a unique mix of algebra and analysis and touches on numerous methods and results. The
book details many different topics from analysis, operator theory and algebra, such as divided
differences, convexity, positive definiteness, integral representations of function classes, Pick
interpolation, rational approximation, orthogonal polynomials, continued fractions, and more.
Most applications of Loewner’s theorem involve the easy half of the theorem. A great number
of interesting techniques in analysis are the bases for a proof of the hard half. Centered on
one theorem, eleven proofs are discussed, both for the study of their own approach to the
proof and as a starting point for discussing a variety of tools in analysis. Historical background
and inclusion of pictures of some of the main figures who have developed the subject, adds
another depth of perspective. The presentation is suitable for detailed study, for quick review or
reference to the various methods that are presented. The book is also suitable for independent
study. The volume will be of interest to research mathematicians, physicists, and graduate
students working in matrix theory and approximation, as well as to analysts and mathematical
physicists.
Due 2019-10-23
1st ed. 2020, Approx. 150 p.
Softcover
ISBN 978-3-030-23688-5
Presents classical theory and some of the newest techniques
Discusses a number of future challenges
Authored by two highly recognized experts
This book is aimed at mathematicians, scientists, and engineers, studying models that involve a
discontinuity, or studying the theory of nonsmooth systems for its own sake. It is divided in two
complementary courses: piecewise-smooth flows and maps, respectively. Starting from well
known theoretical results, the authors bring the reader into the latest challenges in the field,
going through stability analysis, bifurcation, singularities, decomposition theorems and an
introduction to kneading theory. Both courses contain many examples which illustrate the
theoretical concepts that are introduced.
Due 2019-10-05
1st ed. 2019, XIX, 436 p. 40 illus.
Hardcover
ISBN 978-3-030-24400-2
Provides complete treatise about the most recent multiplicative ideal theory
in commutative rings
Includes a dependence chart for the various sections of the book
Exercises included at the end of each section
This book presents a systematic exposition of the various applications of closure operations in
commutative and noncommutative algebra. In addition to further advancing multiplicative ideal
theory, the book opens doors to the various uses of closure operations in the study of rings
and modules, with emphasis on commutative rings and ideals. Several examples,
counterexamples, and exercises further enrich the discussion and lend additional flexibility to
the way in which the book is used, i.e., monograph or textbook for advanced topics courses.
Due 2019-11-23
1st ed. 2019, Approx. 450 p.
Hardcover
ISBN 978-3-030-23853-7
Provides an essential overview of modern topics in Clifford analysis
Dedicated to Prof. Wolfgang Sprosig
Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions.
The unique starting point of Wolfgang Sprosig’s work was the application of quaternionic
analysis to elliptic differential equations and boundary value problems. Over the years, Clifford
analysis has become a broad-based theory with a variety of applications both inside and
outside of mathematics, such as higher-dimensional function theory, algebraic structures,
generalized polynomials, applications of elliptic boundary value problems, wavelets, image
processing, numerical and discrete analysis. The aim of this volume is to provide an essential
overview of modern topics in Clifford analysis, presented by specialists in the field, and to
honor the valued contributions to Clifford analysis made by Wolfgang Sprosig throughout his
career.
Due 2020-04-12
1st ed. 2020, Approx. 500 p.
Hardcover
ISBN 978-3-030-23283-2
Updates readers on developments in module theory that have led to current research
Is essentially self-contained
Features a list of open research problems
Broadens our understanding of the directions in which the research in this field is moving
This book collects and coherently presents the research that has been undertaken since the
author’s previous book Module Theory (1998). In addition to some of the key results since
1995, it also discusses the development of much of the supporting material. In the twenty
years following the publication of the Camps-Dicks theorem, the work of Facchini, Herbera,
Shamsuddin, Puninski, Prihoda and others has established the study of serial modules and
modules with semilocal endomorphism rings as one of the promising directions for moduletheoretic
research. Providing readers with insights into the directions in which the research in
this field is moving, as well as a better understanding of how it interacts with other research
areas, the book appeals to undergraduates and graduate students as well as researchers
interested in algebra.
Proceedings of the 6th International Colloquium on Differential Geometry and its Related Fields
6th International Colloquium on Differential Geometry and its Related Fields, Veliko Tarnovo, Bulgaria, 4 ? 8 September 2018
https://doi.org/10.1142/11454
December 2019Pages: 240
This volume contains papers by the main participants in the meeting of the 6th International Colloquium on Differential Geometry and its Related Fields (ICDG2018).
The volume consists of papers devoted to the study of recent topics in geometric structures on manifolds ? which are related to complex analysis, symmetric spaces and surface theory ? and also in discrete mathematics.
Thus, it presents a broad overview of differential geometry and provides up-to-date information to researchers and young scientists in this field, and also to those working in the wide spectrum of mathematics.
Einstein Manifolds
Symmetric and Homogeneous Spaces
G_2-Structures
Information Geometry
Tensors and Discrete Geometry
Professionals, researchers and graduate students in differential geometry, complex analysis, probability theory and mathematical physics.