Product Description
2014 / xii + 793 pages / Hardcover / ISBN: 978-1-611973-47-1 /
Keywords:
variational analysis, calculus of variations, optimization, Sobolev spaces, partial differential equations
This second edition replaces Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (MP06, ISBN 978-0-898716-00-9), which is no longer available.
This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision.
The section of Chapter 5 on capacity theory and elements of potential theory now includes the concepts of quasi-open sets and quasi-continuity.
Chapter 6 includes an increased number of examples in the areas of linearized elasticity system, obstacles problems, convection-diffusion, and semilinear equations.
Chapter 11 has been expanded to include a section on mass transportation problems and the Kantorovich relaxed formulation of the Monge problem.
A new subsection on stochastic homogenization in Chapter 12 establishes the mathematical tools coming from ergodic theory, and illustrates them in the scope of statistically homogeneous materials.
Chapter 16 has been augmented by examples illustrating the shape optimization procedure.
Chapter 17 is an entirely new and comprehensive chapter devoted to gradient flows and the dynamical approach to equilibria.
The book is intended for Ph.D. students, researchers, and practitioners who want to approach the field of variational analysis in a systematic way.
Hedy Attouch is a professor in the Institut de Mathematique et de Modelisation de Montpellier II, where he also has been director of the Laboratory of Convex Analysis and of ACSIOM. His research focuses on variational analysis, convex analysis, continuous optimization, semialgebraic optimization, gradient flows, the interaction among these fields of research, and their applications. He has published more than 100 articles in international journals and has written 6 books. He serves as editor for several journals on continuous optimization and is responsible for several international research programs.
Giuseppe Buttazzo is a professor in the Department of Mathematics at the University of Pisa. He has been a keynote speaker at many international conferences and workshops on the fields of calculus of variations, nonlinear PDEs, applied mathematics, control theory, and related topics. He is the author of more than 180 scientific publications and 20 books, and he serves as an editor of several international journals.
Gerard Michaille is a professor at the University of Nimes and member of the UMR-CNRS Institut de Mathematique et de Modelisation de Montpellier. He works in the areas of variational analysis, homogenization, and the applications of PDEs in mechanics and physics.
Publication planned for: March 2015
availability: Not yet published - available from March 2015
format: Hardback
isbn: 9781107079922
Hardback
Random matrix theory is at the intersection of linear algebra, probability theory and integrable systems, and has a wide range of applications in physics, engineering, multivariate statistics and beyond. This volume is based on a Fall 2010 MSRI program which generated the solution of long-standing questions on universalities of Wigner matrices and beta-ensembles and opened new research directions especially in relation to the KPZ universality class of interacting particle systems and low-rank perturbations. The book contains review articles and research contributions on all these topics, in addition to other core aspects of random matrix theory such as integrability and free probability theory. It will give both established and new researchers insights into the most recent advances in the field and the connections among many
1. Universality conjecture for all Airy, sine and Bessel kernels in the complex plane Gernot Akemann and Michael Phillips
2. On a relationship between high rank cases and rank one cases of Hermitian random matrix models with external source Jinho Baik and Dong Wang
3. Riemann?Hilbert approach to the six-vertex model Pavel Bleher and Karl Liechty
4. CLT for spectra of submatrices of Wigner random matrices, II: stochastic evolution Alexei Borodin
5. Critical asymptotic behavior for the Korteweg?de Vries equation and in random matrix theory Tom Claeys and Tamara Grava
6. On the asymptotics of a Toeplitz determinant with singularities Percy Deift, Alexander Its and Igor Krasovsky
7. Conservation laws of random matrix theory Nicholas M. Ercolani
8. Asymptotics of spacing distributions fifty years later Peter Forrester
9. Applications of random matrix theory for sensor array imaging with measurement noise Josselin Garnier and Knut Solna
10. Convolution symmetries of integrable hierarchies, matrix models and t-functions John Harnad and Alexander Orlov
11. Universality limits via 'old style' analysis Doron Lubinsky
12. Fluctuations and large deviations of some perturbed random matrices Mylene Maida
13. Whittaker functions and related stochastic processes Neil O'Connell
14. How long does it take to compute the eigenvalues of a random symmetric matrix? Christian Pfrang, Percy Deift and Govind Menon
15. Replica analysis of the one-dimensional KPZ equation Tomohiro Sasamoto
16. Asymptotic expansions for B matrix models and their applications to the universality conjecture Mariya Shcherbina
17. Experimental realization of Tracy?Widom distributions and beyond: KPZ interfaces in turbulent liquid crystal Kazumasa Takeuchi
18. Random matrices: the four-moment theorem for Wigner ensembles Terence Tao and Van Vu.
Publication planned for: November 2014
availability: Not yet published - available from January 2015
format: Paperback
isbn: 9781107460317
Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.
Introduction
1. Two notions of formality
2. On the very notion of a formal language
3. The history, purposes and limitations of formal languages
4. How we do reason, and the need for counterbalance in science
5. Formal languages and extended cognition
6. De-semantification
7. The debiasing effect of formalization
Conclusion.
Advanced Lectures in Mathematics, Volume 29.1
Hardcover
1418 pages
Comprising volumes 28 and 29 of the ALM series, this outstanding collection presents all the survey papers of Shing-Tung Yau published to date (through 2013), each with Yau’s own commentary. Among these are several papers not otherwise easily accessible. Also presented are several commentaries on Yau’s work written by outstanding scholars from around the world especially for publication here.
Shing-Tung Yau’s work is mainly in differential geometry, and he is one of the originators of the broad subject of geometric analysis?in which he remains one of the most active participants. His contributions have had an influence on both physics and mathematics, and he has long been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated?sixty years after its discovery?that Einstein’s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists?using Calabi-Yau compactification?to show that string theory is a viable candidate for a unified theory of nature. Calabi-Yau manifolds are part of the standard toolkit of string theorists today. He was awarded the Fields Medal in 1982 and the Wolf Prize in 2010, and has received many other honors.
The Selected Expository Works of Shing-Tung Yau with Commentary provides the reader with systematic commentary on all aspects of mathematics by a contemporary master. The reader can thereby see the world of mathematics through his particular perspective, and gain understanding of the motivation and evolution of mathematical ideas.
This is a set comprising the following volumes, which may be purchased independently:
Selected Expository Works of Shing-Tung Yau with Commentary, Volume I (vol. 28 of the ALM series)
Selected Expository Works of Shing-Tung Yau with Commentary, Volume II (vol. 29 of the ALM series)
Series: Mathematics Research Developments
Pub. Date: 2014 4th Quarter
Pages (Approximate): 241 pages (7x10) ? (NBC-C)
Binding: Hardcover
ISBN: 978-1-63463-221-8
After presenting the first volume of this two-volume book, presenting a lot of mathematical and theoretical studies and research related to non-integer calculus, the second volume illustrates applications related to this domain. This volume is made up of 11 chapters. The first chapter presents the heuristic power of the non-integer differential operators in physics starting from the chaos to the emergence, the auto-organizations and the holistic rules. The second chapter shows the dynamics of the fractional order chaotic systems along with some applications. The third chapter represents the pressure control of gas engines by non-integer order controllers by showing a novel trend in the application of the fractional calculus to automotive systems. Chapter 4 shows the way to model fractional order equations using state space modeling along with some applications. Another application related to this domain is the thermal diffusive interface. Chapter 5 shows the analysis of a semi-infinite diffuse plane medium along with the equations that model this medium, and some frequency and time domain responses. However, Chapter 6 treats this problem by controlling this plant using the well-known CRONE controller. Chapter 8 presents the adaptive second-order fractional sliding mode control with an application to a water tanks level system. Chapter 9 treats the mechanical aspect by showing the features of the fractional operators applied to this domain. Also, Chapter Nine presents the theory of diffusive stresses based on the fractional advection-diffusion equation. The modeling of drug diffusion during general anesthesia using Fractional Calculus is shown in Chapter 10 and is considered as another application related to the biomedical field. Finally, Chapter 11 represents an overview of the fractional fuzzy controllers by showing the analysis, the synthesis and the implementation of this module. To sum up, this second volume presents applications of fractional calculus in several engineering domains as the thermal, the automotive, the mechanical, the biomedical and much more. Note that this volume was preceded by a first volume that focuses on the mathematical and theoretical aspects of fractional calculus.