Series: Frontiers in Mathematics
2007, Approx. 200 p., Softcover
ISBN: 978-3-7643-8507-1
Due: August 2007
About this book
A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals are worked out completely.
Written for:
Graduates and researchers in (finite) geometry
Table of contents
Introduction.- 1. q-Clans and Their Geometries.- 2. The Fundamental Theorem.- 3. Aut(GQ(C)).- 4. The Cyclic q-Clans.- 5. Applications to the Known Cyclis q-Clans.- 6. The Subiaco Oval Stabilizers.- 7. The Adelaide Oval Stabilizers.- 8. The Payne q-Clans.- 9. Other Good Stuff.- Bibliography.
Series: Trends in Mathematics
2007, Approx. 350 p., Hardcover
ISBN: 978-3-7643-8477-7
Due: October 2007
About this book
This book presents nine well-organized survey articles addressing topics surrounding positivity, with a strong emphasis on functional analysis. The book assembles for the first time a wide spectrum of research into positivity, providing up-to-date information on a variety of topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. Coverage extends to a broad range of areas, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.
Written for:
Postgraduates and researchers in functional analysis, topology, operator algebras, lattice-ordered groups and frames
Table of contents
Preface.- 9 Survey articles.
Series: Progress in Mathematics , Vol. 263
2007, Approx. 350 p., Hardcover
ISBN: 978-3-7643-8528-6
Due: September 2007
About this book
The walks on ordinals and analysis of their characteristics is a subject matter started by the author some twenty years ago in order to disprove a particular extension of the Ramsey theorem. A further analysis has shown however that the resulting method is quite useful in detecting critical mathematical objects in contexts where only rough classifications are possible. For example, many of the characteristics of walks on countable ordinals lead naturally to uncountable linear orderings whose Cartesian squares can be covered by countably many chains which turns out to be critical objects in the category of all linear orderings. Recently the method has lead us to solutions to some other problems in a variety of disciplines such as for example a natural extension of the unconditional basic sequence problem from the Banach space theory or the famous L-space problem from topology. The book gives a careful and comprehensive account of the method and gathers many of these application in a unified and comprehensive manner.
Written for:
Graduates, postgraduates and researchers in combinatorial set theory, model theory, general topology, Banach space theory
Table of contents
1. Introduction.- 2. Walks on Countable Ordinals.- 3. Metric Theory of Countable Ordinals.- 4. Coherent Mappings and Trees.- 5. The Square Bracket Operation on Countable Ordinals.- 6. General Walks and Their Characteristics.- 7. Square Sequences.- 8. The Oscillation Mapping and The Square-Bracket Operation.- 9. Unbounded Functions.- 10. Higher Dimensions.- Bibliography.- Index.
Series: Publications of the Scuola Normale Superiore
Subseries: CRM Series , Vol. 5
2008, Approx. 400 p., Softcover
ISBN: 978-88-7642-307-9
Due: January 2008
About this book
In the last years a growing attention has been dedicated to many body quantum systems from the point of view of quantum information. Indeed, after the initial investigation of simple systems as single or two qubits, the need of understanding the characteristics of a realistic quantum information device leads necessarily to the study of many body quantum systems. These studies are also driven by the very fast development of experiments which in the last years reach the goal of coherent control of a few qubits (ion traps, charge qubits, etc.) with a roadmap for further scaling and improvement of coherent control and manipulation techniques.
This book gives a selection of current research topics in the field of quantum information for many body quantum systems together with open problems.
Written for:
Graduate students and researchers that want to get an overview and introduction to current developments in the field
Table of contents
Preface.- Entanglement percolation in quantum networks.- Classical simulation of strongly correlated systems.- Quantum information and many body theory.- Electronic Hong-Ou-Mandel interferometer for multi-mode entanglement detection.- Energy, entanglement, and information transfer in many body systems.- Infinite spin chains and algebras.- New results on MPS.- A quantum approach to classical statistical mechanics.- Atom-light teleportation.- Lieb Robinson bounds in quantum spin systems and application to quantum information theory.- A metric approach to phase transitions.