Bednarek / Cesari Dynamical Systems

Proceedings of a University of Florida International Symposium
1. Auflage 2014
ISBN: 978-1-4832-6782-1
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 534 Seiten

Dynamical Systems compiles the lectures and contributed papers read at the International Symposium on Dynamical Systems held at the University of Florida in Gainesville, Florida on March 24-26, 1976. This book discusses the principle of exchange of stability; weak-invariance and rest points in control systems; local controllability in nonlinear systems; and unitary treatment of various types of systems in stability-theory. The optimization of structural geometry; dispersal manifolds in partial differential games; remarks on existence theorems for Pareto optimality; and stability of solutions bifurcating from steady or periodic solutions are also elaborated. This compilation likewise covers the linear neutral functional differential equations on a Banach space; radiation reaction in electrodynamics; and buckling of cylindrical shells with small curvature. This publication is beneficial to students and researchers working on dynamical systems.

Autoren/Hrsg.

Bednarek, A. R.

Cesari, L.

Inhaltsverzeichnis

1;Front Cover;1
2;Dynamical Systems;4
3;Copyright Page;5
4;Table of Contents;6
5;List of Contributors;10
6;List of Participants;14
7;Preface;16
8;Part I:
Dynamical Systems: Proceedings of a University of Florida International Symposium;18
8.1;CHAPTER 1. PERTURBATIONS OF LIÉNARD SYSTEMS WITH SYMMETRIES;20
8.1.1;1. INTRODUCTION;20
8.1.2;2. THE FIRST EXISTENCE THEOREM;21
8.1.3;3. THE SECOND EXISTENCE THEOREM;26
8.1.4;REFERENCES;29
8.2;CHAPTER 2. AN ABSTRACT EXISTENCE THEOREM ACROSS A POINT OF RESONANCE;30
8.2.1;1. INTRODUCTION;30
8.2.2;2. NOTATIONS AND MAIN ASSUMPTIONS;32
8.2.3;3. THE BOUNDED CASE;33
8.2.4;4. THE CASE OF SLOW GROWTH;38
8.2.5;REFERENCES;43
8.3;CHAPTER 3.
THE PRINCIPLE OF EXCHANGE OF STABILITY;46
8.3.1;1. THE EQUILIBRIUM CASE;48
8.3.2;2. THE TIME PERIODIC CASE;51
8.3.3;REFERENCES;59
8.4;CHAPTER 4.
ALMOST PERIODIC PROCESSES AND ALMOST PERIODIC SOLUTIONS OF EVOLUTION EQUATIONS;62
8.4.1;1. INTRODUCTION;62
8.4.2;2. ALMOST PERIODIC TRAJECTORIES OF ALMOST PERIODIC PROCESSES;63
8.4.3;3. PROOFS;67
8.4.4;4. EVOLUTION EQUATIONS WITH STRICTLY MONOTONE OPERATORS;71
8.4.5;5. EVOLUTION EQUATIONS WITH UNIFORMLY MONOTONE OPERATORS;73
8.4.6;REFERENCES;76
8.5;CHAPTER 5.
SEMILINEAR ELLIPTIC PROBLEMS WITH NONLINEARITIES NEAR THE FIRST EIGENVALUE;78
8.5.1;1. INTRODUCTION;78
8.5.2;2. ON THE LINEAR PART OF;79
8.5.3;3. ON THE NONLINEAR PART OF;79
8.5.4;4. THE NON-RESONANT PROBLEM;81
8.5.5;5. THE RESONANT CASE;83
8.5.6;REFERENCE;88
8.6;CHAPTER 6.
WEAK-INVARIANCE AND REST POINTS IN CONTROL SYSTEMS;90
8.6.1;1. INTRODUCTION;90
8.6.2;2. WEAKLY AND COMPLEMENTARY WEAKLY O-INVARIANT SETS;92
8.6.3;3. O-CONSTRAINED SETS AND SOME GENERALIZATIONS;96
8.6.4;4. REST POINTS IN PLANAR CONTROL SYSTEMS;101
8.6.5;REFERENCES;105
8.7;CHAPTER 7.
HIGH ORDER CONTROLLED STABILITY AND CONTROLLABILITY;108
8.7.1;INTRODUCTION;108
8.7.2;1. THE GEOMETRIC APPROACH;111
8.7.3;2. CALCULATION OF TANGENT CONES TO ATTAINABLE SETS;114
8.7.4;REFERENCES;117
8.8;CHAPTER 8.
ON THE BEHAVIOR OF LINEAR UNDAMPED ELASTIC SYSTEMS PERTURBED BY FOLLOWER FORCES;120
8.8.1;I. INTRODUCTION;120
8.8.2;II. WELL-POSEDNESS;123
8.8.3;III. STABILITY;124
8.8.4;IV. BECK'S PROBLEM;129
8.8.5;REFERENCES;131
8.9;CHAPTER 9.
RANDOM OPERATOR EQUATIONS;132
8.9.1;1. INTRODUCTION;132
8.9.2;2. PREREQUISITES;135
8.9.3;3. ITERATIVE TECHNIQUES AND RANDOM OPERATOR EQUATIONS;137
8.9.4;4. INVERSE OF A RANDOM OPERATOR AND ITS MEASURABILITY;141
8.9.5;5. RANDOM CORRESPONDENCES;144
8.9.6;6. MULTIVALUED VERSION OF THE NASHED AND SALEHI THEOREM;148
8.9.7;7. STOCHASTIC APPROXIMATION;149
8.9.8;REFERENCES;154
8.10;CHAPTER 10.
SOME ASYMPTOTIC PROPERTIES OF SOLUTIONS OF THE NAVIER-STOKES EQUATIONS;158
8.10.1;1. INTRODUCTION;158
8.10.2;2. REPRESENTATION OF THE DISTURBANCE;161
8.10.3;3. STATEMENT OF THE RESULTS;164
8.10.4;4. PROOF OF THE ESTIMATES;167
8.10.5;REFERENCES;174
8.11;CHAPTER 11.
LOCAL CONTROLLABILITY IN NONLINEAR SYSTEMS;176
8.11.1;1. INTRODUCTION;176
8.11.2;2. VARIABLE JUMP-POINTS: LOCAL TAYLOR EXPANSION;177
8.11.3;4. THE FORMULA FOR GENERAL D;185
8.11.4;5. APPLICATION TO CONTROL PROBLEMS;187
8.11.5;REFERENCES;193
8.12;CHAPTER 12.
NEW STABILITY RESULTS FOR NONAUTONOMOUS SYSTEMS;194
8.12.1;1. INTRODUCTION;194
8.12.2;2. LIAPUNOV FUNCTIONS AND THE LOCATION OF POSITIVE LIMIT SETS;196
8.12.3;3. THEOREMS ON STABILITY AND INSTABILITY;198
8.12.4;REFERENCES;201
8.13;CHAPTER 13. BRANCHING OF SOLUTIONS OF TWO-PARAMETER BOUNDARY VALUE PROBLEMS FOR SECOND ORDER DIFFERENTIAL EQUATIONS;204
8.13.1;1. INTRODUCTION;204
8.13.2;2. METHOD OF ATTACK;205
8.13.3;3. BRANCHING RESULTS;206
8.13.4;REFERENCE;210
8.14;CHAPTER 14.
PERIODIC SOLUTIONS OF NONLINEAR TELEGRAPH EQUATIONS;212
8.14.1;1. INTRODUCTION;212
8.14.2;2. THE LINEAR CASE;213
8.14.3;3. A FIRST NONLINEAR NONRESONANCE CASE;216
8.14.4;4. A SECOND NONLINEAR NONRESONANCE CASE;218
8.14.5;5. A THIRD NONLINEAR NONRESONANCE CASE;222
8.14.6;6. A FIRST NONLINEAR RESONANCE CASE;223
8.14.7;7. A SECOND NONLINEAR RESONANCE CASE;224
8.14.8;8. REMARKS ON THE GPS OF NONLINEAR HEAT EQUATIONS;227
8.14.9;REFERENCES;227
8.15;CHAPTER 15. NON-SELFADJOINT SEMILINEAR EQUATIONS AT SIMPLE RESONANCE IN THE ALTERNATIVE METHOD;230
8.15.1;1. INTRODUCTION;230
8.15.2;2. PRELIMINARIES;231
8.15.3;3. THE MAIN CONSTRUCTION;233
8.15.4;4. BOUNDED NONLINEARITIES FOR FREDHOLD INDICES;235
8.15.5;REFERENCES;237
8.16;CHAPTER 16.
PERIODIC SOLUTIONS OF SOME NONLINEAR INTEGRAL EQUATIONS;240
8.16.1;Introduction;240
8.16.2;1. A NEW GLOBAL BIFURCATION THEOREM;241
8.16.3;2. PERIODIC SOLUTIONS OF SOME NONLINEAR INTEGRAL EQUATIONS;254
8.16.4;3. UNIQUENESS OF SOLUTIONS;256
8.16.5;REFERENCES;268
8.17;CHAPTER 17. UNITARY TREATMENT OF VARIOUS TYPES OF SYSTEMS IN STABILITY-THEORY;270
8.17.1;1. INTRODUCTION;270
8.17.2;2. SYSTEMS;271
8.17.3;3. STABILITY;272
8.17.4;4. SATURABILITY;272
8.17.5;6. THE CORE OF THE SATURABILITY-TECHNIQUE;274
8.17.6;7. AN EXAMPLE;275
8.17.7;8. AN EXAMPLE WITH TWO NONLINEARITIES;279
8.17.8;9. FINAL COMMENTS;281
8.17.9;REFERENCES;281
8.18;CHAPTER 18.
OPTIMIZATION OF STRUCTURAL GEOMETRY;284
8.18.1;1. INTRODUCTION;284
8.18.2;2. OPTIMALITY CONDITION FOR TRUSSES;285
8.18.3;3. TRUSS-LIKE CONTINUA;288
8.18.4;4. OPTIMALITY CONDITION FOR GRILLAGES;295
8.18.5;5. MATCHING OF REGIONS;298
8.18.6;REFERENCES;312
8.19;CHAPTER 19.
ON THE CESARI INDEX AND THE BROWDER-PETRYSHIN DEGREE;314
8.19.1;1. INTRODUCTION;314
8.19.2;2. THE CONSTRUCTION OF SUITABLE PROJECTIONS Pv, Qv;316
8.19.3;3. RETURN TO PROBLEM;323
8.19.4;5. A REMARK NOT ASSUMING;329
8.19.5;REFERENCES;330
8.20;CHAPTER 20.
DISPERSAL MANIFOLDS IN PARTIAL DIFFERENTIAL GAMES;332
8.20.1;1. INTRODUCTION;332
8.20.2;2. THE DIFFERENTIAL GAME;333
8.20.3;3. SOLUTION OF THE INITIAL-BOUNDARY VALUE PROBLEM;335
8.20.4;4. THE OPTIMIZATION PROBLEM;336
8.20.5;REFERENCES;341
8.21;CHAPTER 21.
CONDITIONS FOR CONSTRAINED PARETO OPTIMA ON A BANACH SPACE WITH A FINITE NUMBER OF CRITERIA;342
8.21.1;1. INTRODUCTION;342
8.21.2;2. FIRST ORDER NECESSARY CONDITIONS;344
8.21.3;3. FIRST ORDER SUFFICIENT CONDITIONS;347
8.21.4;4. SECOND ORDER SUFFICIENT CONDITIONS;348
8.21.5;REFERENCES;352
8.22;CHAPTER 22.
REMARKS ON EXISTENCE THEOREMS FOR PARETO OPTIMALITY;354
8.22.1;1. INTRODUCTION;354
8.22.2;2. A LOWER CLOSURE THEOREM FOR PARETO OPTIMALITY;355
8.22.3;3. MAYER PROBLEMS;362
8.22.4;4. LAGRANGE PROBLEMS;364
8.22.5;REFERENCES;366
8.23;CHAPTER 23.
THE STABILITY OF SOLUTIONS BIFURCATING FROM STEADY OR PERIODIC SOLUTIONS;368
8.23.1;1. INTRODUCTION;368
8.23.2;2. THE LYAPOUNOV-SCHMIDT BIFURCATION;370
8.23.3;3. THE POINCARÉ BIFURCATION FOR A TIME PERIODIC SYSTEM;374
8.23.4;4. THE POINCARÉ BIFURCATION IN AN AUTONOMOUS SYSTEM;375
8.23.5;5. THE HOPF BIFURCATION;380
8.23.6;REFERENCES;384
8.24;CHAPTER 24.
MODELING GONORRHEA;386
8.24.1;INTRODUCTION;386
8.24.2;MATHEMATICAL EPIDEMIOLOGY;389
8.24.3;GONORRHEA EPIDEMIOLOGY;394
8.24.4;BIOTHEOREM;398
8.24.5;ACKNOWLEDGEMENT;400
8.24.6;REFERENCES;400
9;Part II: Contributed Papers;402
9.1;CHAPTER 25.
ON THE SOLUTIONS OF SECOND AND THIRD ORDER DIFFERENTIAL EQUATIONS;404
9.1.1;REFERENCES;406
9.2;CHAPTER 26.
FIXED POINT THEOREMS FOR NONLINEAR FUNCTIONAL OPERATORS;408
9.2.1;REFERENCES;410
9.3;CHAPTER 27.
ON THE CONVERGENCE OF SOLUTIONS OF LIENARD'S EQUATION WITH A FORCING TERM;412
9.3.1;REFERENCES;414
9.4;CHAPTER 28.
APPROXIMATE AND COMPLETE CONTROLLABILITY OF NONLINEAR SYSTEMS TO A CONVEX TARGET SET;416
9.4.1;Introduction;416
9.4.2;Notations;417
9.4.3;REFERENCES;419
9.5;CHAPTER 29.
LINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS ON A BANACH SPACE;422
9.5.1;REFERENCE;424
9.6;CHAPTER 30.
PERIODIC SOLUTOINS OF DIFFERENTIAL SYSTEMS OF LIENARD AND RAYLEIGH TYPE;426
9.6.1;REFERENCES;430
9.7;CHAPTER 31.
EXISTENCE OF AN OPTIMAL CONTROL FOR STOCHASTIC SYSTEMS GOVERNED BY ITO EQUATIONS;432
9.7.1;REFERENCES;434
9.8;CHAPTER 32.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS;436
9.8.1;REFERENCES;438
9.9;CHAPTER 33. BEFORE BIFURCATION AND NONLINEARITY: SOLUTIONS OF THE LINEAR PROBLEMS;440
9.9.1;I. INTRODUCTION;440
9.9.2;II. BASIC IDEAS;440
9.9.3;III. NUMERICAL APPROXIMATIONS;441
9.9.4;REFERENCES;443
9.10;CHAPTER 34.
SUMS OF RANGES OF OPERATORS AND APPLICATIONS;444
9.10.1;REFERENCES;446
9.11;CHAPTER 35.
RADIATION REACTION IN ELECTRODYNAMICS;448
9.11.1;REFERENCES;451
9.12;CHAPTER 36. INVARIANT SETS FOR CERTAIN LIÉNARD EQUATIONS WITH DELAY;452
9.12.1;REFERENCES;454
9.13;CHAPTER 37.
OSCILLATION OF A FORCED NON-LINEAR SECOND ORDER DIFFERENTIAL EQUATION;456
9.14;CHAPTER 38.
SOLUTIONS OF ALGEBRAIC MATRIX EQUATIONS RELATED TO OPTIMAL CONTROL THEORY;458
9.14.1;1. INTRODUCTION;458
9.14.2;2. NECESSARY CONDITIONS;459
9.14.3;3. SUFFICIENT CONDITIONS;460
9.14.4;RERERENCES;461
9.15;CHAPTER 39.
RAZUMIKHIN TYPE THEOREM FOR DIFFERENTIAL EQUATIONS WITH INFINITE DELAY;462
9.15.1;REFERENCES;464
9.16;CHAPTER 40.
PERIODIC AND NONPERIODIC MOTIONS OF HOMOGENEOUS TURBULENCE;466
9.16.1;REFERENCES;469
9.17;CHAPTER 41.
BUCKLING OF CYLINDRICAL SHELLS WITH SMALL CURVATURE;470
9.17.1;REFERENCES;472
9.18;CHAPTER 42.
FUNCTION SPACE CONTROLLABILITY OF RETARDED SYSTEMS: A DERIVATION FROM ABSTRACT OPERATOR CONDITIONS;474
9.18.1;REFERENCES;478
9.19;CHAPTER 43.
PASSIVITY AND EVENTUAL PASSIVITY OF ELECTRICAL NETWORKS;480
9.19.1;REFERENCES;483
9.20;CHAPTER 44.
INEQUALITIES FOR THE ZEROS OF BESSEL FUNCTIONS;486
9.20.1;REFERENCES;487
9.21;CHAPTER 45.
A HOMOGENEOUS, NONADIABATIC MODEL OF DELTA CEPHEI;488
9.21.1;1. INTRODUCTION;488
9.21.2;2. THE INTERNAL STRUCTURE OF A HOMOGENEOUS STAR;488
9.21.3;3. INTEGRATION OF THE DYNAMICAL AMPLITUDES;489
9.21.4;4. A FITTING THEORY;490
9.21.5;5. DISCUSSION OF THE MODEL;491
9.21.6;REFERENCES;493
9.22;CHAPTER 46.
EXPLOSIONS IN COMPLETELY UNSTABLE DYNAMICAL SYSTEMS;494
9.22.1;REFERENCES;496
9.23;CHAPTER 47.
AN ALTERNATIVE PROBLEM WITH AN ASYMPTOTICALLY LINEAR NONLINEARITY;498
9.23.1;REFERENCES;500
9.24;CHAPTER 48.
POSITIVE INVARIANCE OF CLOSED SETS FOR SYSTEMS OF DELAY-DIFFERENTIAL EQUATIONS;502
9.24.1;REFERENCES;504
9.25;CHAPTER 49.
NONEXISTENCE OF ALMOST PERIODIC SOLUTION;506
9.25.1;REFERENCES;508
9.26;CHAPTER 50.
A GENERALIZATION OF THE PROBLEM OF LURIE TO FUNCTIONAL EQUATIONS;510
9.26.1;1. NON-LINEAR PLANT EQUATION;510
9.26.2;REFERENCES;512
9.27;CHAPTER 51.
ON THE INTERNAL REALIZATION OF NONLINEAR BEHAVIORS;514
9.27.1;REFERENCES;517
9.28;CHAPTER 52.
INVERSE PROBLEMS FOR DYNAMICAL SYSTEMS IN THE PLANE;520
9.28.1;REFERENCES;523
9.29;CHAPTER 53.
ON THE ALGEBRAIC CRITERIA FOR LOCAL PARETO OPTIMA;524
9.29.1;REFERENCES;526
9.30;CHAPTER 54.
STABILITY OF AN INFINITE SYSTEM OF DIFFERENTIAL EQUATIONS FOR THE KINETICS OF POLYMER DEGRADATION;528
9.30.1;REFERENCES;531
9.31;CHAPTER 55.
BILINEAR INTEGRAL EQUATIONS IN BANACH SPACE;534
9.31.1;REFERENCES;537

Leseproben

List of Contributors
SHOSHANA ABRAMOVICH,     Department of Mathematics, University of Haifa, Mt. Carmel, Haifa, Israel 31999 S.R. BERNFELD,     Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019 YURI BIBIKOV,     Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912 R.L. BOWDEN,     Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 T.T. BOWMAN,     Department of Mathematics, University of Florida, Gainesville, Florida 32611 LAMBERTO CESARI,     Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104 ETHELBERT N. CHUKWU,     Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115 MICHAEL G. CRANDALL,     Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 C.M. DAFERMOS,     Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island 02912 RICHARD DATKO,     Department of Mathematics, Georgetown University, Washington, D.C. 20057 D.G. DEFIGUEIREDO,     Department of Mathematics, University of Brasillia, Brasilia, Brasil RICHARD I. DeVRIES,     Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104 R.D. DRIVER,     Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881 ROBERT M. GOOR,     Research Laboratories, General Motors Corporation, General Motors Technical Center, Warren, Michigan 48090 JOHN R. GRAEF,     Department of Mathematics, Mississippi State University, Mississippi State, Mississippi 39762 JOHN GREGORY,     Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, Illinois 62901 JAN M. GRONSKI,     Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115 CHAITAN P. GUPTA,     Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115 M.L.J. HAUTUS,     Technological University Eindhoven, P. O. Box 513, Eindhoven, Netherlands H. HERMES,     Department of Mathematics, University of Colorado, Boulder, Colorado 80302 MICHAEL HEYMANN,     Department of Electrical Engineering, Technion, Haifa, Israel DEH-PHONE K. HSING,     Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881 J. INCIURA,     Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada E.F. INFANTE,     Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912 GARY D. JONES,     Department of Mathematics, Murray State University, Murray, Kentucky 42071 JOHN JONES, JR.,     Air Force Institute of Technology, Wright Patterson Air Force Base, Dayton, Ohio 45433 R. KANNAN,     Department of Mathematics, University of Missouri at St. Louis, 8001 Natural Bridge Road, St. Louis, Missouri 63121 JUNJI KATO,     Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 GEORGE H. KNIGHTLY,     Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01002 H.W. KNOBLOCH,     Mathematisches Institut, Universität Würzburg, West Germany V. LAKSHMIKANTHAM,     Department of Mathematics, Univ. of Texas at Arlington, Arlington, Texas 76019 J.P. LaSALLE,     Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island 02912 JON LEE,     Flight Dynamics Laboratory, Wright Patterson AFB, Dayton, Ohio 45433 W.S. LOUD,     Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 ROGER C. McCANN,     Department of Mathematics, Case Western Reserve Univeristy, Cleveland, Ohio 44106 P.J. McKENNA,     Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104 JOHN MALLET-PARET,     Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912 A. MANITIUS,     Centre de Recherches Mathematiques, Case Postal 6128, Montreal H3C 3J7, Canada T. MATSUMOTO,     Department of Electrical Engineering, Waseda University, Shinjuku, Tokio 160, Japan JEAN MAWHIN,     Institut Mathematique, Chemin du Cyclotron 2, B-1348 Louvain La Neuve, Belgium PETER J. MELVIN,     Liberal Arts and Sciences Administration, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 R. MENIKOFF,     Department of Mathematics, John Hopkins University, Baltimore, Maryland 28218 ZBIGNIEW NITECKI,     Department of Mathematics, Tufts University, Medford, Massachusetts 02155 ANNETT NOLD,     Institute for Physical Science & Technology, Space Science Building, University of Maryland, College Park, Maryland 20742 ROGER D. NUSSBAUM,     Department of Mathematics, Rutgers University, New Brunswick, New Jersey V.M. POPOV,     Department of Mathematics, University of Florida, Gainesville, Florida 32611 W. PRAGER,     Tgess Tgampi 4/27 (7451) Savognin, Switzerland PAUL H. RABINOWITZ,     Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 SAMUEL M. RANKIN, III,     Department of Mathematics, Murray State University, Murray, Kentucky 42071 Y.M. REDDY,     Department of Mathematics, Paul Quinn College, Waco, Texas 76703 E.H. ROTHE,     Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104 EMILIO O. ROXIN,     Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881 G.I.N. ROZVANY,     Department of Civil Engineering, Monash University, Clayton, Victoria 3168, Australia J.D. SCHUUR,     Department of Mathematics, Michigan State University, East Lansing, Michigan 48823 GEORGE SEIFERT,     Department of Mathematics, Iowa State University, Ames, Iowa 50010 YASUTAKA SIBUYA,     Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 CARL P. SIMON,     Department of Mathematics, University of Michigan, Ann Arbor, Michigan...