AMS/IP Studies in Advanced Mathematics, Volume: 42
2008; softcover
ISBN-10: 0-8218-4416-4
ISBN-13: 978-0-8218-4416-8
This volume consists of the proceedings of the Third International Congress of Chinese Mathematicians, held at the Chinese University of Hong Kong in December 2004. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics.
This two-part proceedings contains the contents of lectures given by the plenary speakers and the invited speakers--the major portion comprising new results--together with some expository and survey articles. Eleven major topics are treated: algebra, number theory and cryptography; algebraic geometry and algebraic topology; geometric analysis; complex analysis and complex geometry; harmonic analysis and functional analysis; applied mathematics; dynamical systems, fractals and wavelets; numerical analysis; PDE; probability, statistics, and financial mathematics; and education.
Readership
Research mathematicians interested in all areas of advanced mathematics.
Table of Contents
Part 1
J. A. Smoller and J. B. Temple -- Shock waves and cosmology
C.-Q. Cheng and J. Yan -- Variational construction of diffusion orbits in convex Hamiltonian systems with multiple degrees of freedom
T. L. Lai -- Saddlepoint approximations and boundary crossing probabilities for random fields and their applications
N. Mok -- Recognizing certain rational homogeneous manifolds of Picard number 1 from their varieties of minimal rational tangents
C.-W. Shu -- Discontinuous Galerkin methods for convection dominated partial differential equations
X.-J. Wang -- Singularity behavior of the mean curvature flow
J. Zhou -- Localization and duality
B.-L. Chen and X.-P. Zhu -- Surgical Ricci flow on four-manifolds with positive isotropic curvature
E. Viehweg and K. Zuo -- Special subvarieties of mathcal{A}_g
L. Fu and D. Wan -- Local monodromy of the Kloosterman sheaf at infty
T. Yang -- Hilbert modular functions and their CM values
Y. Hu -- Geometric invariant theory and birational geometry
X. Sun -- Remarks on Gieseker's degeneration and its normalization
W.-S. Cheung and B. Wong -- Bundle rigidity of complex surfaces
S. S.-T. Yau -- CR equivalence problem of strongly pseudoconvex CR manifolds
L. Weiming and X.-Y. Zhou -- Vector bundles on non-primary Hopf manifolds with abelian fundamental group
D.-C. Chang and P. Greiner -- Subelliptic PDE's and subRiemannian geometry
S.-C. Chang -- The Q-curvature flow on a closed 3-manifold of positive
Q-curvature
T.-J. Li -- The space of symplectic structures on closed 4-manifolds
L. Ni -- Ancient solutions to Kahler-Ricci flow
M.-T. Wang -- A convergence result of the Lagrangian mean curvature flow
R.-H. Wang -- On piecewise algebraic variety
B. H. Lian -- An introduction to chiral equivariant cohomology
L. Ji -- Large scale geometry, compactifications and the integral Novikov conjectures for arithmetic groups
M.-D. Choi -- Normal dilations
L. Ge and J. Shen -- On the generator problem of von Neumann algebras
M. K. Kwong -- A survey of results on the ground state of semilinear elliptic equations
E. Kaniuth and A. T. Lau -- Separating and extending subgroups of a locally compact group
N.-C. Wong -- The triangle of operators, topologies, bornologies
X. Zhang -- The positive mass theorem near null infinity
Part 2
C.-H. Chu and Z. Qian -- Dirichlet forms and Markov semigroups on non-associative vector bundles
A. H. Fan and J.P. Kahane -- Decomposition principle and random cascades
Y. Jiang -- Holomorphic motions and normal forms in complex analysis
S.-Y. Li -- On pseudo-Hermitian CR manifolds
Z. Shen -- Recent progress on the Dirichlet problem in Lipschitz domains
X.-R. Dai, D.-J. Feng, and Y. Wang -- Refinable functions with non-integer Dilations
Z.-Y. Wen and L.-F. Xi -- On Whitney's critical sets
P.-M. Wong -- Applications of Nevanlinna theory to geometric problems
Y. Wang -- Some results on Smale's mean value conjecture
J. Deng, T. Y. Hou, and X. Yu -- Localized non-blowup conditions for the 3D incompressible Euler equations
T.-C. Lin and Y.-W. Hsu -- Separation of bound state solutions of systems of nonlinear Schrodinger equations
Z. Liqun -- The C^alpha regularity of a class of ultraparabolic equations
T. Yang and H.-J. Zhao -- Stability of basic wave patterns for gas motions
Z. Lin -- On strong near-epoch dependence
P. Morters and N.-R. Shieh -- Multifractal analysis of branching measure on a Galton-Watson tree
J. Xia and J.-A. Yan -- Convex duality theory for optimal investment
J. Yong -- Backward stochastic Volterra integral equations
M.-C. Chang -- Set addition and set multiplication
C. Y. Ho -- Collineation groups of translation planes
Q. Du -- Intelligent and informative scientific computing, trends and examples
Z. Shen and S. Waldron -- Scattered data interpolation by box splines
Z. Wu -- Piecewise function generated by the solutions of linear ordinary differential equation
Y.-X. Yuan -- Step-sizes for the gradient method
K.-T. Fang and Y. Wang -- Number-theoretic methods in experimental designs
J. Xin -- Ear modeling and sound signal processing
X. Liao and K. Zhang -- The mathematical problem of inertial waves in rapidly rotating planets and stars
S. M. Keung -- Mathematics, mathematics education and the mouse
Collected Works, Volume: 21
2008; 640 pp; hardcover
ISBN-10: 0-8218-4297-8
ISBN-13: 978-0-8218-4297-3
Expected publication date is May 15, 2008.
Alberto Calderon was one of the leading mathematicians of the twentieth century. His fundamental, pioneering work reshaped the landscape of mathematical analysis. This volume presents a wide selection from some of Calderon's most influential papers. They range from singular integrals to partial differential equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from inverse problems to ergodic theory. The depth, originality, and historical impact of these works are vividly illustrated by the accompanying commentaries by some of today's leading figures in analysis. In addition, two biographical chapters preface the volume. They discuss Alberto Calderon's early life and his mathematical career.
Readership
Research mathematicians interested in analysis, harmonic analysis, and singular integrals.
Table of Contents
A. B. Calderon -- On becoming a mathematician: Markers and decisive moments in Alberto P. Calderon's early life
M. Christ, C. E. Kenig, and C. Sadosky -- Alberto P. Calderon the mathematician, his life and works
Calderon selecta papers
A. P. Calderon -- On theorems of M. Riesz and A. Zygmund
A. P. Calderon -- On the behaviour of harmonic functions at the boundary
A. P. Calderon -- On a theorem of Marcinkiewicz and Zygmund
A. P. Calderon and A. Zygmund -- On the existence of certain singular integrals
A. P. Calderon -- A general ergodic theorem
A. P. Calderon and A. Zygmund -- Singular integrals and periodic functions
R. Arens and A. P. Calderon -- Analytic functions of several Banach algebra elements
A. P. Calderon -- On singular integrals
A. P. Calderon and A. Zygmund -- Algebras of certain singular operators
A. P. Calderon and A. Zygmund -- Singular integral operators and differential equations
A. P. Calderon -- Uniqueness in the Cauchy problem for partial differential equations
A. P. Calderon -- Lebesgue spaces of differentiable functions and distributions
A. P. Calderon -- Existence and uniqueness theorems for systems of a partial differential equations
A. Benedek, A. P. Calderon, and R. Panzone -- Convolution operators on Banach space valued functions
A. P. Calderon -- Boundary value problems for elliptic equations
A. P. Calderon -- Intermediate spaces and interpolation, the complex method
A. P. Calderon -- Commutators of singular integral operators
A. P. Calderon -- Spaces between L^1 and L^infty and the theorem of Marcinkiewicz
A. P. Calderon -- Singular integrals
A. P. Calderon -- Algebras of singular integral operators
A. P. Calderon -- The analytic calculation of the index of elliptic equations
A. P. Calderon -- Ergodic theory and translation-invariant operators
A. P. Calderon and R. Vaillancourt -- On the boundedness of pseudo-differential operators
A. P. Calderon and R. Vaillancourt -- A class of bounded pseudo-differential operators
A. P. Calderon -- Cauchy integrals on Lipschitz curves and related operators
A. P. Calderon -- An atomic decomposition of distributions in parabolic
H^p spaces
A. P. Calderon, C. P. Calderon, E. Fabes, M. Jodeit, and N. M. Riviere -- Applications of the Cauchy integral on Lipschitz curves
A. P. Calderon -- Commutators, singular integrals on Lipschitz curves and applications
A. P. Calderon -- On an inverse boundary value problem
A. Bellow, A. P. Calderon, and U. Krengel -- Hopf's ergodic theorem for particles with different velocities and the "strong sweeping out property"
M. Christ, C. E. Kenig, and C. Sadosky -- Harmonic analysis and partial differential equations-Essays in honor of alberto P. Calderon
A. P. Calderon and C. P. Calderon -- A representation formula and its applications to singular integrals
Calderon selecta commentary
D. L. Burkholder -- Comments on (5), (14), (22), (30), and (31)
M. Christ -- Commentary on two papers of A. P. Calderon
C. Fefferman and E. M. Stein -- Commentary on Calderon's papers on interpolation
C. Fefferman and E. M. Stein -- Comments on several papers of A. P. Calderon
P. Malliavin -- On the analytical side of the proof of the index theorem, some personal recollections
Y. Meyer -- Complex analysis and operator theory in Alberto Calderon's work
L. Nirenberg -- Comments on some papers of Alberto P. Calderon
G. Uhlmann -- Commentary on Calderon's paper (29), On an inverse boundary value problem
Student Mathematical Library, Volume: 45
2008; approx. 212 pp; softcover
ISBN-10: 0-8218-4439-3
ISBN-13: 978-0-8218-4439-7
Expected publication date is May 1, 2008.
Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself.
The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument.
Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory.
Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). For his masterly mathematical exposition he was awarded a Steele Prize as well as a Whiteman Prize by the American Mathematical Society.
Readership
Undergraduates, graduate students, and research mathematicians interested in number theory.
Table of Contents
Numbers
The problem Asquare + B = square
Congruences
Double congruences and the Euclidean algorithm
The augmented Euclidean algorithm
Simultaneous congruences
The fundamental theorem of arithmetic
Exponentiation and orders
Euler's phi-function
Finding the order of abmod c
Primality testing
The RSA cipher system
Primitive roots bmod p
Polynomials
Tables of indices bmod p
Brahmagupta's formula and hypernumbers
Modules of hypernumbers
A canonical form for modules of hypernumbers
Solution of Asquare + B = square
Proof of the theorem of Chapter 19
Euler's remarkable discovery
Stable modules
Equivalence of modules
Signatures of equivalence classes
The main theorem
Which modules become principal when squared?
The possible signatures for certain values of A
The law of quadratic reciprocity
Proof of the Main Theorem
The theory of binary quadratic forms
Composition of binary quadratic forms
Cycles of stable modules
Answers to exercises
Bibliography
Index