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Generalized Lie Theory in Mathematics, Physics and Beyond
This book explores the cutting edge of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.
Operator Structures and Dynamical Systems
This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008. These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included.
Algebra, Geometry and Mathematical Physics
This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers and advanced students.
Analysis for Science, Engineering and Beyond
This book project was initiated at The Tribute Workshop in Honour of Gunnar Sparr and the follow-up workshop Inequalities, Interpolation, Non-commutative, Analysis, Non-commutative Geometry and Applications INANGA08, held at the Centre for Mathematical Sciences, Lund University in May and November of 2008. The resulting book is dedicated in celebration of Gunnar Sparr's sixty-fifth anniversary and more than forty years of exceptional service to mathematics and its applications in engineering and technology, mathematics and engineering education, as well as interdisciplinary, industrial and international cooperation. This book presents new advances in several areas of mathematics and engineer...
Noncommutative Geometry and Representation Theory in Mathematical Physics
Mathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test. In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influentialin physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful c...
Commuting Elements In Q-deformed Heisenberg Algebras
Noncommutative algebras, rings and other noncommutative objects, along with their more classical commutative counterparts, have become a key part of modern mathematics, physics and many other fields. The q-deformed Heisenberg algebras defined by deformed Heisenberg canonical commutation relations of quantum mechanics play a distinguished role as important objects in pure mathematics and in many applications in physics. The structure of commuting elements in an algebra is of fundamental importance for its structure and representation theory as well as for its applications. The main objects studied in this monograph are q-deformed Heisenberg algebras — more specifically, commuting elements i...
Mathematical Reviews
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Data Analysis and Related Applications, Volume 1
The scientific field of data analysis is constantly expanding due to the rapid growth of the computer industry and the wide applicability of computational and algorithmic techniques, in conjunction with new advances in statistical, stochastic and analytic tools. There is a constant need for new, high-quality publications to cover the recent advances in all fields of science and engineering. This book is a collective work by a number of leading scientists, computer experts, analysts, engineers, mathematicians, probabilists and statisticians who have been working at the forefront of data analysis and related applications. The chapters of this collaborative work represent a cross-section of current concerns, developments and research interests in the above scientific areas. The collected material has been divided into appropriate sections to provide the reader with both theoretical and applied information on data analysis methods, models and techniques, along with related applications.
