The revealing of the phenomenon of superhydrophobicity (the "lotus-effect") has stimulated an interest in wetting of real (rough and chemically heterogeneous) surfaces. In spite of the fact that wetting has been exposed to intensive research for more than 200 years, there still is a broad field open for theoretical and experimental research, including recently revealed superhydrophobic, superoleophobic and superhydrophilic surfaces, so-called liquid marbles, wetting transitions, etc. This book integrates all these aspects within a general framework of wetting of real surfaces, where physical and chemical heterogeneity is essential.
Wetting of rough/heterogeneous surfaces is discussed through the use of the variational approach developed recently by the author. It allows natural and elegant grounding of main equations describing wetting of solid surfaces, i.e. Young, Wenzel and Cassie-Baxter equations. The problems of superhydrophobicity, wetting transitions and contact angle hysteresis are discussed in much detail, in view of novel models and new experimental data. The second edition surveys the last achievements in the field of wetting of real surfaces, including new chapters devoted to the wetting of lubricated and gradient surfaces and reactive wetting, which have seen the rapid progress in the last decade. Additional reading, surveying the progress across the entire field of wetting of real surfaces, is suggested to the reader. Contents What is surface tension? Wetting of ideal surfaces Contact angle hysteresis Dynamics of wetting Wetting of rough and chemically heterogeneous surfaces: the Wenzel and Cassie Models Superhydrophobicity, superhydrophilicity, and the rose petal effect Wetting transitions on rough surfaces
De Gruyter Studies in Mathematical Physics 19
xix, 178 pages Hardcover ISBN 978-3-11-058106-5
Date of Publication: November 2018
Language of Publication: English
Applied Mathematics Condensed Matter Physics Theoretical and Mathematical Physics
Theoretical Physicists, Materials Scientists, Theoretical Chemists
Numerical analysis deals with the development and analysis of algorithms for scientific computing, and is in itself a very important part of mathematics, which has become more and more prevalent across the mathematical spectrum. This book is an introduction to numerical methods for solving linear and nonlinear systems of equations as well as ordinary and partial differential equations, and for approximating curves, functions, and integrals.
? A compact and concise introduction to numerical analysis ? Covers a wealth of material, from computer arithmetic to the solution of ODE's and PDE's ? Ideal for students and lecturers in mathematics, physics, and engineering Timo Heister, Leo G. Rebholz, and Fei Xue, Clemson University, USA.
De Gruyter Textbook
Approx. xii, 196 pages
Paperback: ISBN 978-3-11-057330-5
Date of Publication: March 2019
Language of Publication: English
Applied Mathematics
Numerical and Computational Mathematics
Students and lecturers in applied and numerical mathematics, physics, and engineerin
Starting with the fundamentals of Q¿ spaces and their relationships to Besov spaces, this book presents all major results around Q¿ spaces obtained in the past 16 years. The applications of Q¿ spaces in the study of the incompressible Navier-Stokes system and its stationary form are also discussed. This selfcontained book can be used as an essential reference for researchers and graduates in analysis and partial differential equations. ? A mathematically rigorous study of Q¿ Analysis on Euclidean spaces. ? Presents the advanced theories in an easy-to-understand way. ? Of interest to researchers and graduate students working in analysis and partial differential equations. Jie Xiao, Memorial University of Newfoundland, St. John's, Canada
Advances in Analysis and Geometry 1
Approx. x, 200 pages
Hardcover: ISBN 978-3-11-060112-1
Date of Publication: April 2019
Language of Publication: English
Analysis Differential Equations and Dynamical Systems
Researchers and graduate students in analysis and partial differential
equations.
ISBN: 978-0-470-90305-6 May 2019 448 Pages
Hardcover
Game-theoretic probability and finance come of age
Glenn Shafer and Vladimir Vovkfs Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Itofs stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory.
Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context.
Praise from early readers
gEver since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.h ? Peter Grunwald, CWI and University of Leiden
gShafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.h ? Ioannis Karatzas, Columbia University
Glenn Shafer is University Professor at Rutgers University.
Vladimir Vovk is Professor in the Department of Computer Science at Royal Holloway, University of London. They are the authors of Probability and Finance: Itfs Only a Game, published by Wiley and co-authors of Algorithmic Learning in a Random World. Shaferfs other previous books include A Mathematical Theory of Evidence and The Art of Causal Conjecture.
Paperback 2019 22.95 17.99
ISBN
9780691149158 200 pp. 6 5/8 x 9 1/4 181 color + 1 b/w illus. forthcoming August 2019
An outrageous graphic novel that investigates key concepts in mathematics
Integers and permutations?two of the most basic mathematical objects?are born of different fields and analyzed with different techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body.
Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics.Travel with Detective von Neumann as he leaves no clue unturned, from shepherdsf huts in the Pyrenees to secret societies in the cafes of Paris, from the hidden codes in the music of the stones to the grisly discoveries in Finite Fields. Tremble at the ferocity of the believers in deep and rigid abstraction. Feel the pain as you work with our young heroine, Emmy Germain, as she blazes a trail for women in mathematical research and learns from Professor Gauss, the greatest forensic detective of them all.
Beautifully drawn and wittily and exquisitely detailed, Prime Suspects is unique, astonishing, and outrageous?a once-in-a-lifetime opportunity to experience mathematics like never before.
Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. Jennifer Granville is an award-winning producer, screenwriter, and director, and the coauthor of The Casting Handbook: For Film and Theatre Makers.
"Properties of integers, polynomials, and permutations are shown to be identical in this beautifully illustrated graphic novel murder mystery that is a fun read for the mathematically inclined."?Dorian Goldfeld, Columbia University
"The reader gets hooked on reading more and more about the mystery of primes and permutations. Prime Suspects presents some real mathematics in such a fresh and novel way!"?Kaisa Matomaki, University of Turku, Finland
Mathematics - Number Theory
Mathematics - Number Systems
Mathematics - Numerical Analysis
Mathematics - General
Comics & Graphic Novels - Nonfiction - General