Series
SpringerBriefs in Mathematics
Due 2018-11-13
1st ed. 2018, X, 131 p. 10 illus.
Softcover
ISBN 978-3-030-00403-3
Offers an axiomatic presentation of the geometric algebra of an orthogonal
geometry
Illustrates topics with a variety of examples and applications
Relates Lipschitz spinorial groups and how they connect with the group of
isometries in a non-degenerate orthogonal geometry
Surveys major areas of application, particularly mathematics, physics and
engineering
This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a
real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they
relate to the group of isometries of that geometry. After a concise mathematical introduction, it
offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it
has established the language of geometric algebra (linear grading of the algebra; geometric,
exterior and interior products; involutions), it defines the spinorial groups, demonstrates their
relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a
variety of examples. Lastly, the book provides pointers to major applications, an extensive
bibliography and an alphabetic index. Combining the characteristics of a self-contained
research monograph and a state-of-the-art survey, this book is a valuable foundation reference
resource on applications for both undergraduate and graduate students.
Series
Research Perspectives CRM Barcelona
Due 2018-11-27
1st ed. 2018, IX, 88 p. 4 illus., 1 illus. in color.
Softcover
ISBN 978-3-030-00026-4
Presents new results of active areas in algebraic geometry
Covers a wide range of topics Includes open problems
This volume contains extended abstracts outlining selected talks and other selected
presentations given by participants of the workshop "Positivity and Valuations", held at the
Centre de Recerca Matematica (CRM) in Barcelona from February 22nd to 26th, 2016. They
include brief research articles reporting new results, descriptions of preliminary work or open
problems, and the outcome of work in groups initiated during the workshop. The general
subject is the application of valuation theory to positivity questions in algebraic geometry. The
topics covered range from purely algebraic problems like finite generation of semigroups and
algebras defined by valuations, and properties of the associated Poincare series, to more
geometric questions like resolution of singularities and properties of Newton-Okounkov bodies,
linked with non-archimedean geometry and tropical geometry. The book is intended for
established researchers, as well as for PhD and postdoctoral students who want to learn more
about the latest advances in these highly active areas of research.
Series
Probability Theory and Stochastic Modelling
Due 2018-11-03
1st ed. 2018, X, 405 p. 4 illus.
Hardcover
ISBN 978-3-319-99536-6
Introduces an interesting and quickly expanding theory
Provides a rigorous treatment of the subject
Presents a tool for application in financial mathematics and many other fields
of applied mathematics and function analysis
One of the main aims of this book is to exhibit some fruitful links between renewal theory and
regular variation of functions. Applications of renewal processes play a key role in actuarial and
financial mathematics as well as in engineering, operations research and other fields of applied
mathematics. On the other hand, regular variation of functions is a property that features
prominently in many fields of mathematics. The structure of the book reflects the historical
development of the authorsf research work and approach ? first some applications are
discussed, after which a basic theory is created, and finally further applications are provided.
The authors present a generalized and unified approach to the asymptotic behavior of renewal
processes, involving cases of dependent inter-arrival times. This method works for other
important functionals as well, such as first and last exit times or sojourn times (also under
dependencies), and it can be used to solve several other problems. For example, various
applications in function analysis concerning Abelian and Tauberian theorems can be studiedas
well as those in studies of the asymptotic behavior of solutions of stochastic
differentialequations. The classes of functions that are investigated and used in a probabilistic
context extend the well-known Karamata theory of regularly varying functions and thus are
also of interest in the theory of functions. The book provides a rigorous treatment of the
subject and may serve as an introduction to the field.
Series
Applied Mathematical Sciences
Due 2018-11-23
1st ed. 2018, XIV, 412 p. 12 illus., 8 illus. in color.
Hardcover
ISBN 978-3-030-00637-2
Relatively self-contained, although some familiarity with functional analysis is desirable
The presentation is very progressive, starting with simple one-dimensional
problems which can be solved explicitly and introducing progressively new
difficulties and new problems
Rigorous mathematical study of singular perturbation problems for some
elliptic and parabolic problems
Singular perturbations occur when a small coefficient affects the highest order derivatives in a
system of partial differential equations. From the physical point of view singular perturbations
generate in the system under consideration thin layers located often but not always at the
boundary of the domains that are called boundary layers or internal layers if the layer is
located inside the domain. Important physical phenomena occur in boundary layers. The most
common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a
whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid
mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph
is devoted to the study of certain classes of singular perturbation problems mostly related to
thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a
bounded domain are considered. This book is a fairly unique resource regarding the rigorous
mathematical treatment of boundary layer problems. The explicit methodology developed in
this book extends in many different directions the concept of correctors initially introduced by J.
L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions
are obtained in the setting of functional analysis. The review of differential geometry and
treatment of boundary layers in a curved domain is an additional strength of this book. In the
context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the
Navier-Stokes equations is investigated in this book and solved for a number of particular, but
physically relevant cases.
Series
Applied Mathematical Sciences
Due 2018-11-30
1st ed. 2018, VIII, 548 p.
17 illus., 10 illus. in color.
Hardcover
ISBN 978-3-030-01505-3
Allows readers and graduate students with no background to start with the basic concepts
The application-oriented readers will see how the abstract results apply to biological and physical problems
Learn the fundamental theories on abstract equations
Several types of differential equations, such as functional differential equation, age-structured
models, transport equations, reaction-diffusion equations, and partial differential equations with
delay, can be formulated as abstract Cauchy problems with non-dense domain. This
monograph provides a self-contained and comprehensive presentation of the fundamental
theory of non-densely defined semilinear Cauchy problems and their applications. Starting from
the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph
introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the
existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of
solutions with respect to the state variable, and time differentiability of solutions. Combining
the functional analysis method and bifurcation approach in dynamical systems, then the
nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation,
and normal form theory are established for abstract Cauchy problems with non-dense domain.
Finally applications to functional differential equations, age-structured models, and parabolic
equations are presented. This monograph will be very valuable for graduate students and
researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems,
and their applications in biological, chemical, medical, and physical problems.
Series
Springer Proceedings in Mathematics & Statistics
Due 2018-11-28
1st ed. 2018, XIII, 407 p.
87 illus., 52 illus. in color.
Hardcover
ISBN 978-981-13-2094-1
Discusses recent advances in mathematics and statistics and their applications in computing
Presents research papers on areas of current interest, like operations
research, soft computing, applied mathematical modeling, cryptology, and security analysis
Is useful to aspiring researchers in various areas of mathematics
This book discusses recent advances and research in applied mathematics, statistics and their
applications in computing. It features papers presented at the fourth conference in the series
organized at the Indian Institute of Technology (Banaras Hindu University), Varanasi, India, on
9 ? 11 January 2018 on areas of current interest, including operations research, soft
computing, applied mathematical modelling, cryptology, and security analysis. The conference
has emerged as a powerful forum, bringing together leading academic scientists, experts from
industry, and researchers and offering a venue to discuss, interact and collaborate to stimulate
the advancement of mathematics and its applications in computer science. The education of
future consumers, users, producers, developers and researchers of mathematics and its
applications is an important challenge in modern society, and as such, mathematics and its
application in computer science are of vital significance to all spectrums of the community, as
well as to mathematicians and computing professionals across different educational levels and
disciplines. With contributions by leading international experts, this book motivates and creates
interest among young researchers.