# A tribute to Professor William F. Ames on his 80th birthday

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J. Math. Anal. Appl. 333 (2007) 17www.elsevier.com/locate/jmaa

Introduction

A tribute to Professor William F. Ameson his 80th birthday

William Francis Ames was born on December 8, 1926, in Brandon, Manitoba, Canada. Heis a Navy veteran of WW II and the Korean War. He obtained his undergraduate (Phi BetaKappa) as well as graduate degrees in applied mathematics from the University of Wisconsin(Madison) in 1950 and 1954, respectively. He started his carrier as an instructor of mathematicsin the same university, and in 1955 joined DuPont as a senior engineer (applied mathematics).His next move was in 1959 to the University of Delaware, where he joined as a professor ofmechanical engineering and of statistics and computer science. He joined as a professor of me-

0022-247X/$ see front matter 2007 Published by Elsevier Inc.doi:10.1016/j.jmaa.2007.03.059

2 Editorial / J. Math. Anal. Appl. 333 (2007) 17

chanics and hydraulics at the University of Iowa in 1967, and then became the chairman ofthe Iowa Program in Applied Mathematics in 1970. In 1975, he joined the Georgia Institute ofTechnology and became the director of the School of Mathematics in 1982. He continued inthis position until 1987, and then became chairman of the University Center of Mathematics in1988. Currently, he is Regents Emeritus Professor of Mathematics there. He has held visitingpositions at several places, including Stanford University (19631964), University of Salta in Ar-gentina (1972), University of Karlsruhe (19721973) and five other times, University of Georgia(19771979), University of Waterloo (1989), and University of Witwatersrand in South Africa(1990).

Bill Ames was an NSF Faculty Fellow from 1963 to 1964, a National Academy of SciencesRomanian Exchange Professor in 1970, a NATO Senior Fellow in Science in 1972, and a GermanHumboldt Foundation U.S. Senior Scientist in 19741975 and in 1980. He was also a memberof the Society of Engineering Science, International Association for Mathematics and Comput-ers in Simulation, Society for Natural Philosophy, Gesellschaft fr Angewandte Mathematik undMechanik, and the Society for Industrial and Applied Mathematics. He served as SIAM Lec-turer and a council member for two terms. He has been a principal investigator for UDRF, NIH,NSF, Bu. Stds., EPA, Army, NATO, and other industrial grants. He was the director of two NSFAdvanced Science Seminars. He has also been a consultant for textile and chemical industries,Academic Press, and the Naval Underwater Systems Center. He was also the director of ProjectThemis at the University of Iowa for six years.

His main scholarly contributions are in applied and computational mathematics. He has suc-cessfully tackled a wide variety of applied problems, mainly related to mechanics. He produceddozens of masters and 30 Ph.D. students: S.E. Jones, S.Y. Lee, V. Kucher, H. de la Cuesta,W. Walston, J. Zaiser, A.L. Laganelli, J.A. Friedhoffer, A.A. Vicario Jr., G.E. Mueller, J.F. Son-towski, H.S. Woodard, H.I. Padmanabhan, M. Ginsberg, V. Kuo, A. Unione, D. Davy, K. Matusi,M. Hsiao, H. Shen, R.E. Boisvert, V.J. Ervin, M. Brown, J.E. Peters, F.V. Postell, D.J. Arrigo,T. Bright, P.J.C. Richards, W. Rufeger, and M.L. Abell. Currently, most of them enjoy very highpositions in industries or at academic institutions. Among several others, his main collaboratorsare E.A. Adams, C. Rogers, A. Donato, R. Lohner, M.C. Nucci, K.A. Ames, and D. Lee. It is fairto say that his books Nonlinear Partial Differential Equations in Engineering, Academic Press,New York, vol. I (1965) and vol. II (1972), did much to stimulate research interest in analyticapproaches to nonlinear problems in the physical sciences. In particular, in the area of Backlundtransformations he did much to encourage the seminal NSF meeting on the subject held at Van-derbilt University in 1974. This meeting, organized by Robert Miura, was the first internationalgathering on the subject.

Bill Ames has served as a member of the editorial boards of several international journals,including International Journal of Nonlinear Mechanics, Nonlinear Analysis, Journal of theFranklin Institute, Journal of Engineering Mathematics, and Numerical Heat Transfer. He joinedthe editorial board of the Journal of Mathematical Analysis and Applications more than a quarterof a century ago. He became co-editor-in-chief in 1991. Throughout this long period, Bill Ameshas shown exceptional levels of devoted service to the editorial process. He has striven to main-tain the highest levels of mathematical scholarship so necessary for the successful functioningof a major journal, and to provide the mathematical community with the services that it needs

and expects. Bills unabated devotion has continued, especially during recent years, when theelectronic revolution in publishing made its effects most keenly felt.

Editorial / J. Math. Anal. Appl. 333 (2007) 17 3

Throughout his long career Bill has always been a wonderful enthusiast and generous in hisencouragement for all matters pertaining to the nonlinear sciences. Bill is a fine gentleman and ithas been a privilege to have him as a friend over these many years. We wish him many enjoyableyears to come.

Ravi P. AgarwalSteven G. Krantz

E-mail address: agarwal@fit.edu (R.P. Agarwal)

4 December 2006

Available online 27 March 2007

Bibliography

Research publications

[1] W.F. Ames, B.H. Eckstein, E.H. Olsen, Response to environmental changes and an equation of state for nylonyarn, Tex. Res. Journal 8 (1958) 700.

[2] W.F. Ames, H.G. Lauterbach, Cord stresses in inflated tires, Tex. Res. Journal 11 (1959) 800.[3] W.F. Ames, H.G. Lauterbach, Stresses in deflated tires, in: Proc. Intl. Rubber Conf., 1959, p. 50.[4] W.F. Ames, Evaluation of rate constants in systems of differential equations, Ind. Eng. Chem. 52 (1960) 517.[5] W.F. Ames, V.C. Behn, Application of the method of composition and linear regression analysis to a problem

involving a pseudoplastic suspension, Trans. Soc. Rheology 5 (1961) 53.[6] W.F. Ames, Stresses in cylindrically symmetric membranes reinforced with extensible cords, J. Franklin Inst. 272

(1961) 185190.[7] W.F. Ames, Regression analysis as applied to an equation of state for nylon yarn, Tex. Res. Journal 32 (1962) 8.[8] W.F. Ames, V.C. Behn, Trickling filter design and performance, Proc. Amer. Soc. Civil Eng. 1 (1962) 31.[9] W.F. Ames, V.C. Behn, W.Z. Collings, Transient operation of the trickling filter, Proc. Amer. Soc. Civil Eng. 3

(1962) 21.[10] W.F. Ames, R.D. Swope, Canonical forms for nonlinear kinetics differential equations, Ind. Eng. Chem. Fund. 1

(1962) 214.[11] W.F. Ames, H. de la Cuesta, Techniques for the determination of heat transfer in fluids and non-homogeneous

solids I, Eng. Chem. Fund. 2 (1963) 21.[12] W.F. Ames, H. de la Cuesta, Solutions of a class of linear partial differential equations with variable coefficients,

J. Math. Phys. 42 (1963) 301306.[13] W.F. Ames, M.H. Cobble, Extension of a method of solution for Poissons equation, J. Appl. Mech. (1963) 415.[14] W.F. Ames, A.E. Hoerl, Mathematics Section, Perrys Chemical Engineering Handbook, fourth ed., McGrawHill,

1963, fifth ed., 1973.[15] W.H. Walston, W.F. Ames, L.G. Clark, Dynamic stability of rotating shafts in viscous fluids, J. Appl. Mech. (1964)

291.[16] W.F. Ames, J.A. Robinson, The model T computer, J. Eng. (1964) 338.[17] W.F. Ames, K. Keshaven, V.C. Behn, Kinetics of aerobic removal of organic wastes, Proc. A.S.C.E. (1964) 99.[18] W.F. Ames, Similarity for the nonlinear diffusion equation, Ind. Eng. Chem. Fund. 4 (1965) 72.[19] W.F. Ames, W.H. Walston, Design and analysis of inflated reinforced membranes I, Textile Research J. 35 (1965)

10881097.[20] W.F. Ames, J. Sontowski, Multiparameter perturbation solution of algebraic equations, J. Appl. Mech. 218 (1966)

124.[21] W.F. Ames, S.Y. Lee, Similarity solutions for non-Newtonian fluids, A.I.Ch.E.J. 124 (1966) 700.[22] S.E. Jones, W.F. Ames, Nonlinear superposition, J. Math. Anal. Appl. 17 (1967) 484487.

[23] S.E. Jones, W.F. Ames, Similarity variables and first integrals of ordinary differential equations, Int. J. Nonlinear

Mech. 2 (1967) 257260.

4 Editorial / J. Math. Anal. Appl. 333 (2007) 17

[24] W.F. Ames, Ad-hoc exact techniques for nonlinear partial differential equations, in: Proc. of the 1965 NSFDelaware Conference, Academic Press, New YorkLondon, 1967, pp. 5572.

[25] W.F. Ames, S.E. Jones, Equations equivalent to a first order equation under differentiation, Quart. Appl. Math. 25(1967) 302.

[26] W.F. Ames, A.L. Laganelli, On the analysis of transportation cooling in a laminar boundary layer with solid wallupstream effects, AIAA J. 6 (1968) 193.

[27] W.F. Ames, S.E. Jones, Integrated Lagrange expansions for a MongeAmpere equation, J. Math. Anal. Appl. 21(1968) 479484.

[28] W.F. Ames, S.Y. Lee, J.N. Zaiser, Nonlinear vibrations of a traveling threadline, Int. J. Nonlinear Mech. 3 (1968)449.

[29] W.F. Ames, J.F. Sontowski, On stability of the flow of a stratified gas over a liquid, Quart. Appl. Math. 27 (1969)335.

[30] W.F. Ames, Longitudinal wave propagation on a travelling threadline I, in: 11th Midwest Mechanics Conf. Proc.,Ames, Iowa, 1969, pp. 733746.

[31] W.F. Ames, Recent developments in the nonlinear equations of transport processes, Ind. Eng. Chem. Fund. 8(1969) 522.

[32] W.F. Ames, Longitudinal wave propagation on a traveling threadline II, Int. J. Nonlinear Mech. 5 (1970) 413.[33] W.F. Ames, J.F. Kennedy, Wake deformation in density stratified fluids, J. Eng. Math. 4 (1970) 229.[34] W.F. Ames, Discontinuity formation in solutions of homogeneous non-linear hyperbolic equations possessing

smooth initial data, Int. J. Nonlinear Mech. 5 (1970) 605615.[35] W.F. Ames, Waves in tirestraveling wave analyses, Textile Res. J. 40 (1970) 504.[36] W.F. Ames, On wave propagation in one-dimensional rubberlike materials, J. Math. Anal. Appl. 34 (1971) 214

222.[37] W.F. Ames, H.S. Woodward, Similarity solutions for partial differential equations generated by finite and infini-

tesimal groups, Iowa Institute of Hydraulic Research Report No. 132, Iowa City, 1971, p. 93.[38] W.F. Ames, Ad-hoc methods for nonlinear partial differential equations, Appl. Mech. Rev. 25 (1972) 10211031.[39] W.F. Ames, K.E. Lonngren, Self-similar solution of an RC transmission line, Amer. J. Phys. 40 (1972) 484.[40] W.F. Ames, D. Davy, An asymptotic solution of an initial value problem for a nonlinear viscoelastic rod, Int. J.

Nonlinear Mech. 8 (1973) 59.[41] W.F. Ames, Implicit ad-hoc methods for nonlinear partial differential equations, J. Math. Anal. Appl. 42 (1973)

2028.[42] S.Y. Lee, W.F. Ames, A class of general solutions to the nonlinear dynamic equations of elastic strings, Trans.

ASME Ser. E, J. Appl. Mech. 40 (1973) 10351039.[43] I. Suliciu, S.Y. Lee, W.F. Ames, Nonlinear traveling waves for a class of rate-type materials, Collection of articles

dedicated to Salomon Bochner, J. Math. Anal. Appl. 42 (1973) 313322.[44] W.F. Ames, Some computation-steeples in fluid mechanics, in: Twentieth Anniversary of the Society for Industrial

and Applied Mathematics (special lectures, Philadelphia, PA, 1972), SIAM Rev. 15 (1973) 524552.[45] W.F. Ames, E. Adams, A family of exact solutions for laminar boundary layer equations, Z. Angew. Math.

Mech. 54 (1974) 180181.[46] W.F. Ames, E. Adams, Jets and other planar perturbations of parallel basic flows, Ing.Arch. 44 (1975) 385397.[47] W.F. Ames, Nonlinear algebraic equations in continuum mechanics, in: Numerical Solution of Systems of Non-

linear Algebraic Equations, Univ. Pittsburgh, Pittsburgh, PA, 1972, in: NSFCBMS Reg. Conf., Academic Press,New York, 1973, pp. 126.

[48] H.C.S. Hsuan, K.E. Lonngren, W.F. Ames, Self-similar behavior of plasma fluid equations, J. Eng. Math. 8 (1974)303309.

[49] W.F. Ames, K.E. Lonngren, Field penetration into a plasma with nonlinear conductivity, Phys. Fluids 17 (1974)1919.

[50] H. Shen, W.F. Ames, On invariant solutions of the KortewegdeVries equation, Phys. Lett. A 49 (1974) 313314.[51] K.E. Lonngren, H.C.S. Hsuan, W.F. Ames, On the soliton, invariant, and shock solutions of a fourth-order nonlinear

equation, J. Math. Anal. Appl. 52 (1975) 538545.[52] A.W. Marris, W.F. Ames, On complex-lamellar motions, Arch. Ration. Mech. Anal. 59 (1975) 131148.[53] W.F. Ames, M. Ginsberg, Bilateral algorithms and their applications, in: Computational Mechanics, Int. Conf. on

Computational Methods in Nonlinear Mech., Austin, TX, 1974, in: Lecture Notes in Math., vol. 461, Springer,Berlin, 1975, pp. 131.[54] W.F. Ames, E. Adams, Monotonically convergent numerical two-sided bounds for a differential birth and deathprocess, in: Interval Mathematics, in: Lecture Notes in Comput. Sci., vol. 29, Springer-Verlag, 1975, pp. 135140.

Editorial / J. Math. Anal. Appl. 333 (2007) 17 5

[55] W.F. Ames, E. Adams, Monotonically convergent two-sided bounds for some invariant parabolic boundary prob-lems, Z. Angew. Math. Mech. 56 (1976) 240242.

[56] W.F. Ames, E. Adams, Exact shooting and eigenparameter problems, Nonlinear Anal. 1 (1976) 7582.[57] R. Chand, D.T. Davy, W.F. Ames, On the similarity solutions of wave propagation for a general class of non-linear

dissipative materials, Int. J. Nonlinear Mech. 11 (1976) 191205.[58] W.F. Ames, Some ad-hoc techniques for nonlinear partial differential equations, in: Mathematical Physics and

Physical Mathematics, Proc. Int. Symp., Warsaw, 1974, in: Math. Phys. Appl. Math., vol. 2, Reidel, DordrechtBoston, MA, 1976, pp. 99134.

[59] A.W. Marris, W.F. Ames, Addendum: On complex-lamellar motions (Arch. Ration. Mech. Anal. 59 (1975) 131148), Arch. Ration. Mech. Anal. 64 (1977) 371379.

[60] W.F. Ames, Monotonically convergent upper and lower bounds for classes of conflicting populations, in: NonlinearSystems and Applications, Proc. Int. Conf., Univ. Texas, Arlington, 1976, Academic Press, New York, 1977, pp. 314.

[61] W.F. Ames, Nonlinear superposition for operator equations, in: Nonlinear Equations in Abstract Spaces, Proc. Int.Symp., Univ. Texas, Arlington, 1977, Academic Press, New York, 1978, pp. 4366.

[62] W.F. Ames, M. Padmanabhan, C.S. Martin, Numerical analysis of pressure transients in bubbly two phase mixtureby explicitimplicit methods, J. Eng. Math. 12 (1978) 8393.

[63] W.F. Ames, N.H. Ibragimov, Utilization of group properties in computation, Proc. of IUTAM/IMU Symposium onGroup Theoretical Methods in Mechanics, Novosibirsk, USSR, 1978, pp. 923.

[64] W.F. Ames, Examples of Backlund transformations and some applications of Backlund transformations, in: R. An-derson, N.H. Ibragimov (Eds.), LieBacklund Transformations and Applications, in: SIAM Stud. Appl. Math.,vol. 1, 1979 (two chapters).

[65] W.F. Ames, E. Adams, Nonlinear boundary and eigenvalue problems for the EmdenFowler equations by groupmethods, Int. J. Nonlinear Mech. 14 (1979) 3542.

[66] E. Adams, W.F. Ames, On contracting interval iteration for nonlinear problems in Rn , I, in: Applied NonlinearAnalysis, Proc. Third Int. Conf., Univ. Texas, Arlington, 1978, Academic Press, New YorkLondon, 1979, pp. 311.

[67] V.L. Turner, W.F. Ames, Two-sided bounds for linked unknown nonlinear boundary conditions of reactiondiffusion, J. Math. Anal. Appl. 71 (1979) 366378.

[68] W.F. Ames, E. Adams, Contracting interval iteration for a class of nonlinear parabolic partial differential equations,in: Proc. of the Third IMACS Conference on Numerical Methods for Partial Differential Equations, Lehigh Univ.,1979, pp. 7376.

[69] E. Adams, W.F. Ames, On contracting interval iteration for nonlinear problems in Rn , I. Theory, Nonlinear Anal. 3(1979) 773794.

[70] W.F. Ames, J. Falco, R. Lohner, Mathematical analysis of models for pollutant transport and dissipation, in: Pro-ceedings of the Second International Conference on Mathematical Modelling, vols. I, II, St. Louis, MO, 1979,Univ. Missouri-Rolla, Rolla, MO, 1980, pp. 974974d.

[71] W.F. Ames, R. Lohner, Nonlinear models of reactiondiffusion in rivers, in: Advances in Computer Methods forPartial Differential Equations, Fourth IMACS International Symposium, Lehigh Univ., 1981, pp. 217219.

[72] E. Adams, W.F. Ames, On contracting interval iteration for nonlinear problems in Rn , II. Applications, NonlinearAnal. 5 (1981) 525542.

[73] W.F. Ames, R.J. Lohner, E. Adams, Group properties of utt = [f (u)ux ]x , Int. J. Nonlinear Mech. 16 (1981)439447.

[74] W.F. Ames, I. Suliciu, Some exact solutions for wave propagation in viscoelastic, viscoplastic and electrical trans-mission lines, Int. J. Nonlinear Mech. 17 (1982) 223230.

[75] W.F. Ames, A survey of finite difference schemes for parabolic partial differential equations, in: Numerical Prop-erties and Methodologies in Heat Transfer, Proc. Second Natl. Symposium, Univ. Maryland, 1981, 1982.

[76] W.F. Ames, R.E. Boisvert, U.N. Srivastava, Solutions of the NavierStokes equations by group methods, in: Proc.10th IMACS World Congress, vol. 3, North-Holland, 1983, pp. 3135.

[77] K.A. Ames, W.F. Ames, On group analysis of the von Krmn equations, Nonlinear Anal. 6 (1982) 845853.[78] E. Adams, W.F. Ames, Linear or nonlinear hyperbolic wave problems with input sets, J. Eng. Math. 16 (1982)

2345.[79] W.F. Ames, Optimization of nonlinear kinetic equation computation, in: Numerical Integration of Differential

Equations and Large Linear Systems, Bielefeld, 1980, in: Lecture Notes in Math., vol. 968, Springer, BerlinNewYork, 1982, pp. 165189.[80] R.E. Boisvert, W.F. Ames, U.N. Srivastava, Group properties and new solutions of NavierStokes equations, J. Eng.Math. 17 (1983) 203221.

6 Editorial / J. Math. Anal. Appl. 333 (2007) 17

[81] W. Zulehner, W.F. Ames, Group analysis of a semilinear vector diffusion equation, Nonlinear Anal. 7 (1983)945969.

[82] W.F. Ames, A survey of finite difference schemes for parabolic partial differential equations, in: Numerical Prop-erties and Methodologies in Heat Transfer, College Park, MD, 1981, in: Ser. Comput. Methods Mech. ThermalSci., Hemisphere, Washington, DCLondon, 1983, pp. 315.

[83] W.F. Ames, V.J. Ervin, E. Adams, Nonlinear waves in pellet fusion, in: Wave Phenomena: Modern Theory andApplications, North-Holland, 1984, pp. 199210.

[84] D. Fusco, A. Donato, W.F. Ames, Group analysis for a linear hyperbolic equation arising from a quasilinearreducible system, Wave Motion 6 (1984) 517524.

[85] K.A. Ames, W.F. Ames, Analysis of the von Krmn equations by group methods, in: Transactions of the FirstArmy Conference on Applied Mathematics and Computing, Washington, DC, 1983, ARO Rep., 84-1, US ArmyRes. Office, Research Triangle Park, NC, 1984, pp. 289299.

[86] W.F. Ames, Invariant solutions of the underwater acoustic wave equation, in: Computational Ocean Acoustics,New Haven, CN, 1984, Comput. Math. Appl. 11 (1985) 681685.

[87] W.F. Ames, R.C. Nicklas, Accurate elliptic differential equation solver, in: Accurate Scientific Computations, BadNeuenahr, 1985, in: Lecture Notes in Comput. Sci., vol. 235, Springer, Berlin, 1986, pp. 7085.

[88] E. Adams, W.F. Ames, R. Lang, Approximate practical stability for nonlinear evolution PDEs, in: NumericalMathematics and Applications, Oslo, 1985, in: IMACS Trans. Sci. Comput., vol. 85, I, North-Holland, Amsterdam,1986, pp. 125134.

[89] K.A. Ames, W.F. Ames, Analysis of the von Krmn equations by group methods, Int. J. Nonlinear Mech. 20(1985) 201209.

[90] W.F. Ames, M.C. Nucci, Analysis of fluid equations by group methods, J. Eng. Math. 20 (1986) 181187.[91] W.F. Ames, R. Lohner, E. Adams, Untersuchung der praktischen Stabilitt von Losungen nichtlinearer hyperboli-

scher Anfangsrandwertaufgaben, Z. Angew. Math. Mech. 65 (1985) 7678.[92] W.F. Ames, M.C. Nucci, Analysis of fluid equations by group methods, in: Transactions of the Third Army Con-

ference on Applied Mathematics and Computing, Atlanta, GA, 1985, ARO Rep., 86-1, US Army Res. Office,Research Triangle Park, NC, 1986, pp. 589596.

[93] W.F. Ames, D. Lee, Current development in the numerical treatment of ocean acoustic propagation, Appl. Numer.Math. 3 (1987) 2547.

[94] W.F. Ames, M.C. Nucci, Corrigendum: Analysis of fluid equations by group methods (J. Eng. Math. 20 (2)(1986) 181187), J. Eng. Math. 21 (1987) 261262.

[95] W.F. Ames, Analysis of mathematical models for pollutant transport and dissipation, in: The Mathematics ofSystems and Computations, Atlanta, GA, 1986, Comput. Math. Appl. 16 (1988) 939965.

[96] W.F. Ames, M.C. Nucci, Analysis of fluid equations by group methods, in: Computational Acoustics, vol. I,New Haven, CN, 1986, North-Holland, Amsterdam, 1988, pp. 259276.

[97] P.C. Richards, W.F. Ames, Invariant solutions of equations arising in ocean acoustics, in: Computational Acoustics,vol. I, New Haven, CN, 1986, North-Holland, Amsterdam, 1988, pp. 277285.

[98] W.F. Ames, A. Donato, On the evolution of weak discontinuities in a state characterized by invariant solutions, Int.J. Nonlinear Mech. 23 (1988) 167174.

[99] W.F. Ames, A. Donato, M.C. Nucci, Analysis of the threadline equations, in: Nonlinear Wave Motion, in: PitmanMonogr. Surveys Pure Appl. Math., vol. 43, Longman Sci. Tech., Harlow, 1989, pp. 110.

[100] W.F. Ames, Applications of group theory in computationa survey, in: Numerical and Applied Mathematics,Part I, Paris, 1988, in: IMACS Ann. Comput. Appl. Math., vol. 1.1, Baltzer, Basel, 1989, pp. 4755.

[101] W.F. Ames, Optimal numerical algorithms, in: Computational Acoustics, vol. 1, Princeton, NJ, 1989, North-Holland, Amsterdam, 1990, pp. 19.

[102] W.F. Ames, J.E. Peters, M. Abell, Symmetry and semi-symmetry reduction in wave propagation and lubrication,in: Lie Theory, Differential Equations and Representation Theory, Montreal, PQ, 1989, Univ. Montral, Montreal,QC, 1990, pp. 1324.

[103] J.E. Peters, W.F. Ames, Group properties of the nonlinear dynamic equations of elastic strings, Int. J. NonlinearMech. 25 (1990) 107115.

[104] K.A. Ames, W.F. Ames, Addenda: Analysis of the von Krmn equations by group methods (Int. J. NonlinearMech. 20 (1985) 201209), Int. J. Nonlinear Mech. 25 (1990) 451.

[105] M. Abell, W.F. Ames, Symmetry reduction of Reynolds equation and applications to film lubrication, Trans. ASMEJ. Appl. Mech. 59 (1992) 206210.[106] W.F. Ames, F.V. Postell, E. Adams, Optimal numerical algorithms. A Festschrift to honor Professor Garrett Birk-hoff on his eightieth birthday, Appl. Numer. Math. 10 (1992) 235259.

Editorial / J. Math. Anal. Appl. 333 (2007) 17 7

[107] M. Nakayama, W.F. Ames, D.P. Mason, Symmetry reduction of a partial differential equation describing nonlinearwaves in a compacting medium, in: Computational and Applied Mathematics, II, Dublin, 1991, North-Holland,Amsterdam, 1992, pp. 193199.

[108] M.L. Abell, M.F. Ames, Semi-symmetry reduction of partial differential equations, in: Computational and AppliedMathematics, II, Dublin, 1991, North-Holland, Amsterdam, 1992, pp. 101105.

[109] W.F. Ames, Symmetry in nonlinear mechanics, in: Nonlinear Equations in the Applied Sciences, in: Math. Sci.

Eng., vol. 185, Academic Press, Boston, MA, 1992, pp. 3178.

[110] E. Adams, W.F. Ames, W. Khn, W. Rufeger, H. Spreuer, Computational chaos may be due to a single local error,J. Comput. Phys. 104 (1993) 241250.

[111] W.F. Ames, M.C. Nucci, Symmetry analysis for waves in hole enlargement, in: Nonlinear Hyperbolic Problems:Theoretical, Applied, and Computational Aspects, Taormina, 1992, in: Notes Numer. Fluid Mech., vol. 43, Vieweg,Braunschweig, 1993, pp. 1014.

[112] M.C. Nucci, W.F. Ames, Classical and nonclassical symmetries for the Helmholtz equation, J. Math. Anal.Appl. 178 (1993) 584591.

[113] W.F. Ames, M.C. Nucci, M. Lauster, E. Adams, D. Straub, Comparison of classical and alternative fluid equationsusing symmetry methods, Z. Angew. Math. Mech. 75 (1995) 379388.

Books

[1] W.F. Ames, Nonlinear Problems of Engineering, Academic Press, New York, 1964.[2] W.F. Ames (Ed.), Nonlinear Problems of Engineering, Proc. of the 1963 NSF Delaware Conference, Academic

Press, New York, 1964.[3] W.F. Ames, Nonlinear Partial Differential Equations in Engineering, Academic Press, New York, 1965.[4] W.F. Ames (Ed.), Nonlinear Partial Differential Equations: A Symposium on Methods of Solution, Proc. of the

1965 NSF Delaware Conference, Academic Press, New York, 1967.[5] W.F. Ames, A.E. Hoerl, Mathematics Section of Engineers Manual, McGrawHill, New York, 1967.[6] W.F. Ames, Nonlinear Ordinary Differential Equations in Transport Processes, Academic Press, New York, 1968.[7] W.F. Ames, Numerical Methods for Partial Differential Equations, Barnes & Noble, Inc., New York, 1969.[8] W.F. Ames, Nonlinear Partial Differential Equations in Engineering, vol. II, Academic Press, New York, 1972.[9] W.F. Ames, A.E. Hoerl, Engineering Manual, Mathematics Section, third ed., McGrawHill, New York, 1976.

[10] W.F. Ames, Numerical Methods for Partial Differential Equations, second ed., Academic Press, New York, 1977.[11] W.F. Ames, R. Vichnevetsky, S. Sankar (Eds.), Proc. of the 10th IMACS World Congress, North-Holland, 1983

(4 volumes).[12] C. Rogers, W.F. Ames, Nonlinear Boundary Value Problems in Science and Engineering, Academic Press, Boston,

MA, 1989.[13] W.F. Ames (Ed.), IMACS Annals on Computing and Applied Mathematics, vol. 1, Baltzer Pub. Co., 1989.[14] W.F. Ames, Numerical Methods for Partial Differential Equations, third ed., Academic Press, Boston, MA, 1992.[15] W.F. Ames, C. Rogers (Eds.), Nonlinear Equations in the Applied Sciences, Academic Press, Boston, MA, 1992.[16] W.F. Ames, P.J. van der Houwen, Computational and Applied Mathematics. II, Differential Equations, in: Papers

from the IMACS Thirteenth World Congress held in Dublin, July 1991, North-Holland Publishing Co., Amster-dam, 1992.

[17] W.F. Ames, E.M. Harrell II, J.V. Herod (Eds.), Differential Equations with Applications to Mathematical Physics,Academic Press, Boston, MA, 1993.

[18] W.F. Ames, R.L. Anderson, V.A. Dorodnitsyn, E.V. Ferapontov, R.K. Gazizov, N.H. Ibragimov, S.R. Svir-shchevski, CRC Handbook of Lie Group Analysis of Differential Equations, vol. 1. Symmetries, Exact Solutionsand Conservation Laws, CRC Press, Boca Raton, FL, 1994.

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