Series: Fundamental Theories of Physics , Vol. 155
2006, XXXIII, 369 p., Hardcover
ISBN-10: 1-4020-5234-0
ISBN-13: 978-1-4020-5234-7
About this book
Carl Friedrich von Weizsacker‘s "Aufbau der Physik",
first published in 1985, was intended as an overview of his
lifelong concern: an understanding of the unity of physics. That
is, the idea of a quantum theory of binary alternatives (the so-called
ur-theory), a unified quantum theoretical framework in which
spinorial symmetry groups are considered to give rise to the
structure of space and time.
The book saw numerous reprints, but it was published in German
only.
The present edition, in English, provides a newly arranged and
revised version, in which some original chapters and sections
have been deleted, and a new chapter about further insights and
results of ur-theoretic research of the late 1980’s and 1990’s,
mainly by the work of Thomas Gornitz, has been included, as well
as a general introduction to Weizsacker’s Philosophy of Physics.
Carl Friedrich von Weizsacker also enjoys high esteem by a much
broader audience for his socio-cultural, political and religious
thoughts and writings. In him the intercultural and
interdisciplinary dialogue has found one of its most important
proponents: a great thinker who combines the perspectives of
science, philosophy, religion and politics with a view towards
the challenges as well as the responsibilities of our time.
Table of Contents
Series: Lecture Notes in Mathematics , Vol. 1894
2007, X, 132 p., Softcover
ISBN-10: 3-540-39942-9
ISBN-13: 978-3-540-39942-1
About this book
Spectral theory of bounded linear operators teams up with von
Neumann’s theory of unbounded operators in this monograph to
provide a general framework for the study of stable methods for
the evaluation of unbounded operators. An introductory chapter
provides numerous illustrations of unbounded linear operators
that arise in various inverse problems of mathematical physics.
Before the general theory of stabilization methods is developed,
an extensive exposition of the necessary background material from
the theory of operators on Hilbert space is provided. Several
specific stabilization methods are studied in detail, with
particular attention to the Tikhonov-Morozov method and its
iterated version.
Written for:
Graduate students and researchers
Keywords:
approximation
ill-posed problem
inverse problem
stabilization
unbounded operator
Table of contents
Preface.- 1. Some Problems Leading to Unbounded Operators.- 2.
Hilbert Space Background.- 3. A General Approach to Stabilization.-
4. The Tikhonov-Morozov Method.- 5. Finite-Dimensional
Approximations.- References.- Index.
Series: Lecture Notes in Mathematics , Vol. 1895
2007, XIV, 236 p., Softcover
ISBN-10: 3-540-39944-5
ISBN-13: 978-3-540-39944-5
About this book
Over the past several decades, the territory of preserver
problems has been continuously enlarging within the frame of
linear analysis. The aim of this work is to present a sort of
cross-section of the modern theory of preservers on infinite
dimensional spaces (operator spaces and function spaces) through
the author's corresponding results. Special emphasis is put on
preserver problems concerning some structures of Hilbert space
operators which appear in quantum mechanics. Moreover, local
automorphisms and local isometries of operator algebras and
function algebras are discussed in details.
Written for:
Graduate students and researchers
Keywords:
function algebras
local transformations
operator algebras
preservers
quantum structures
Table of contents
Preface.- Introduction .- 1. Some Linear and Multiplicative
Preserver Problems on Operator Algebras and Function Algebras.- 2.
Preservers on Quantum Structures.- 3. Local Automorphisms and
Local Isometries of Operator Algebras and Function Algebras.-
Appendix.- Recent Results Added in Revision.- References.- Index.
Series: Springer Monographs in Mathematics
2007, Approx. 265 p., 14 illus., Hardcover
ISBN-10: 3-540-38585-1
ISBN-13: 978-3-540-38585-1
About this book
The central theme of this book is the restoration of Poincare
duality on stratified singular spaces by using Verdier-self-dual
sheaves such as the prototypical intersection chain sheaf on a
complex variety.
After carefully introducing sheaf theory, derived categories,
Verdier duality, stratification theories, intersection homology,
t-structures and perverse sheaves, the ultimate objective is to
explain the construction as well as algebraic and geometric
properties of invariants such as the signature and characteristic
classes effectuated by self-dual sheaves.
Highlights never before presented in book form include complete
and very detailed proofs of decomposition theorems for self-dual
sheaves, explanation of methods for computing twisted
characteristic classes and an introduction to the author's theory
of non-Witt spaces and Lagrangian structures.
Written for:
Researchers and graduate students in Topology
Keywords:
Characteristic Classes
Intersection Homology
Self-dual Sheaves
Singularities
Stratified Spaces
Series: Universitext
2007, Softcover
ISBN-10: 3-540-45895-6
ISBN-13: 978-3-540-45895-1
About this textbook
This book is based on lectures given at a summer school on
motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid,
Norway, in August 2002. Aimed at graduate students in algebraic
topology and algebraic geometry, it contains background material
from both of these fields, as well as the foundations of motivic
homotopy theory. It will serve as a good introduction as well as
a convenient reference for a broad group of mathematicians to
this important and fascinating new subject. Vladimir Voevodsky is
one of the founders of the theory and received the Fields medal
for his work, and the other authors have all done important work
in the subject.
Written for:
Researchers and professionals
Keywords:
Grothendieck topologies
Model categories
Motivic spaces and spectra
Nisnevich topology
Simplicial sets Print version
Recommend to others
Table of contents
Introduction.- Part I. Algebraic Topology by B. Dundas.- Part II.
Background From Algebraic Geometry by Marc Levine.- Part III.
Motivic Homotopy Theory by V.Voevodsky, O.Rondigs, and P.A.Ostvar.