Series: Springer Undergraduate Mathematics Series
2nd ed., 2005, XII, 276 p. 21 illus., Softcover
ISBN: 1-85233-934-9
About this textbook
The geometry of the hyperbolic plane has been an active and
fascinating field of mathematical inquiry for most of the past
two centuries. This book provides a self-contained introduction
to the subject, providing the reader with a firm grasp of the
concepts and techniques of this beautiful area of mathematics.
Topics covered include the upper half-space model of the
hyperbolic plane, Mobius transformations, the general Mobius
group and the subgroup preserving path length in the upper half-space
model, arc-length and distance, the Poincare disc model, convex
subsets of the hyperbolic plane, and the Gauss-Bonnet formula for
the area of a hyperbolic polygon and its applications.
Table of contents
Preamble to the Second Edition
Preamble to the First Edition
The Basic Spaces
The General Mobius Group
Length and Distance in H
Planar Models of the Hyperbolic Plane
Convexity, Area and Trigonometry
Non-planar models
Solutions to Exercises
References;
List of Notation
Index
Series: Texts and Monographs in Physics
2005, X, 471 p. 140 illus., Hardcover
ISBN: 3-540-21052-0
About this textbook
A large number of modern problems in physics, chemistry, and
quantum electronics require a consideration of population
dynamics in complex multilevel quantum systems. The purpose of
this book is to provide a systematic treatment of these questions
and to present a number of exactly solvable problems. It
considers the different dynamical problems frequently encountered
in different areas of physics from the same perspective, based
mainly on the fundamental ideas of group theory and on the idea
of ensemble average. Also treated are concepts of complete
quantum control and correction of decoherence induced errors that
are complementary to the idea of ensemble average. Coherent
Dynamics of Complex Quantum Systems is aimed at senior-level
undergraduate students in the areas of atomic, molecular, and
laser physics, physical chemistry, quantum optics and quantum
informatics. It should help them put particular problems in these
fields into a broader scientific context and thereby take
advantage of the well-elaborated technique of the adjacent fields.
Table of contents
Complex Systems and Statistical Description.- Examples of Complex
Systems.- Two-Level and Level-Band Systems.- Two-Band System.-
Soluble Time-Dependent Systems.- Time-Dependent Complex Systems.-
Dynamics of 1-D Relay Type System.- Composed Complex Quantum
Systems.- Bibliography and Problems.- References.
Summary
Reverse Mathematics is a program of research in the foundations
of mathematics, motivated by the foundational questions of what
are appropriate axioms for mathematics, and what are the logical
strengths of particular axioms and particular theorems. The book
contains 24 original papers by leading researchers. These
articles exhibit the exciting recent developments in reverse
mathematics and subsystems of second order arithmetic.
Details
ISBN: 1-56881-263-9
Year: 2005
Format: Hardcover
Pages: 416
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