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.
Product category : Monograph
Softcover
ISBN 978-981-13-6583-6
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
Product category : Monograph
Softcover
ISBN 978-981-13-6502-7
Provides a rigorous mathematical perspective on error-correcting codes
Offers a pathway from the basics to the state-of-the-art, suitable for either
independent study or the classroom
Corresponds to a one-semester course, where each chapter suits a two-hour
lecture
Includes numerous helpful exercises with selected solutions provided
This textbook provides a rigorous mathematical perspective on error-correcting codes, starting
with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and
geometric approaches to coding theory are adopted with the aim of highlighting how coding
can have an important real-world impact. Because it carefully balances both theory and
applications, this book will be an indispensable resource for readers seeking a timely treatment
of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s
theorem, asymptotically good codes and linear codes. The book then goes on to cover other
types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC
codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the
helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an
interdisciplinary audience at the Masters level, including students of mathematics, engineering,
physics, and computer science. Advanced undergraduates will find this a useful resource as
well. An understanding of linear algebra is assumed.
Due 2020-07-08
1st ed. 2020, XIII, 177 p.
12 illus., 5 illus. in color.
Softcover
ISBN 978-3-030-41152-7
Product category : Graduate/advanced undergraduate textbook
Series : Compact Textbooks in Mathematics
Explores current and potential statistical methodology systems for global
health research
Features data using R
Provides researchers and students access to new methods for collecting new
data
This book examines statistical methods and models used in the fields of global health and
epidemiology. It includes methods such as innovative probability sampling, data harmonization
and encryption, and advanced descriptive, analytical and monitory methods. Program codes
using R are included as well as real data examples. Contemporary global health and
epidemiology involves a myriad of medical and health challenges, including inequality of
treatment, the HIV/AIDS epidemic and its subsequent control, the flu, cancer, tobacco control,
drug use, and environmental pollution. In addition to its vast scales and telescopic perspective;
addressing global health concerns often involves examining resource-limited populations with
large geographic, socioeconomic diversities. Therefore, advancing global health requires new
epidemiological design, new data, and new methods for sampling, data processing, and
statistical analysis. This book provides global health researchers with methods that will enable
access to and utilization of existing data. Featuring contributions from both epidemiological and
biostatistical scholars, this book is a practical resource for researchers, practitioners, and
students in solving global health problems in research, education, training, and consultation.
1st ed. 2020, XV, 403 p.
161 illus., 129 illus. in color.
Hardcover
ISBN 978-3-030-35259-2
Product category : Contributed volume
Series : ICSA Book Series in Statistics
Presents the essentials of efficiently combining graph analysis algorithms
and high performance computing
Describes several parallel algorithms used in distributed graph analytics in a
high level notation along with examples
Includes suggestive results on different platforms, which highlight the theory
and practice covered in the book
Illustrates many of the concepts using Falcon, a domain-specific language for
graph algorithms
This book brings together two important trends: graph algorithms and high-performance
computing. Efficient and scalable execution of graph processing applications in data or network
analysis requires innovations at multiple levels: algorithms, associated data structures, their
implementation and tuning to a particular hardware. Further, programming languages and the
associated compilers play a crucial role when it comes to automating efficient code generation
for various architectures. This book discusses the essentials of all these aspects. The book is
divided into three parts: programming, languages, and their compilation. The first part
examines the manual parallelization of graph algorithms, revealing various parallelization
patterns encountered, especially when dealing with graphs. The second part uses these
patterns to provide language constructs that allow a graph algorithm to be specified.
Programmers can work with these language constructs without worrying about their
implementation, which is the focus of the third part. Implementation is handled by a compiler,
which can specialize code generation for a backend device. The book also includes suggestive
results on different platforms, which illustrate and justify the theory and practice covered.
Together, the three parts provide the essential ingredients for creating a high-performance
graph application. The book ends with a section on future directions, which offers several
pointers to promising topics for future research. This book is intended for new researchers as
well as graduate and advanced undergraduate students.
1st ed. 2020, XI, 207 p. 44
illus.
Hardcover
ISBN 978-3-030-41885-4
Product category : Monograph
Application of indicial notation to vectors and tensors, applying this to fluid
mechanics to provide physical interpretation
Derivation of complex variables in general terms, viewing them as a non
(Cartesian coordinate transformation. )
This derivation uses the coordinate
transformations presented earlier in the text using indicial notation (covariant
and contra variant vector components)
Applications of the first and second order partial differential equations in
engineering. The applications of second order partial differential equations
are to fluid mechanics, groundwater flow, heat flow, linear elasticity, and soil
mechanics
Treatment of singularities in elliptic partial differential equations, and
discontinuiti
This textbook presents the application of mathematical methods and theorems tosolve
engineering problems, rather than focusing on mathematical proofs. Applications of Vector
Analysis and Complex Variables in Engineering explains the mathematical principles in a
manner suitable for engineering students, who generally think quite differently than students
of mathematics. The objective is to emphasize mathematical methods and applications, rather
than emphasizing general theorems and principles, for which the reader is referred to the
literature. Vector analysis plays an important role in engineering, and is presented in terms of
indicial notation, making use of the Einstein summation convention.This text differs from most
texts in that symbolic vector notation is completely avoided, as suggested in the textbooks on
tensor algebra and analysis written in German by Duschek and Hochreiner, in the 1960s
1st ed. 2020, XIV, 216 p. 86
illus. in color.
Hardcover
ISBN 978-3-030-41167-1
Product category : Graduate/advanced undergraduate textbook
Offers a wide range of control problems successfully solved within the
framework of the SMC theory
Includes a selection of reduced-order differential equations with desired
solutions
Shows the potential and advantages of the developed control methods and
outlines areas of efficient application
This book is devoted to control of finite and infinite dimensional processes
with continuoustime and discrete timecontrol,
focusing on suppression problems and new methods of
adaptation applicable for systems with sliding motions only. Special mathematical methods are
needed for all the listed control tasks. These methods are addressed in the initial chapters,
with coverage of the definition of the multidimensional sliding modes, the derivation of the
differential equations of those motions, and the existence conditions. Subsequent chapters
discusses various areas of further research. The book reflects the consensus view of the
authors regarding the current status of SMC theory. It is addressed to a broad spectrum of
engineers and theoreticians working in diverse areas of control theory and applications. It is
well suited for use in graduate and postgraduate courses in such university programs as
Electrical Engineering, Control of Nonlinear Systems, and Mechanical Engineering.
1st ed. 2020, XIV, 127 p. 35
illus., 20 illus. in color.
Softcover
ISBN 978-3-030-41708-6
Product category : Brief
Series : SpringerBriefs in Mathematics