Due 2019-05-13
1st ed. 2019, XV, 508 p.
244 illus., 201 illus. in color.
Hardcover
ISBN 978-981-13-6580-5
Explores the well-posedness of boundary value problems for partial
differential equations in mathematical physics
Uses the perturbative method for modeling modulated matter-wave
propagation in nonlinear transmission networks
Investigates the properties of matter-wave solitons for problems of
transmission networks and Bose?Einstein condensates
Discusses the problem of the well-posedness of boundary value problems in
mathematical physics
This book explores the diverse types of Schrodinger equations that appear in nonlinear
systems in general, with a specific focus on nonlinear transmission networks and Bose?Einstein
Condensates. In the context of nonlinear transmission networks, it employs various methods to
rigorously model the phenomena of modulated matter-wave propagation in the network,
leading to nonlinear Schrodinger (NLS) equations. Modeling these phenomena is largely based
on the reductive perturbation method, and the derived NLS equations are then used to
methodically investigate the dynamics of matter-wave solitons in the network. In the context of
Bose?Einstein condensates (BECs), the book analyzes the dynamical properties of NLS
equations with the external potential of different types, which govern the dynamics of
modulated matter-waves in BECs with either two-body interactions or both two- and three-body
interatomic interactions. It also discusses the method of investigating both the well-posedness
and the ill-posedness of the boundary problem for linear and nonlinear Schrodinger equations
and presents new results. Using simple examples, it then illustrates the results on the
boundary problems. For both nonlinear transmission networks and Bose?Einstein condensates,
the results obtained are supplemented by numerical calculations and presented as figures.
Due 2019-06-04
1st ed. 2019, Approx. 300 p.
Hardcover
ISBN 978-981-13-6499-0
States systemically the theory of singular integrals and Fourier multipliers
on the Lipschitz graphs and surfaces
Elaborates the basic framework, essential thoughts and main results
Reveals the equivalence between the operator algebra of the singular
integrals, Fourier multiplier
Operators and the Cauchy-Dunford functional calculus of the Dirac operators
The main purpose of this book is to provide a detailed and comprehensive survey of the theory
of singular integrals and Fourier multipliers on Lipschitz curves and surfaces, an area that has
been developed since the 1980s. The subject of singular integrals and the related Fourier
multipliers on Lipschitz curves and surfaces has an extensive background in harmonic analysis
and partial differential equations. The book elaborates on the basic framework, the Fourier
methodology, and the main results in various contexts, especially addressing the following
topics: singular integral operators with holomorphic kernels, fractional integral and differential
operators with holomorphic kernels, holomorphic and monogenic Fourier multipliers, and
Cauchy-Dunford functional calculi of the Dirac operators on Lipschitz curves and surfaces, and
the high-dimensional Fueter mapping theorem with applications. The book offers a valuable
resource for all graduate students and researchers interested in singular integrals and Fourier
multipliers
Due 2019-06-22
Approx. 250 p.
Hardcover
ISBN 978-3-030-12276-8
This book will appeal anyone familiar with Yingkang Hu and his research in
classical and numeric approximation theory
The volume covers a variety of areas in approximation theory, harmonic
analysis and related fields
It contains longer survey papers
Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory
and related topics are covered in this volume. The topics included are Fourier analysis, Pade
approximation, dynamical systems and difference operators, splines, Christoffel functions, best
approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of
this collection were originated from the International Conference in Approximation Theory, held
in Savannah, GA in 2017, and organized by the editors of this volume.
Due 2019-07-23
1st ed. 2019, X, 115 p.
Softcover
ISBN 978-981-13-6240-8
Serves as an accessible introductory textbook on the analysis of doubly
truncated data for students of statistics, mathematics, and econometrics
Provides illustrative examples from biostatistics, economics, and other fields,
with R codes to help readers analyze their data
Presents clearer and more detailed explanations than those found in most
journal papers
This book introduces readers to statistical methodologies used to analyze doubly truncated
data. The first book exclusively dedicated to the topic, it provides likelihood-based methods,
Bayesian methods, non-parametric methods, and linear regression methods. These procedures
can be used to effectively analyze continuous data, especially survival data arising in
biostatistics and economics. Because truncation is a phenomenon that is often encountered in
non-experimental studies, the methods presented here can be applied to many branches of
science. The book provides R codes for most of the statistical methods, to help readers analyze
their data. Given its scope, the book is ideally suited as a textbook for students of statistics,
mathematics, econometrics, and other fields.
Due 2019-06-04
1st ed. 2019, Approx. 200 p.
Hardcover
ISBN 978-981-13-6627-7
Highlights the latest research on representations of p-adic groups
Features survey articles and original research articles by respected experts
Presents a survey by Anne-Marie Aubert on the hugely influential local
Langlands program
Includes a survey by Colin Bushnell on the fine structure of the local
Langlands correspondence for general linear groups
This book consists of survey articles and original research papers in the representation theory
of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the
enormously influential local Langlands conjectures. The survey gives a precise and accessible
formulation of many aspects of the conjectures, highlighting recent refinements, due to the
author and her collaborators, and their current status. It also features an extensive account by
Colin Bushnell of his work with Henniart on the fine structure of the local Langlands
correspondence for general linear groups, beginning with a clear overview of Bushnell?Kutzkofs
construction of cuspidal types for such groups. The remaining papers touch on a range of
topics in this active area of modern mathematics: group actions on root data, explicit character
formulas, classification of discrete series representations, unicity of types, local converse
theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of
exposition. The book should be a valuable resource to graduate students and experienced
researchers alike.
Due 2019-06-04
1st ed. 2019, XV, 235 p. 70
illus., 29 illus. in color.
Softcover
ISBN 978-3-030-13546-1
Contains a historically motivated introduction to Stochastic Geometry
Gives a unique and accessible overview, up to the frontiers of recent research,
of the most active fields in Stochastic Geometry
Numerous figures illustrate the chapters
This volume offers a unique and accessible overview of the most active fields in Stochastic
Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French
research structure GDR GeoSto has been preceded by two introductory courses. This book
contains five of these introductory lectures. The first chapter is a historically motivated
introduction to Stochastic Geometry which relates four classical problems (the Buffon needle
problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel
problem) to current topics. The remaining chapters give an application motivated introduction
to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject:
understanding spatial point patterns through intensity and conditional intensities; stochastic
methods for image analysis; random fields and scale invariance; and the theory of Gibbs point
processes. Exposing readers to a rich theory, this book will encourage further exploration of the
subject and its wide applications.