For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory.
Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics.
The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.
Format Hardback | 192 pages
Dimensions 156 x 234mm
Publication date 17 Feb 2020
Language English
ISBN13 9780198853404
Open Access
2020, IX, 772 p. 1illus.
Hardcover
ISBN 978-3-030-36713-8
Series :Monographs in Mathematics
Self-contained and written in an accessible style
Provides an overview of the theory of boundary triplet techniques
This open access book presents a comprehensive survey of modern operator techniques for
boundary value problems and spectral theory, employing abstract boundary mappings and
Weyl functions. It includes self-contained treatments of the extension theory of symmetric
operators and relations, spectral characterizations of selfadjoint operators in terms of the
analytic properties of Weyl functions, form methods for semibounded operators, and functional
analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract
methods for various applications, including Sturm-Liouville operators, canonical systems of
differential equations, and multidimensional Schrödinger operators, where the abstract Weyl
function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann
map. The book is a valuable reference text for researchers in the areas of differential
equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its
detailed exposition of the theory, it is also accessible and useful for advanced students and
researchers in other branches of natural sciences and engineering.
2019, XII, 119 p. 1illus.
Hardcover
ISBN 978-981-15-1730-3
Series: Theoretical Biology
Includes reviews of representative topics of chases and escapes as well as
collective behavior in one book
Describes the new research topic of group chase and escape with concrete
examples
Is written in a readable manner for those from related fields of mathematics,
biology, physics, and engineering
Can be used as a supplementary text in applied mathematics, engineering,
and physics for upper-undergraduate to graduate courses
This book presents a unique fusion of two different research topics. One is related to the
traditional mathematical problem of chases and escapes. The problem mainly deals with a
situation where a chaser pursues an evader to analyze their trajectories and capture time. It
dates back more than 300 years and has developed in various directions such as differential
games. The other topic is the recently developing field of collective behavior, which investigates
origins and properties of emergent behavior in groups of self-driving units. Applicationsinclude
schools of fish, flocks of birds, and traffic jams. This book first reviews representative topics,
both old and new, from these two areas. Then it presents the combined research topic of
"group chase and escape", recently proposed by the authors. Although the combination is
simple and straightforward, the book describes the emergence of rather intricate behavior,
provoking the interest of readers for further developments and applications of related topics.
Due 2020-02-14
1st ed. 2019, IX, 112 p. 33 illus., 11 illus. in color.
Softcover
ISBN 978-981-15-1856-0
Series :JSS Research Series in Statistics
Presents the Bayesian estimation method for the discrete/continuous choice
approach for demand under block rate pricing
Explains the model coherency inherent in discrete/continuous choice and its
connection to microeconomic theory
Applies the estimation method to real-world datasets for the analysis of
demand under block rate pricing, which can be used for prediction as well as
policymaking
This book focuses on the structural analysis of demand under block rate pricing, a type of
nonlinear pricing used mainly in public utility services. In this price system, consumers are
presented with several unit prices, which makes a naive analysis biased. However, the response
to the price schedule is often of interest in economics and plays an important role in
policymaking. To address this issue, the book adopts a structural approach, referred to as the
discrete/continuous choice approach in the literature, to develop corresponding statistical
models for analysis.The resulting models are extensions of the Tobit model, a well-known
statistical model in econometrics, and their hierarchical structure fits well in Bayesian
methodology. Thus, the book takes the Bayesian approach and develops the Markov chain
Monte Carlo method to conduct statistical inferences. The methodology derived is then applied
to real-world datasets, microdata collected in Tokyo and the neighboring Chiba Prefecture, as a
useful empirical analysis for prediction as well as policymaking.
Due 2020-01-28
1st ed. 2019, XIII, 139 p. 22 illus.
Hardcover
ISBN 978-3-030-34639-3
Series: Moscow Lectures
Using basic tools from the first year of university studies, the book leads a
reader to the impressive achievements of mathematics of the 21st century
Studying the book, the reader will get acquainted with analytical and
harmonic functions, as well as with the main results of the theory of Riemann
surfaces. The reader will also get acquainted with the modern use of these
results for solving classical problems of practical importance. These
applications are based on the theory of integrable systems, which is also
discussed in the book
Practical all the statements are given in the book with full proofs
This book is devoted to classical and modern achievements in complex analysis. In order to
benefit most from it, a first-year university background is sufficient; all other statements and
proofs are provided. We begin with a brief but fairly complete course on the theory of
holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory,
and discuss a representation of the moduli space of Riemann surfaces of a fixed topological
type as a factor space of a contracted space by a discrete group. Next, we consider compact
Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We
also construct theta functions that are very important for a range of applications. After that, we
turn to modern applications of this theory. First, we build the (important for mathematics and
mathematical physics) Kadomtsev-Petviashvilihierarchyand use validated results to arrive at
important solutions to these differential equations.
*
Due 2020-03-17
1st ed. 2020, X, 114 p. 24 illus., 6 illus. in color.
Softcover
ISBN 978-3-030-36914-9
Series: SpringerBriefs in Mathematics
Introduces the concept of topological derivative in a simple and pedagogical
manner using a direct approach based on calculus of variations combined
with compound asymptotic analysis
Offers numerical methods in shape optimization, including algorithms and
applications in the context of compliance structural topology optimization
and topology design of compliant mechanisms
Explores the mathematical aspects of topological asymptotic analysis as well
as on applications of the topological derivative in computational mechanics,
including shape and topology optimization
This book presents the topological derivative method through selected examples, using a direct
approach based on calculus of variations combined with compound asymptotic analysis. This
new concept in shape optimization has applications in many different fields such as topology
optimization, inverse problems, imaging processing, multi-scale material design and mechanical
modeling including damage and fracture evolution phenomena. In particular, the topological
derivative is used here in numerical methods of shape optimization, with applications in the
context of compliance structural topology optimization and topology design of compliant
mechanisms. Some exercises are offered at the end of each chapter, helping the reader to
better understand the involved concepts.
Due 2020-03-13
1st ed. 2020, XVI, 169 p. 3 illus.
Hardcover
ISBN 978-1-0716-0330-7
Series: Applied and Numerical Harmonic Analy
Explores recent developments in the field of time-frequency analysis,
particularly focusing on the topic of modulation spaces
Presents valuable applications of modulation spaces to pseudodifferential
operators and partial differential equations
Appeals to a wide audience with its clear and self-contained presentation
This monograph serves as a much-needed, self-contained reference on the topic of modulation
spaces. By gathering together state-of-the-art developments and previously unexplored
applications, readers will be motivated to make effective use of this topic in future research.
Because modulation spaces have historically only received a cursory treatment, this book will
fill a gap in time-frequency analysis literature, and offer readers a convenient and timely
resource. Foundational concepts and definitions in functional, harmonic, and real analysis are
reviewed in the first chapter, which is then followed by introducing modulation spaces. The
focus then expands to the many valuable applications of modulation spaces, such as linear
and multilinear pseudodifferential operators, and dispersive partial differential equations.
Because it is almost entirely self-contained, these insights will be accessible to a wide audience
of interested readers. Modulation Spaces will be an ideal reference for researchers in timefrequency analysis and nonlinear partial differential equations. It will also appeal to graduate
students and seasoned researchers who seek an introduction to the time-frequency analysis of
nonlinear dispersive partial differential equations.