Surveys in Applied Mathematics: Essays Dedicated to S.M. Ulam covers the proceedings of the First Los Alamos Symposium on Mathematics in the Natural Sciences. The book focuses on the processes, principles, methodologies, and applications of mathematics in the natural sciences.
The selection first offers information on the role of applied mathematics, shape of a curve, and biased versus unbiased estimation. Discussions focus on the James-Stein estimator, automorphic forms and Poincaré series, Poincaré metrics, Schottky space and augmented Schottky space, and Schottky groups and Riemann surfaces. The text then examines algorithms, Whitney numbers of geometric lattices, and continued fraction expansion of algebraic numbers.
The book takes a look at bifurcations in reaction-diffusion problems, survey of some finite element methods proposed for treating the Dirichlet problem, and mathematics of quantum fields. Topics include Dirichlet problem, chemical waves and reaction-diffusion equations, and bifurcation theorems. The text then ponders on almost periodic behavior of nonlinear waves, turbulence theory, and renormalization group methods.
The selection is a valuable source of information for mathematicians and researchers interested in applied mathematics.
Inhalt
Contributors
Preface
Introduction
On the Role of Applied Mathematics
On the Shape of a Curve
Automorphic Forms for Schottky Groups
Biased Versus Unbiased Estimation
Algorithms
Whitney Numbers of Geometric Lattices
Continued Fraction Expansion of Algebraic Numbers
Random Time Evolution of Infinite Particle Systems
Bifurcations In Reaction-Diffusion Problems
Singular Perturbation
A Survey of Some Finite Element Methods Proposed for Treating the Dirichlet Problem
The Mathematics of Quantum Fields
Renormalization Group Methods
Remarks on Turbulence Theory
On an Explicitly Soluble System of Nonlinear Differential Equations Related to Certain Toda Lattices
Three Integrable Hamiltonian Systems Connected with Isospectral Deformations
Almost Periodic Behavior of Nonlinear Waves
A Constructive Definition of the Real Numbers