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| Author | : Giovanni Molica Bisci |
| Publisher | : Cambridge University Press |
| Total Pages | : 401 |
| Release | : 2016-03-11 |
| Genre | : Mathematics |
| ISBN | : 1107111943 |
A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.
| Author | : Giovanni Molica Bisci |
| Publisher | : Cambridge University Press |
| Total Pages | : 401 |
| Release | : 2016-03-11 |
| Genre | : Mathematics |
| ISBN | : 1316571696 |
This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.
| Author | : Daniel Bulacu |
| Publisher | : Cambridge University Press |
| Total Pages | : 546 |
| Release | : 2019-02-21 |
| Genre | : Mathematics |
| ISBN | : 1108632653 |
This is the first book to be dedicated entirely to Drinfeld's quasi-Hopf algebras. Ideal for graduate students and researchers in mathematics and mathematical physics, this treatment is largely self-contained, taking the reader from the basics, with complete proofs, to much more advanced topics, with almost complete proofs. Many of the proofs are based on general categorical results; the same approach can then be used in the study of other Hopf-type algebras, for example Turaev or Zunino Hopf algebras, Hom-Hopf algebras, Hopfish algebras, and in general any algebra for which the category of representations is monoidal. Newcomers to the subject will appreciate the detailed introduction to (braided) monoidal categories, (co)algebras and the other tools they will need in this area. More advanced readers will benefit from having recent research gathered in one place, with open questions to inspire their own research.
| Author | : Steven R. Finch |
| Publisher | : Cambridge University Press |
| Total Pages | : 783 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 1108470599 |
Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
| Author | : Serena Dipierro |
| Publisher | : Springer |
| Total Pages | : 162 |
| Release | : 2017-03-14 |
| Genre | : Mathematics |
| ISBN | : 8876426019 |
These lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.
| Author | : Andrei Yu. Khrennikov |
| Publisher | : Cambridge University Press |
| Total Pages | : 256 |
| Release | : 2018-04-26 |
| Genre | : Mathematics |
| ISBN | : 1108102905 |
Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.
| Author | : Kevin Broughan |
| Publisher | : Cambridge University Press |
| Total Pages | : 349 |
| Release | : 2017-11-02 |
| Genre | : Mathematics |
| ISBN | : 110719704X |
This first volume of two presents classical and modern arithmetic equivalents to the Riemann hypothesis. Accompanying software is online.
| Author | : Kevin Broughan |
| Publisher | : Cambridge University Press |
| Total Pages | : 513 |
| Release | : 2017-11-02 |
| Genre | : Mathematics |
| ISBN | : 1108187021 |
The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.
| Author | : Kevin Broughan |
| Publisher | : Cambridge University Press |
| Total Pages | : 349 |
| Release | : 2017-11-02 |
| Genre | : Mathematics |
| ISBN | : 1108187005 |
The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.
| Author | : Grzegorz Tomkowicz |
| Publisher | : Cambridge University Press |
| Total Pages | : 368 |
| Release | : 2016-06-14 |
| Genre | : Mathematics |
| ISBN | : 1316571556 |
The Banach–Tarski Paradox is a most striking mathematical construction: it asserts that a solid ball can be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large. This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, set theory, and logic. This new edition of a classic book unifies contemporary research on the paradox. It has been updated with many new proofs and results, and discussions of the many problems that remain unsolved. Among the new results presented are several unusual paradoxes in the hyperbolic plane, one of which involves the shapes of Escher's famous 'Angel and Devils' woodcut. A new chapter is devoted to a complete proof of the remarkable result that the circle can be squared using set theory, a problem that had been open for over sixty years.
