Part of Australian Mathematical Society Lecture Series
available from September 2020
FORMAT: Paperback
ISBN: 9781108794459
Paperback
The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, special functions and random walks. This friendly and concise introduction to the Mahler measure is a valuable resource for both graduate courses and self-study. It provides the reader with the necessary background material, before presenting the recent achievements and the remaining challenges in the field. The first part introduces the univariate Mahler measure and addresses Lehmer's question, and then discusses techniques of reducing multivariate measures to hypergeometric functions. The second part touches on the novelties of the subject, especially the relation with elliptic curves, modular forms and special values of L-functions. Finally, the Appendix presents the modern definition of motivic cohomology and regulator maps, as well as Deligne-Beilinson cohomology. The text includes many exercises to test comprehension and challenge readers of all abilities.
Bridges the gap between the arithmetic theory of algebraic numbers and complex analysis
Displays the source of general connections between regulators and the values of L-functions
Gives numerous applications to concrete number-theoretical problems of hypergeometric and modular functions
Part of Cambridge Tracts in Mathematics
available from November 2020
FORMAT: Hardback
ISBN: 9781108478717
Matrix positivity is a central topic in matrix theory: properties that generalize the notion of positivity to matrices arose from a large variety of applications, and many have also taken on notable theoretical significance, either because they are natural or unifying. This is the first book to provide a comprehensive and up-to-date reference of important material on matrix positivity classes, their properties, and their relations. The matrix classes emphasized in this book include the classes of semipositive matrices, P-matrices, inverse M-matrices, and copositive matrices. This self-contained reference will be useful to a large variety of mathematical, engineering and social scientists and graduate students. The generalizations of positivity and the connections observed provide a unique perspective, along with theoretical insight into applications and future challenges. Direct applications can be found in data analysis, differential equations, mathematical programming, computational complexity, models of the economy, population biology, dynamical systems and control theory.
Covers several new topics in matrix classes that have not appeared in book form previously
Unified coverage presented by the leaders in the field of matrix positivity
Matrix classes are compared and interrelated, and their theory is developed in a natural order, which will lend to a well-rounded understanding of the theory, as well as its historical and scientific development
Background
1. Positivity classes
2. Semipositive matrices
3. P-matrices
4. Inverse M-matrices
5. Copositive matrices.
Published March 4, 2020
Textbook - 350 Pages - 36 B/W Illustrations
ISBN 9780367510459 - CAT# 376356
The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students, faculty, and professionals in scientific fields such as computer science, mathematics, engineering, and physics. Unlike previous books, the only prerequisites are knowledge of first year calculus and a little programming experience a background that can be assumed of the intended audience. The book is written in a lean and lively style, with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures, while also discussing the inherent and practical limitations of these systems
1 Introduction
2 Computer Algebra Systems
3 Big Number Arithmetic
4 Polynomial Manipulation
5 Algebraic Simpli cation
6 Factorization
7 Symbolic Integration
8 Grobner Bases
9 Mathematical Correctness
The book illustrates the theoretical results of fractional derivatives via
applications in signals and systems, covering continuous and discrete
derivatives, and the corresponding linear systems. Both time and frequency
analysis are presented. Some advanced topics are included like derivatives of
stochastic processes. It is an essential reference for researchers in mathematics,
physics, and engineering.
Presents the theory and applications of fractional derivatives in signals and
systems.
Both time and frequency analysis are presented.
Of interest to mathematicians and physicists as well as to engineers.
Manuel Duarte Ortigueira, Universidade Nova de Lisboa, Portugal;Duarte
Valrio, Instituto Superior Tcnico, Portugal.
Fractional Calculus in Applied Sciences
and Engineering
7 xvii, 281 pages, 50 Figures (bw),
30 Schedule (bw)
Hardcover:
ISBN 978-3-11-062129-7
Date of Publication: March 2020
Language of Publication: English
Subjects: Applied Mathematics Electrical Engineering Signal Processing
Of interest to: Applied mathematicians, statistical physicists, computer scientists,and engineers
This work concerns the computational modelling of the dynamics of partially
ionized gases, with emphasis on electrodischarge processes. Understanding gas
discharges is fundamental for many processes in mechanics, manufacturing,
materials science, and aerospace engineering.
This second edition has been expanded to include the latest developments in the
field, especially regarding the drift-diffusion model and rarefied hypersonic
flow.
Special focus on two-dimensional problems (electric arc; radiofrequency,
microwave, optical discharges).
With discussion of the use of glow discharges in aerospace technology.
Includes many examples from modern computational
magnetohydrodynamics.
Sergey T. Surzhikov, Institute for Problems in Mechanics, Russian Academy of
Sciences, Moscow, Russia.
Texts and Monographs in Theoretical Physics
Approx. xi,300 pages, 111 Figures (bw), 147 Figures (c),
Hardcover:
ISBN 978-3-11-064635-1
Date of Publication: April 2020
Language of Publication: English
Subjects: Applied Mathematics
Modeling and Simulations
Technical and Applied Physics
Theoretical and Mathematical Physics
Of interest to: Researches and postgraduate students in Physics, Mathematics,
Engineering; practitioners in aerospace engineering
The contributions by leading experts in this book focus on a variety of
topics of
current interest related to information-based complexity, ranging from function
approximation, numerical integration, numerical methods for the sphere, and
algorithms with random information, to Bayesian probabilistic numerical
methods and numerical methods for stochastic differential equations.
Presents the state-of-the-art around information-based complexity
Includes contributions by leading experts in the field
Covers both theoretical and numerical results as well as their applications
Fred J. Hickernell, Illinois Institute of Technology, USA; Peter Kritzer,
Johann Radon Institute, Austria.
Radon Series on Computational and Applied Mathematics 27
Approx. xii, 170 pages, 4 Figures (bw), 16 Figures (c)
Hardcover:
ISBN 978-3-11-063311-5
Date of Publication: May 2020
Language of Publication: English
Subjects: Algorithms
Applied Mathematics
Numerical and Computational Mathematics
Probability and Statistics
Of interest to: Researchers and graduate
students in applied and numerical
mathematics and in computer scien
This self-contained book covers the theory of semilinear equations with sectorial
operator going back to the studies of Yosida, Henry, and Pazy, which are deeply
extended nowadays. The treatment emphasizes existence-uniqueness theory as a
topic of functional analysis and examines abstract evolutionary equations, with
applications to the Navier-Stokes system, the quasi-geostrophic equation, and
fractional reaction-diffusion equations.
A self-contained book on parabolic problems with critical nonlinearities
Includes applications to the Navier-Stokes equations, the quasi-geostrophic
equation, and reaction-diffusion systems
Of interest to researchers and graduate students alike
Tomasz W. D‚otko, University of Silesia in Katowice, Poland; Yejuan Wang,
Lanzhou University, P. R. China.
De Gruyter Series in Nonlinear Analysis and Applications 34
Approx. xii, 300 pages
Hardcover:
ISBN 978-3-11-059755-4
Date of Publication: May 2020
Language of Publication: English
Subjects: Analysis
Of interest to: Researchers and graduate students in partial differential equatio