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This book covers various topics related to direct integral theory, including Borel spaces, direct integral of Hilbert spaces and operators, direct integrals of representations, direct integrals and types of von Neumann algebras, and measures on the quasi-dual representations.
John von Neumann and Marshall Stone were two giants of Twentieth Century mathematics. In honor of the 100th anniversary of their births, a mathematical celebration was organized featuring developments in fields where both men were major influences. This volume contains articles from the AMS Special Session, Operator Algebras, Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of John von Neumann and Marshall H. Stone. Papers range from expository and refereed and cover a broad range of mathematical topics reflecting the fundamental ideas of von Neumann and Stone. Most contributions are expanded versions of the talks and were written exclusively for this volume. Included, among Also featured is a reprint of P.R. Halmos's The Legend of John von Neumann. The book is suitable for graduate students and researchers interested in operator algebras and applications, including noncommutative geometry.
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C*-algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra.Also examined are C*-algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A. Rieffel for the study of the Yang-Mills problem.Cutting across traditional separations between fields of specialization, the book addresses a broad audience of graduate students and researchers.
If organisations are not working as well as they could, it is because they are still being managed by obsolete principles rooted in the Industrial Age. Until now, management has been a very one-dimensional discipline, in which only profits mattered. Having eyes fixed squarely upon the bottom line has endangered the planet, increased inequality, and disengaged employees. It is an unsustainable situation that calls for the radical redesign of management philosophical foundations. This book shows how to liberate organisations from the constraining assumptions and structures that hold them back, and how to build more conscious, humane, efficacious, and responsible forms of enterprise. 3D Management is an application of Ken Wilber’s ground-breaking Integral Theory that embodies the next stage of management evolution: smarter, nimbler, wiser, fairer, and fitter for the forthcoming metamodern times. This disruptive theory denies the imperialism of the bottom line and replaces it with a harmonic triumvirate that takes profit, people, planet, and purpose into account equally. An integral organisation is made up of three fundamental and irreducible dimensions: science, arts, and ethics, which refer respectively to the techno-economical, developmental, and moral aspects of organisational reality. These three aspects are woven together into an essential unit by the spiritual dimension, which strives for unity and meaning. 3D Management is a summum bonum of these four key dimensions to achieve sustainable excellence, spur organisational development, and create radically engaging workplaces, as well as making a better world. The text features more than 60 vanguard organisations, harbingers of the teal consciousness that will define the future of management. “One thing is certain: the more a truly integral business catches on, the more whole and fulfilled that humanity’s future will be. And 3D Management will have helped pave the way.” (from Ken Wilber’s foreword)
Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
""Based on the proceedings of the first conference on superconvergence held recently at the University of Jyvaskyla, Finland. Presents reviewed papers focusing on superconvergence phenomena in the finite element method. Surveys for the first time all known superconvergence techniques, including their proofs.
Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts.
This volume presents the refereed proceedings of the Guangzhou International Symposium on Computational Mathematics, held at the Zhongshan University, People's Republic of China. Nearly 90 international mathematicians examine numerical optimization methods, wavelet analysis, computational approximation, numerical solutions of differential and integral equations, numerical linear algebra, inverse and ill-posed problems, geometric modelling, and signal and image processing and their applications.
"Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."