Seminaires et Congres 19 (2009), xxi+187 pages
Diophantine approximation, Khintchine's theorem, torus geometry and Hausdorff dimension
M. M. Dodson
Seminaires et Congres 19 (2009), 1-20
Ubiquity and a general logarithm law for geodesics
Victor Beresnevich, Sanju Velani
Seminaires et Congres 19 (2009), 21-36
Arithmetical and geometrical aspects of homogeneous diophantine approximation by algebraic numbers in a given number field
Francois Maucourant
Seminaires et Congres 19 (2009), 37-48
Transference principles and locally symmetric spaces
Cornelia Dru?u
Seminaires et Congres 19 (2009), 51-70
Unipotent flows on products of 's
Nimish A. Shah
Seminaires et Congres 19 (2009), 71-106
Multiplicative Diophantine approximation
Yann Bugeaud
Seminaires et Congres 19 (2009), 107-127
An introduction to Littlewood's Conjecture
Martine Queffelec
Seminaires et Congres 19 (2009), 129-152
On the characteristic exponents of the Jacobi-Perron algorithm
Anne Broise-Alamichel
Seminaires et Congres 19 (2009), 153-173
Approximation and billiards
Serge Troubetzkoy
Seminaires et Congres 19 (2009), 175-187
ISBN: 978-0-470-76948-5
Paperback
368 pages
August 2011
Reliability and validity are the most important quality aspects of survey questions. Featuring contributions from prominent researchers in the field of survey methodology, Question Evaluation Methods supplies various points of views on common question evaluation methods and provides insightful observations on best practices for data collection that can be applied across the health and social sciences. A must-read for government statisticians, survey methodologists, researchers, and practitioners, this unique volume introduces an interdisciplinary, cross-method conversation that is essential for advancing knowledge about data quality and ensuring the quality of Federal statistics.
The combination of two of the twentieth century’s most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level. The fundamental unit of computation is no longer the bit but the quantum bit or qubit. This comprehensive introduction to the field offers a thorough exposition of quantum computing and the underlying concepts of quantum physics, explaining all the relevant mathematics and offering numerous examples. With its careful development of concepts and thorough explanations, the book makes quantum computing accessible to students and professionals in mathematics, computer science, and engineering. A reader with no prior knowledge of quantum physics (but with sufficient knowledge of linear algebra) will be able to gain a fluent understanding by working through the book.
The text covers the basic building blocks of quantum information processing, quantum bits and quantum gates, showing their relationship to the key quantum concepts of quantum measurement, quantum state transformation, and entanglement between quantum subsystems; it treats quantum algorithms, discussing notions of complexity and describing a number of simple algorithms as well as the most significant algorithms to date; and it explores entanglement and robust quantum computation, investigating such topics as quantifying entanglement, decoherence, quantum error correction, and fault tolerance.
“The authors have given us an introduction to the new field of quantum information, accessible to anyone familiar with college-level mathematics. It will be the easiest way for anyone to go from knowing no quantum mechanics to understanding cutting-edge problems in quantum computing. It will also be the most comprehensive and current book on the subject.”
?Michael B. Heaney, Applied Quantum Technology Solar, Inc.
“The authors’ aim is to make quantum computation accessible to a broad audience, and they have done a very good job in breaking down its elements?mathematics, physics, computer science?into comprehensible pieces. The book should be a good addition to the educational literature on the subject.”
Karoline Wiesner, School of Mathematics and Center for Complexity Science,
University of Bristol
Series: Lecture Notes of the Unione Matematica Italiana, Vol. 12
2011, X, 190 p.
Softcover, ISBN 978-3-642-21398-4
Due: July 2011
Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea. A network is a graph with edge-weights that need not be symmetric. This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory. Random walks and electrical networks are important sources for the advancement of the theory.
1 Laplace Operators on Networks and Trees.- 2 Potential Theory on Finite Networks.- 3 Harmonic Function Theory on Infinite Networks.- 4 Schrodinger Operators and Subordinate Structures on Infinite Networks.- 5 Polyharmonic Functions on Trees.
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Series: Operator Theory: Advances and Applications, Vol. 217
2011, XVIII, 528 p.
Hardcover, ISBN 978-3-7643-9995-5
Due: June 2011
Only book covering this spectrum of problems and methods of the Herglotz-Nevanlinna functions realization First comprehensive coverage of the realization theory for Herglotz-Nevanlinna matrix functions Contains useful and important applications
This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems. The main feature of the monograph is a new approach to the realization theory profoundly involving developed extension theory in triplets of rigged Hilbert spaces and unbounded operators as state-space operators of linear systems. The connections of the realization theory to systems with accretive, sectorial, and contractive state-space operators as well as to the Phillips-Kato sectorial extension problem, the Krein-von Neumann and Friedrichs extremal extensions are provided. Among other results the book contains applications to the inverse problems for linear systems with non-self-adjoint Schrodinger operators, Jacobi matrices, and to the Nevanlinna-Pick system interpolation.
Preface.- 1 Extensions of Symmetric Operators.- 2 Rigged Hilbert Spaces.- 3 Bi-extensions of Closed Symmetric Operators.-.4 Quasi-self-adjoint Extensions.- 5 The Livsic Canonical Systems with Bounded Operators.- 6 Herglotz-Nevanlinna functions and Rigged Canonical Systems.- 7 Classes of realizable Herglotz-Nevanlinna functions.- 8 Normalized Canonical Systems.- 9 Canonical L-systems with Contractive and Accretive Operators.- 10 Systems with Schrodinger operator.- 11 Non-self-adjoint Jacobi Matrices and System Interpolation.- 12 Non-canonical Systems.- Notes and Comments.- References.- Index.
Series: Lecture Notes in Mathematics, Vol. 2027
2011, 250 p.
Softcover, ISBN 978-3-642-21743-2
Due: August 2011
Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.
Introduction.- Black Holes and First Order Flows in Supergravity.- Representations of Super Lie Groups: Some Remarks.- On Chiral Quantum Superspaces.- On the Construction of Chevalley Supergroup.- Indecomposable Finite-dimensional Representations of a Class o f Lie algebras and Lie Superalgebras.- On the Geometry of Super Riemann Surfaces.- Charge Orbits and Moduli Spaces of Black Hole Attractors.- Maximal Supersymmetry.- Lie Supergroups, Unitary Representations, and Invariant Cones.- Geometry of Dual Pairs of Complex Supercurves.- On the Superdimension of an Irreducible Representation.
Series: Lecture Notes in Mathematics, Vol. 2029
2011, X, 160 p. 4 illus.
Softcover, ISBN 978-3-642-21773-9
Due: August 2011
This work introduces tools from the field of category theory that make it possible to tackle a number of representation problems that have remained unsolvable to date (e.g. the determination of the range of a given functor). The basic idea is: if a functor lifts many objects, then it also lifts many (poset-indexed) diagrams.
1 Background.- 2 Boolean Algebras Scaled with Respect to a Poset.- 3 The Condensate Lifting Lemma (CLL).- 4 Larders from First-order Structures.- 5 Congruence-Preserving Extensions.- 6 Larders from von Neumann Regular Rings.- 7 Discussion.