Tabla de Contenidos:
  • Front Cover
  • Surveys in Applied Mathematics: Essays dedicated to S.M. Ulam
  • Copyright Page
  • Table of Contents
  • CONTRIBUTORS
  • PREFACE
  • INTRODUCTION
  • Chapter 1. On the Role of Applied Mathematics
  • I. INTRODUCTION
  • II. WHAT IS APPLIED MATHEMATICS?
  • III. EDUCATION
  • IV. RECOMMENDATIONS
  • V. APPENDIX
  • REFERENCES
  • Chapter 2. On the Shape of a Curve
  • REFERENCES
  • Chapter 3. Automorphic Forms for Schottky Groups
  • 1. SCHOTTKY GROUPS
  • 2. SCHOTTKY SPACE AND AUGMENTED SCHOTTKY SPACE
  • 3. SCHOTTKY GROUPS AND RIEMANN SURFACES
  • ""4. POINCARE METRICS""""5. AUTOMORPHIC FORMS AND POINCAR�A? SERIES""; ""6. PROOFS OF THEOREMS 2 AND 3""; ""7. PROOF OF THEOREM 4""; ""REFERENCES""; ""Chapter 4. Biased Versus Unbiased Estimation""; ""1. INTRODUCTION""; ""2. THE JAMES�a�?STEIN ESTIMATOR""; ""3. THREE EXAMPLES OF BIASED ESTIMATION IN PRACTICE""; ""REFERENCES""; ""Chapter 5. Algorithms""; ""COMPUTATIONAL COMPLEXITY""; ""SOME RECENT POSITIVE RESULTS""; ""ADDITIONAL COMMENTS AND CONCLUSIONS""; ""SUMMARY AND CONCLUSIONS""; ""REFERENCES""; ""Chapter 6. Whitney Numbers of Geometric Lattices""; ""INTRODUCTION""; ""1. PRELIMINARIES""
  • ""2. THE SHEAVES Z AND M""""3. THE SHEAF W""; ""4. A SPECTRAL SEQUENCE""; ""5. STANDARD RESOLUTIONS""; ""REFERENCES""; ""Chapter 7. Continued Fraction Expansion of Algebraic Numbers""; ""REFERENCES""; ""Chapter 8. Random Time Evolution of Infinite Particle Systems""; ""REFERENCES""; ""Chapter 9. Bifurcations in Reaction-Diffusion Problems""; ""I. BIFURCATION THEOREMS""; ""II. CHEMICAL WAVES AND REACTION�a�?DIFFUSION EQUATIONS""; ""REFERENCES""; ""Chapter 10. Singular Perturbation""; ""REFERENCES""
  • Chapter 11. A Survey of Some Finite Element Methods Proposed for Treating the Dirichlet Problem1. INTRODUCTION
  • 2. THE NEUMANN PROBLEM
  • 3. THE DIRICHLET PROBLEM
  • REFERENCES
  • Chapter 12. The Mathematics of Quantum Fields
  • REFERENCES
  • Chapter 13. Renormalization Group Methods
  • 1. INTRODUCTION
  • 2. MULTIPLE SCALES
  • 3. THE RENORMALIZATION GROUP: TECHNIQUE
  • 4. THE RENORMALIZATION GROUP: CONSEQUENCES
  • 5. OUTLOOK
  • REFERENCES
  • Chapter 14. Remarks on Turbulence Theory
  • 1. INTRODUCTION
  • 2. THE DYNAMICAL EQUATIONS
  • 3. ABSOLUTE EQUILIBRIUM DISTRIBUTIONS4. NONEQUILIBRIUM: CASCADE PHENOMENA
  • 5. EDDY VISCOSITY AND RENORMALIZATION
  • 6. CONVECTION INVARIANCE AND LAGRANGIAN COORDINATES
  • 7. WHAT CAN WE CALCULATE?
  • ACKNOWLEDGMENT
  • REFERENCES
  • Chapter 15. On an Explicitly Soluble System of Nonlinear Differential Equations Related to Certain Toda Lattices
  • REFERENCES
  • Chapter 16. Three Integrable Hamiltonian Systems Connected with Isospectral Deformations
  • 1. INTRODUCTION
  • 2. ISOSPECTRAL DEFORMATIONS