Peking University Series in Mathematics - Vol. 1
This introductory book uses the moving frame as a tool and
develops Finsler geometry on the basis of the Chern connection
and the projective sphere bundle. It systematically introduces
three classes of geometrical invariants on Finsler manifolds and
their intrinsic relations, analyzes local and global results from
classic and modern Finsler geometry, and gives non-trivial
examples of Finsler manifolds satisfying different curvature
conditions.
Contents:
Finsler Manifolds
Geometric Quantities on a Minkowski Space
Chern Connection
Covariant Differentiation and Second Class of Geometric
Invariants
Riemann Invariants and Variations of Arc Length
Geometry of Projective Sphere Bundle
Relation Among Three Classes of Invariants
Finsler Manifolds with Scalar Curvature
Harmonic Maps from Finsler Manifolds
Readership: Researchers and graduate students in pure mathematics.
128pp Pub. date: Apr 2006
ISBN 981-256-793-3
Modern theory of elliptic operators, or simply elliptic
theory, has been shaped by the Atiyah?Singer Index Theorem
created 40 years ago. Reviewing elliptic theory over a broad
range, 32 leading scientists from 14 different countries present
recent developments in topology; heat kernel techniques; spectral
invariants and cutting and pasting; noncommutative geometry; and
theoretical particle, string and membrane physics, and
Hamiltonian dynamics.
The first of its kind, this volume is ideally suited to graduate
students and researchers interested in careful expositions of
newly-evolved achievements and perspectives in elliptic theory.
The contributions are based on lectures presented at a workshop
acknowledging Krzysztof P Wojciechowski's work in the theory of
elliptic operators.
Readership: Researchers in modern global analysis and particle
physics.
552pp Pub. date: Apr 2006
ISBN 981-256-805-0
Contents
Operations research uses quantitative models to analyze and
predict the behavior of systems and to provide information for
decision makers. Two key concepts in operations research are
optimization and uncertainty. This volume consists of a
collection of peer reviewed papers from the International
Workshop on Recent Advances in Stochastic Operations Research (RASOR
2005), August 25?26, 2005, Canmore, Alberta, Canada. In
particular, the book focusses on models in stochastic operations
research, including queueing models, inventory models, financial
engineering models, reliability models, and simulations models.
Readership: Advanced undergraduates and graduate students in
operations research and systems science, and operation research
analysis, and industrial and systems engineers.
450pp (approx.) Pub. date: Scheduled Summer 2006
ISBN 981-256-704-6
This book is an introduction to quantum mechanics and mathematics that leads
to the solution of the Schrodinger equation. It is can be read and understood
by undergraduates without sacrificing the mathematical detail necessary
for a complete solution giving the shapes of molecular orbitals seen in
every chemistry text. Readers are introduced to many mathematical topics
new to the undergraduate curriculum, such as basic representation theory,
Schur’s lemma, and the Legendre polynomials.
Contents:
Rutherford, Bohr and Balmer
Some Important Experiments
Early Quantum Mechanics: The Atom
New Assumptions
Zetetics
Classical Waves
Particle-in-a-Box
Exploring the Analogy
Dr Schrodinger, I Presume?
The Quantum Numbers
Pleased to Meet You, Dr Schur
The Spherical Harmonics
More French Mathematicians
Reprise: The Quantum Numbers
Chemistry and Bonding
Valence Shell Electron Pair Repulsion
The Shape of an Orbital
Molecular Orbital Theory
Valence Bond Theory
Other Kinds of Bonding
Case Study: Dye Molecules
Readership: Introductory undergraduate courses in chemistry,
quantum mechanics, and physics, courses in partial differential
equations and mathematical physics.
150pp (approx.) Pub. date: Scheduled Fall 2006
ISBN 981-256-705-4
ISBN 981-256-706-2(pbk)
This book presents a unified treatise of the theory of measure
and integration. In the setting of a general measure space, every
concept is defined precisely and every theorem is presented with
a clear and complete proof with all the relevant details. Counter-examples
are provided to show that certain conditions in the hypothesis of
a theorem cannot be simply dropped.
The dependence of a theorem on earlier theorems is explicitly
indicated in the proof, not only to facilitate reading but also
to delineate the structure of the theory. The precision and
clarity of presentation make the book an ideal textbook for a
graduate course in real analysis while the wealth of topics
treated also make the book a valuable reference work for
mathematicians.
Contents:
Measure and Outer Measure
Regularity of Measures
Measurable Mappings
Completion of a Measure Space
Convergence Almost Everywhere
Almost Uniform Convergence
Convergence in Measure
Integration with Respect to a Measure
Generalized Convergence Theorems for Integrals
Signed Measures
Absolute Continuity of a Measure with Respect to Another
Monotone Functions and Functions of Bounded Variation on R
Absolutely Continuous Functions
Convex Functions, Differentiation of an Indefinite Integral
Banach Spaces
Lp Spaces for p in (0, \)
Bounded Linear Functionals
Integration on a Locally Compact Hausdorff Space
Extension of Additive Set Functions to Measures
Lebesgue?Stieltjes Measure Space
Product Measure Spaces
Convolution of Functions
Integration with Respect to Lebesgue Measure on Euclidean Spaces
Integral and Linear Transformations of the Integral
Hardy?Littlewood Maximal Theorem
Lebesgue Differentiation Theorem
Change of Variable of Integration by Differentiable
Transformations
Hausdorff Measures on Euclidean Spaces
Hausdorff Dimensions
Transformation of Hausdorff Measures
750pp (approx.) Pub. date: Scheduled Fall 2006
ISBN 981-256-653-8
ISBN 981-256-654-6(pbk)