American Mathematical Society Translations--Series 2, Volume: 232
2014; approx. 229 pp; hardcover
ISBN-13: 978-1-4704-1551-8
This book presents the proceedings of the international workshop, "Advances in Mathematical Analysis of Partial Differential Equations" held at the Institut Mittag-Leffler, Stockholm, Sweden, July 9-13, 2012, dedicated to the memory of the outstanding Russian mathematician Olga A. Ladyzhenskaya. The volume contains papers that engage a wide set of modern topics in the theory of linear and nonlinear partial differential equations and applications, including variational and free boundary problems, mathematical problems of hydrodynamics, and magneto-geostrophic equations.
Research mathematicians interested in partial differential equations and related topics.
H. B. da Veiga -- On singular parabolic p-Laplacian systems under non-smooth external forces. Regularity up to the boundary
S. Boccia and N. V. Krylov -- On the fundamental matrix solution for higher-order parabolic systems
N. V. Filimonenkova and N. M. Ivochkina -- On variational ground of the m-Hessian operators
S. Friedlander, W. Rusin, and V. Vicol -- The magneto-geostrophic equations: a survey
M. Fuchs -- Variations on Liouville's theorem in the setting of stationary flows of generalized Newtonian fluids in the plane
A. V. Fursikov -- On the normal-type parabolic system corresponding to the three-dimensional Helmholtz system
S. Hildebrandt and F. Sauvigny -- On Plateau's problem in Riemannian manfiolds
H. Kim and M. Safonov -- The boundary Harnack principle for second order ellitpic equations in John and unfiorm domains
V. Kozlov and A. Nazarov -- Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients
G. A. Seregin and T. N. Shilkin -- The local regularity theory for the Navier-Stokes equations near the boundary
V. A. Solonnikov -- Lp-theory of free boundary problems of magnetohydrodynamics in simply connected domains
Contemporary Mathematics, Volume: 619
2014; 247 pp; softcover
ISBN-13: 978-1-4704-1077-3
This volume contains the proceedings of the workshop on Variational and Optimal Control Problems on Unbounded Domains, held in memory of Arie Leizarowitz, from January 9-12, 2012, in Haifa, Israel.
The workshop brought together a select group of worldwide experts in optimal control theory and the calculus of variations, working on problems on unbounded domains.
The papers in this volume cover many different areas of optimal control and its applications. Topics include needle variations in infinite-horizon optimal control, Lyapunov stability with some extensions, small noise large time asymptotics for the normalized Feynman-Kac semigroup, linear-quadratic optimal control problems with state delays, time-optimal control of wafer stage positioning, second order optimality conditions in optimal control, state and time transformations of infinite horizon problems, turnpike properties of dynamic zero-sum games, and an infinite-horizon variational problem on an infinite strip.
Graduate students and research mathematicians interested in variational and optimal control problems.
S. M. Aseev and V. M. Veliov -- Needle variations in infinite-horizon optimal control
A. Berman, F. Goldberg, and R. Shorten -- Comments on Lyapunov ƒ¿-stability with some extensions
V. S. Borkar and K. S. Kumar -- Small noise large time asymptotics for the normalized Feynman-Kac semigroup
Y. Dolgin and E. Zeheb -- Linear constraints for convex approximation of the stability domain of a polynomial in coefficients space
V. Y. Glizer -- Singular solution of an infinite horizon linear-quadratic optimal control problem with state delays
I. Ioslovich and P.-O. Gutman -- Time-optimal control of wafer stage positioning using simplified models
J. Kogan and Y. Malinovsky -- Robust stability and monitoring threshold functions
E. Ocana and P. Cartigny -- One dimensional singular calculus of variations in infinite horizon and applications
N. P. Osmolovskii -- Second order optimality conditions in optimal control problems with mixed inequality type constraints on a variable time interval
I. Shafrir and I. Yudovich -- An infinite-horizon variational problem on an infinite strip
D. Wenzke, V. Lykina, and S. Pickenhain -- State and time transformations of infinite horizon optimal control problems
A. J. Zaslavski -- Turnpike properties of approximate solutions of discrete-time optimal control problems on compact metric spaces
A. J. Zaslavski -- Turnpike theory for dynamic zero-sum games
History of Mathematics, Volume: 41
2014; approx. 449 pp; hardcover
ISBN-13: 978-1-4704-1493-1
The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory.
Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in the East and West, and the study of the extent to which contact between the two sides was possible.
Graduate students and research mathematicians interested in algebraic semi-groups and the history of mathematics during the Cold War.
Algebra at the beginning of the twentieth century
Communication between East and West
Anton Kazimirovich Sushkevich
Unique factorisation in semigroups
Embedding semigroups in groups
The Rees Theorem
The French school of 'demi-groupes'
The expansion of the theory in the 1940s and 1950s
The post-Sushkevich Soviet school
The development of inverse semigroups
Matrix representations of semigroups
Books, seminars, conferences, and journals
Basic theory
Notes
Bibliography
List of abbreviations of journal titles
Name index
Subject index
Graduate Studies in Mathematics, Volume: 154
2014; approx. 393 pp; hardcover
ISBN-13: 978-0-8218-9847-5
Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces.
The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level.
This text is intended as a fairly detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.
Graduate students interested in complex analysis, conformal geometry, Riemann surfaces, uniformization, harmonic functions, differential forms on Riemann surfaces, and the Riemann-Roch theorem.
From i to z: the basics of complex analysis
From z to the Riemann mapping theorem: some finer points of basic complex analysis
Harmonic functions
Riemann surfaces: definitions, examples, basic properties
Analytic continuation, covering surfaces, and algebraic functions
Differential forms on Riemann surfaces
The theorems of Riemann-Roch, Abel, and Jacobi
Uniformization
Review of some basic background material
Bibliography
Index