Surveys in Applied Mathematics: Essays Dedicated to S.M.Ulam

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Content: ""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� 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�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�DIFFUSION EQUATIONS"" ""REFERENCES"" ""Chapter 10. Singular Perturbation"" ""REFERENCES"" ""Chapter 11. A Survey of Some Finite Element Methods Proposed for Treating the Dirichlet Problem""""1. 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 DISTRIBUTIONS""""4. 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""