Introduces a new method called Yang?Baxter deformation to perform
integrable deformations systematically
Presents very recent progress in this method, not found in any similar book
Begins with the basics of classical integrability and introduces this method
pedagogically
In mathematical physics, one of the fascinating issues is the study of integrable systems. In
particular, non-perturbative techniques that have been developed have triggered significant
insight for real physics. There are basically two notions of integrability: classical integrability
and quantum integrability. In this book, the focus is on the former, classical integrability. When
the system has a finite number of degrees of freedom, it has been well captured by the
Arnold?Liouville theorem. However, when the number of degrees of freedom is infinite, as in
classical field theories, the integrable structure is enriched profoundly. In fact, the study of
classically integrable field theories has a long history and various kinds of techniques,
including the classical inverse scattering method, which have been developed so far. In
previously published books, these techniques have been collected and well described and are
easy to find in traditional, standard textbooks. One of the intriguing subjects in classically
integrable systems is the investigation of deformations preserving integrability. Usually, it is not
considered systematic to perform such a deformation, and one must study systems case by
case and show the integrability of the deformed systems by constructing the associated Lax
pair or action-angle variables. Recently, a new, systematic method to perform integrable
deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in
2002, and the integrability of the deformed sigma models was shown in 2008. The original
work was done for 2D principal chiral models, but it has been generalized in various directions
nowadays
1st ed. 2021, XII, 70 p. 2 illus.
Softcover
ISBN 978-981-16-1702-7
Product category : Brief
Series : SpringerBriefs in Mathematical Physics
Mathematics : Mathematical Physics
Eigenvarieties, families of Galois representations, p-adic L-functions
Offers a comprehensive and solid introduction to the theory
Includes exercises and solutions
Presents a unique collection of knowledge on this theory not available
elsewhere
This book discusses thep-adic modular forms, the eigencurve that parameterize them, and thepadicL
-functions one can associate to them. These theories and their generalizations to
automorphic forms for group of higher ranks are of fundamental importance in number theory.
For graduate students and newcomers to this field, the book provides a solid introduction to
this highly active area of research. For experts, it will offer the convenience of collecting into
one place foundational definitions and theorems with complete and self-contained proofs.
Written in an engaging and educational style, the book also includes exercises and provides
their solution.
Due 2021-08-03
1st ed. 2021, XI, 314 p. 16 illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-77262-8
Product category : Graduate/advanced undergraduate textbook
Series : Pathways in Mathematics
Mathematics : Number Theory
Presents a concise introduction to bootstrap methods
Includes implementations of the algorithms in R, focusing on comprehensibility
Emphasizes goodness-of-fit tests
Provides complete proofs for those interested in theory and various
applications for those interested in practice
This book provides a compact introduction to the bootstrap method. In addition to classical
results on point estimation and test theory, multivariate linear regression models and
generalized linear models are covered in detail. Special attention is given to the use of
bootstrap procedures to perform goodness-of-fit tests to validate model or distributional
assumptions. In some cases, new methods are presented here for the first time. The text is
motivated by practical examples and the implementations of the corresponding algorithms are
always given directly in R in a comprehensible form. Overall, R is given great importance
throughout. Each chapter includes a section of exercises and, for the more mathematically
inclined readers, concludes with rigorous proofs. The intended audience is graduate students
who already have a prior knowledge of probability theory and mathematical statistics.
Due 2021-08-15
1st ed. 2021, XVI, 256 p. 36 illus., 28 illus. in color.
ISBN 978-3-030-73479-4
Product category : Graduate/advanced undergraduate textbook
Statistics : Statistical Theory and Methods
Develops fundamental concepts in algebra, geometry, and number theory
from the foundations of set theory
Engages readers through challenging examples and problems inspired by
mathematical contests
Illuminates the historical context of key mathematical developments
This textbook offers a rigorous presentation of mathematics before the advent of calculus.
Fundamental concepts in algebra, geometry, and number theory are developed from the
foundations of set theory along an elementary, inquiry-driven path. Thought-provoking
examples and challenging problems inspired by mathematical contests motivate the theory,
while frequent historical asides reveal the story of how the ideas were originally developed.
Beginning with a thorough treatment of the natural numbers via Peano’s axioms, the opening
chapters focus on establishing the natural, integral, rational, and real number systems. Plane
geometry is introduced via Birkhoff’s axioms of metric geometry, and chapters on polynomials
traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary
classification of conics is given, followed by an in-depth study of rational expressions.
Exponential, logarithmic, and trigonometric functions complete the picture, driven by
inequalities that compare them with polynomial and rational functions. Axioms and limits
underpin the treatment throughout, offering not only powerful tools, but insights into nontrivial
connections between topics. Elements of Mathematics is ideal for students seeking a
deep and engaging mathematical challenge based on elementary tools. Whether enhancing the
early undergraduate curriculum for high achievers, or constructing a reflective senior capstone,
instructors will find ample material for enquiring mathematics majors. No formal prerequisites
are assumed beyond high school algebra, making the book ideal for mathematics circles and
competition preparation. Readers who are more advanced in their mathematical studies will
appreciate the interleaving of ideas and illuminating historical details.
Due 2021-09-03
1st ed. 2021, VIII, 424 p. 33 illus., 3 illus. in color.
Hardcover
ISBN 978-3-030-75050-3
Product category : Undergraduate textbook
Series : Readings in Mathematics
Mathematics : Real Functions
Solves the problem of the non-self-adjoint Schrodinger operator with periodic
potential complete with construction of the spectral expansion
Presents the complete spectral theory of the non-self-adjoint MathieuSchrodinger operator
Features a detailed classification of the spectrum and spectral expansion of
the Schrodinger operator with a PT-symmetric periodic optical potential
This book gives a complete spectral analysis of the non-self-adjoint Schrodinger operator with
a periodic complex-valued potential. Building from the investigation of the spectrum and
spectral singularities and construction of the spectral expansion for the non-self-adjoint
Schrodinger operator, the book features a complete spectral analysis of the Mathieu
Schrodinger operator and the Schrodinger operator with a parity-time (PT)-symmetric periodic
optical potential. There currently exists no general spectral theorem for non-self-adjoint
operators; the approaches in this book thus open up new possibilities for spectral analysis of
some of the most important operators used in non-Hermitian quantum mechanics and optics.
Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is
ideally suited for graduate students at the intersection of physics and mathematics.
Due 2021-07-21
1st ed. 2021, X, 294 p. 10 illus., 9 illus. in color.
Hardcover
ISBN 978-3-030-72682-9
Product category : Monograph
Physics : Theoretical, Mathematical and Computational Physics
Demonstrates the asymptotic convergence to stationary solutions for global
solutions of abstract parabolic equations
Includes n-dimensional semilinear parabolic equations and higher
dimensional Keller?Segel equations among its topics
Provides the methodology for presenting extremely precise convergence
results
This second volume continues the study on asymptotic convergence of global solutions of
parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution
equations and the ojasiewicz?Simon gradient inequality. In the first volume of the same title,
after setting the abstract frameworks of arguments, a general convergence theorem was
proved under the four structural assumptions of critical condition, Lyapunov function, angle
condition, and gradient inequality. In this volume, with those abstract results reviewed briefly,
their applications to concrete parabolic equations are described. Chapter 3 presents a
discussion of semilinear parabolic equations of second order in general n-dimensional spaces,
and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which
incorporate general roughening functions. In Chapter 5 consideration is given to the Keller?
Segel equations in one-, two-, and three-dimensional spaces. Some of these results had
already been obtained and published by the author in collaboration with his colleagues.
However, by means of the abstract theory described in the first volume, those results can be
extended much more. Readers of this monograph should have a standard-level knowledge of
functional analysis and of function spaces.
Due 2021-07-30
1st ed. 2021, IX, 128 p. 1 illus.
Softcover
ISBN 978-981-16-2662-3
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Analysis