Volume 73 in the series De Gruyter Expositions in Mathematics
https://doi.org/10.1515/9783110780918
The term “stereotype space” was introduced in 1995 and denotes a category of locally convex spaces with surprisingly elegant properties. Its study gives an unexpected point of view on functional analysis that brings this fi eld closer to other main branches of mathematics, namely, to algebra and geometry. This volume contains the foundations of the theory of stereotype spaces, with accurate definitions, formulations, proofs, and numerous examples illustrating the interaction of this discipline with the category theory, the theory of Hopf algebras, and the four big geometric disciplines: topology, differential geometry, complex geometry, and algebraic geometry
the foundations of the theory of stereotype spaces
examples from the theory of Hopf algebras, topology, differential, complex and algebraic geometry
basic general results, like theory of integration, Tannaka's theorem, etc.
Author information
Sergei S. Akbarov, HSE, Moscow Institute of Electronics and Mathematics, Russia.
Algebra and Number Theory
Analysis
Geometry and Topology
Mathematics
Volume 13 in the series De Gruyter Series on the Applications of Mathematics in Engineering and Information Sciences
https://doi.org/10.1515/9783110792850
This work presents the guiding principles of Integral Transforms needed for many applications when solving engineering and science problems. As a modern approach to Laplace Transform, Fourier series and Z-Transforms it is a valuable reference for professionals and students alike.
Prof. Dr. Nita H. Shah, Department of Mathematics, School of Sciences, Gujarat University, Ahmedabad, Gujarat-380009, India.
Applied Mathematics
Basics and Tools
Engineering
Fundamentals of Mechanical Engineering
Introductions and Overviews
Mathematics
Mechanical Engineering
Mechanics
Volume 88 in the series De Gruyter Studies in Mathematics
https://doi.org/10.1515/9783110757828
Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green’s function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.
Provides a general overview complex analysis in a straightforward and accessible format.
Illustrates common methods, practices and applications that will be beneficial to STEM readers and researchers.
Joel L. Schiff, University of Auckland, New Zealand.
Analysis
Applied Mathematics
Mathematics
Volume 89 in the series De Gruyter Studies in Mathematics
This completely revised and updated edition of the one variable part of the author's classic older book Theory of Holomorphic Maps on Taut Manifolds presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. Furthermore, It also contains extensive historical notes and references for further readings.
A revised and updated edition of a classic book in complex dynamics
Written by one of the foremost experts in the field
Of interest to graduate students and researhers in holomorphic dynamics, complex geometry, and geometric function theory
Marco Abate, Universita di Pisa, Italy.
Analysis
Mathematics
New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevators
Series:
Princeton Series in Applied Mathematics
Hardcover
ISBN: 9780691233482
Published (US): Oct 25, 2022
Copyright: 2022
Pages: 512
Paperback
SBN: 9780691233499
Control applications in undersea construction, cable elevators, and offshore drilling present major methodological challenges because they involve PDE systems (cables and drillstrings) of time-varying length, coupled with ODE systems (the attached loads or tools) that usually have unknown parameters and unmeasured states. In PDE Control of String-Actuated Motion, Ji Wang and Miroslav Krstic develop control algorithms for these complex PDE-ODE systems evolving on time-varying domains.
Motivated by physical systems, the book’s algorithms are designed to operate, with rigorous mathematical guarantees, in the presence of real-world challenges, such as unknown parameters, unmeasured distributed states, environmental disturbances, delays, and event-triggered implementations. The book leverages the power of the PDE backstepping approach and expands its scope in many directions.
Filled with theoretical innovations and comprehensive in its coverage, PDE Control of String-Actuated Motion provides new design tools and mathematical techniques with far-reaching potential in adaptive control, delay systems, and event-triggered control.
How a new mathematical field grew and matured in America
Hardcover
ISBN:: 9780691194028
Published (US): Jan 17, 2023
Copyright:2022
Pages:320
Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry?shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois.
Tracing graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included.
A foundational account of a new construction in the p-adic Langlands correspondence
Series:
Annals of Mathematics Studies
Hardcover
ISBN: 9780691241340
Published (US): Dec. 13, 2022
Copyright: 2022
Pages: 312
Paperback
SBN: 9780691241357
Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur’s formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize etale (?, Γ)-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. These stacks are then used to show that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and indeed admit crystalline lifts. The book explicitly describes the irreducible components of the underlying reduced substacks and discusses the relationship between the geometry of these stacks and the Breuil?Mezard conjecture. Along the way, it proves a number of foundational results in p-adic Hodge theory that may be of independent interest.