A publication of the Societe Mathematique de France
Memoires de la Societe Mathematique de France, Volume: 171
2022; 110 pp; Softcover
MSC: Primary 60; 58; 53; 35;
Print ISBN: 978-2-85629-935-7
On a manifold, consider an elliptic diffusion X admitting an invariant measure μ. The goal of this paper is to introduce and investigate the first properties of stochastic domain evolutions (Dt)t∈[0,τ] which are intertwining dual processes for X (where τ is an appropriate positive stopping time before the potential emergence of singularities).
A publication of the Societe Mathematique de France
Memoires de la Societe Mathematique de France, Volume: 172
2022; 123 pp; Softcover
MSC: Primary 35;
Print ISBN: 978-2-85629-955-5
The author proves almost sharp decay estimates for the small data solutions and their derivatives of the Vlasov-Maxwell system in dimension n?4. The smallness assumption concerns only certain weighted L1 or L2 norms of the initial data. In particular, no compact support assumption is required on the Vlasov or the Maxwell fields. The main ingredients of the proof are vector field methods for both the kinetic and the wave equations, null properties of the Vlasov-Maxwell system to control high velocities and a new decay estimate for the velocity average of the solution of the relativistic massive transport equation.
The author also considers the massless Vlasov-Maxwell system under a lower bound on the velocity support of the Vlasov field. As he proves in this book, the velocity support of the Vlasov field needs to be initially bounded away from 0. The author compensates the weaker decay estimate on the velocity average of the massless Vlasov field near the light cone by an extra null decomposition of the velocity vector.
New in Paperback
Paperback
Published: 21 February 2022
800 Pages | Over 280 illustrations/figures
246x171mm
ISBN: 9780192862808
Unique coverage of the broad ground spanned by the lattice Boltzmann method
New connections between fluids, condensed matter, and high energy physics
Multiple ramifications to physics, biology, mathematics, and computer science explored
Flowing matter is all around us, from daily-life vital processes (breathing, blood circulation), to industrial, environmental, biological, and medical sciences. Complex states of flowing matter are equally present in fundamental physical processes, far remote from our direct senses, such as quantum-relativistic matter under ultra-high temperature conditions (quark-gluon plasmas). Capturing the complexities of such states of matter stands as one of the most prominent challenges of modern science, with multiple ramifications to physics, biology, mathematics, and computer science. As a result, mathematical and computational techniques capable of providing a quantitative account of the way that such complex states of flowing matter behave in space and time are becoming increasingly important. This book provides a unique description of a major technique, the Lattice Boltzmann method to accomplish this task.
The Lattice Boltzmann method has gained a prominent role as an efficient computational tool for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales; from fully-developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic sub-nuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this text provides a survey of the major developments which have led to the impressive growth of the Lattice Boltzmann across most walks of fluid dynamics and its interfaces with allied disciplines.
Included are recent developments of Lattice Boltzmann methods for non-ideal fluids, micro- and nanofluidic flows with suspended bodies of assorted nature and extensions to strong non-equilibrium flows beyond the realm of continuum fluid mechanics. In the final part, it presents the extension of the Lattice Boltzmann method to quantum and relativistic matter, in an attempt to match the major surge of interest spurred by recent developments in the area of strongly interacting holographic fluids, such as electron flows in graphene.
Published: 15 April 2022
336 Pages | 109 line drawings and colour images
246x189mm
Hardback
ISBN: 9780192857972
Paperback
ISBN: 9780192857989
Provides broad, up-to-date and in-depth coverage of quantum computing while remaining accessible to those with no training in advanced mathematics or science
Presented in a unique and accessible conversational style
Includes informal exercises (Try Its) and suggestions for further reading throughout
Quantum Computing: From Alice to Bob provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science and quantum computing. The textbook is designed for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics beyond secondary school algebra and a bit of trigonometry. Higher education faculty members and secondary school mathematics, physics, and computer science educators who want to learn about quantum computing and perhaps teach a course accessible to students with wide-ranging backgrounds will also find the book useful and enjoyable.
While broadly accessible, the textbook also provides a solid conceptual and formal understanding of quantum states and entanglement - the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts.
Paperback
Published: 09 June 2022 (Estimated)
432 Pages | 56 line figures and haltones
246x171mm
ISBN: 9780198844921
Based on a first year undergraduate lecture course at Oxford University
Includes end-of-chapter exercises and solved problems for students to test their understanding
Discusses the modern applications of linear algebra in areas such as AI and quantum computing
This textbook provides a modern introduction to linear algebra, a mathematical discipline every first year undergraduate student in physics and engineering must learn. A rigorous introduction into the mathematics is combined with many examples, solved problems, and exercises as well as scientific applications of linear algebra. These include applications to contemporary topics such as internet search, artificial intelligence, neural networks, and quantum computing, as well as a number of more advanced topics, such as Jordan normal form, singular value decomposition, and tensors, which will make it a useful reference for a more experienced practitioner.
Structured into 27 chapters, it is designed as a basis for a lecture course and combines a rigorous mathematical development of the subject with a range of concisely presented scientific applications. The main text contains many examples and solved problems to help the reader develop a working knowledge of the subject and every chapter comes with exercises.
Hardback
Published: 29 July 2022 (Estimated)
304 Pages
234x156mm
ISBN: 9780192866417
Oxford Logic Guides
Demonstrates a uniform approach to the semantics of consequence relations in the framework of various formal languages
Includes a comprehensive presentation of the Lindenbaum-Tarski method
Provides historical notes and an extensive list of references making it an invaluable resource for students and researchers alike
The publication of Rasiowa and Sikorski's The Mathematics of Metamathematics (1970), Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wojcicki's Theory of Logical Calculi (1988) created a niche in the field of mathematical and philosophical logic. This in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky consider the problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand. For the second part of this problem, the concept of the Lindenbaum-Tarski algebra plays a key role, which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages.
The work also includes helpful exercises to aid the reader's assimilation of the book's material. Intended for advanced undergraduate and graduate students in mathematics and philosophy, this book can be used to teach special courses in logic with an emphasis on algebraic methods, for self-study, and also as a reference work.
New mathematical research in arithmetic dynamics
Series: Annals of Mathematics Studies
Paperback
ISBN: 9780691235479
Jun 14, 2022
Pages:252
Hardcover
ISBN: 9780691235462
Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an “unlikely intersection” statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical Andre-Oort conjecture for curves in this context, originally stated by Baker and DeMarco.
This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.