Publications of J.W. Neuberger

  1. "Continuous Products and Nonlinear Integral Equations," Pac. J. of Math., 8 (1958), 529-549.
  2. "Concerning Boundary Value Problems," Pac. J. of Math., 10 (1960), 1385-1392.
  3. "An Analyticity Condition," J. London Math. Soc., 38 (1963), 91-98.
  4. "A Quasi-Analyticity Condition in Terms of Finite Differences," Proc. London Math. Soc., XIV (1964), 245-259.
  5. "A Generator For A Set of Functions," Ill. J. Math., 9 (1965), 31-39.
  6. "The Lack of Self-Adjointness in Three-Point Boundary Value Problems," Pac. J. Math., 28 (1966), 165-168.
  7. "An Exponential Formula for One-Parameter Semigroups of Non-linear Transformations," J. Math. Soc. Japan, 19 (1966), 1954-1957.
  8. "Symmetry in Non-Self-Adjoint Sturm-Liouville Systems," Bull. Amer. Math. Soc., 73 (1967), 701-703.
  9. "Toward a Characterization of the Identity Component in Rings and Nearrings of Continuous Transformations," J. fur die Reine und Angewandte Mathematik, 238 (1969), 100-104.
  10. "Quasi-Analytic Collections Containing Fourier Series Which Are Not Infinitely Differentiable," J. London Math. Soc., 43 (1968), 612-616.
  11. "Tensor Products and Successive Approximations for Partial Differential Equations," Isr. J. Math., 6 (1968), 121-132.
  12. "Existence of a Spectrum for Nonlinear Transformations," Pac. J. Math., 31 (1969), 157-159.
  13. "Product Integral Formulae for Nonlinear Expansive Semigroups and Nonexpansive Evolution Systems," J. of Math. and Mech., 19 (1969), 403-409.
  14. "Analyticity and Quasi-Analyticity for One-Parameter Semigroups," Proc. Amer. Math. Soc., 25 (1970), 488-494.
  15. "Quasi-Analyticity and Semigroups of Bounded Linear Transformations," Bull. Amer. Math. Soc., 78 (1972), 85-87.
  16. "Lie Generators for Strongly Continuous Equi-Uniformly Continuous One Parameter Semigroups on a Metric Space," Ind. Univ Math J., 21 (1971), 961-971.
  17. "Lie Generators for One Parameter Semigroups of Transformations," J. Reine Ang. Math., 258 (1973), 133-136.
  18. "Differentiable Semigroups With a Neighborhood of the Identity Homeomorphic to a Banach Space," Proc. Amer. Math Soc., 34 (1972), 595-600.
  19. "Quasi-Analyticity and Semigroups," Bull. Amer. Math. Soc., 78 (1972), 909-922.
  20. "Quasi-Analytic Semigroups," J. London Math. Soc., (2), 7 (1973), 259-264.
  21. "Norm of Symmetric Product Compared with Norm of Tensor Product," J. Linear Multi-Linear Algebra, 2 (1974), 115-121.
  22. "An Iterative Method for Solving Nonlinear Partial Differential Equations," Advances in Math., 19 (1976), 245-265.
  23. "Differentiability of the Exponential of a Member of a Nearring," Proc. Amer. Math. Soc., 48 (1975), 98-100.
  24. "A Resolvent for an Iteration Method for Nonlinear Partial Differential Equations," Trans. Amer. Math. Soc., 226 (1977), 231-343.
  25. "Projection Methods for Linear and Nonlinear Systems of Partial Differential Equations," Proceedings 1976 Dundee Conference on Differential Equations, Springer-Verlag Lecture Notes, 564, 341-349.
  26. "Square Integrable Solutions to Linear Inhomogenous Systems, J. Differential Equations, 27 (1978), 144-152.
  27. "Boundary Value Problems for Systems of Nonlinear Partial Differential Equations," Functional Analysis and Numerical Analysis, Springer-Verlag Lecture Notes #701, 196-208.
  28. "Iteration for Systems of Nonlinear Partial Differential Equations," Nonlinear Equations in Abstract Spaces, Academic Press (1977), 253-263.
  29. "An Iterative Method for Approximating Solutions to Nonlinear Partial Differential Equations," Applied Nonlinear Analysis, Academic Press, (1979), 287-297.
  30. "Boundary Value Problems for Linear Systems," Proc. Royal Soc., Edinburgh, 83A (1979), 297-302.
  31. "Finite Dimensional Potential Theory Applied to Numerical Analysis," Linear Alg. Appl., 35 (1981), 193-202.
  32. "A Type-Independent Iterative Method for Systems of Non-Linear Partial Differential Equations: Application to the Problem of Transonic Flow," Computers and Mathematics With Applications, 7 (1980), 67-78.
  33. "A Solvability Condition for Systems of Functional Differential Equations," Proceedings Conf. Functional and Integral Equations, Marcel Dekker, Inc., (1981).
  34. "A Type-Independent Numerical Method for Solving Systems of Non-Linear Partial Differential Equations," Proceedings Second International Conf. on Innovative Numerical Analysis, Univ. of Montreal, (1980).
  35. "A Type-Independent Iterative Method Using Finite Elements," Proceedings Third International Conf. on Finite Elements and Flow Theory, University of Calgary, (1980).
  36. "An Iterative Method Based Upon Residual Averaging," Proc. Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics, NASA (1980).
  37. "A Type-Independent Numerical Method with Applications to Navier-Stokes Equations," Proc. Ninth Conference on Numerical Simulation of Plasmas, Northwestern University, (1980).
  38. (With R. J. Renka) "A Portable Software Package for Non-Linear Partial Differential Equations," Oak Ridge National Laboratory, CSD-102 (1982).
  39. "Steepest Descent for Systems of Non-Linear Partial Differential Equations," Oak Ridge National Laboratory, CSD/TM-161 (1981).
  40. "Steepest Descent for General Systems of Linear Differential Equations in Hilbert Space," Springer Lecture Notes 1032 (1983), 390-406.
  41. "Some Global Steepest Descent Results for Nonlinear Systems," Trends Theory Applications Diff. Eq., Marcel Dekker (1984), 413-418.
  42. "Use of Steepest Descent for Systems of Conservation Equations," Proc. Special Year in Partial Differential Equations, Univ. of Houston (1983).
  43. (with D.W. Noid) "Numerical Solution of Eigenvalues for Schroedinger Equation, Chemical Physics Letters, 104 (1984), 1-3.
  44. "Gradient Inequalities and Steepest Descent for Systems of Partial Differential Equations," Proc. Conf. on Numerical Analysis, Texas Tech. University, 1983.
  45. "Steepest Descent and Time-Stepping for the Numerical Solution of Conservation Equations," Proc. Conf. on Physical Math and Nonlinear Differential Equations, Marcel Dekker (1984).
  46. (With D.W. Noid) "Numerical Solution of Eigenvalues for Schroedinger Equation II, Chemical Physics Letters, 112 (1984), 393-395.
  47. "Steepest Descent and Differential Equations," J. Math. Soc. Japan , 37 (1985), 187-195.
  48. "Chaos and Higher Order Differences," Proc. Amer. Math. Soc., 101 (1987), 45-50.
  49. (With D.W. Noid) "Numerical Solutions of Eigenvalues for Schrodinger Equation III," J. Computational Chemistry, 8 (1987), 459-461.
  50. "Semigroups of Steepest Descent," Semesterberich Funktional Analysis, Tubingen University, Funktional Analysis 12 (1987), 57-62.
  51. "A Constructive Lemma for the Deficiency Index Problem, Proceedings Focused Research Program on Spectral Theory, Argonne National Laboratory, 2 (1987).
  52. "Constructive Variational Methods for Differential Equations, J. Nonlinear Analysis 13 (1988), 413-428.
  53. "Quasi-analytic Collections of Square Integrable Functions," Bulletin London Math. Soc., 20 (1988), 321-326.
  54. Editor: Collected works of Arne Beurling (with L. Carleson, P. Malliavin, J. Wermer), Birkhauser (1989).
  55. "Generation of Nonlinear Semigroups by a Partial Differential Equation," Semigroup Forum 40 (1990), 93-99.
  56. "Calculation of Sharp Shocks Using Sobolev Gradients," Contemporary Mathematics, American Mathematical Society 108 (1990), 111-118.
  57. "Beurling's Analyticity Theorem," Mathematics Intelligencer,15 (1993), 34-38.
  58. "Predictability in the Absence of Chaos," J. Math. Anal. Appl., 175 (1993), 321-332.
  59. "Nonlinear Semigroups," Matematisk Institut Aarhus Universitet (1992), 283-305.
  60. "Continuation for Quasiholomorphic Semigroups," Semigroups of Operators, G.R. and J.A. Goldstein, eds., (1993) Kluwer, 241-249.
  61. "A Feasibility Study of Nuclear Superfluorescence" (with B. Balko and I. Kay), Lasers '92, Proceedings of International Conference, C. P. Wong editor (1993), 89-93.
  62. "Lie Generators for Semigroups of Transformations on a Polish Space," (with J. R. Dorroh), Elec. J. Differential Equations (1993), 1-7.
  63. "Minimal Surfaces and Sobolev Gradients" (with R. J. Renka), Siam J. Sci. Comp. (1995), 1412-1427.
  64. "A Theory of Strongly Continuous Semigroups in Terms of Lie Generators" (with J. R. Dorroh), J. Functional Analysis, 136 (1996), 114-126.
  65. "Prevalance of Chaotic Differences for Unpredictable Functions," Acta Scientiarum Math., 61 (1995), 181-196.
  66. "Nuclear Superfluorescence: A Feasibility Study based on the Generalized Haake-Reibold Theory," Physical Rev. B(1995), 858-869 (with B. Balko, I. Kay).
  67. "An Investigation of the Possible Enhancement of Nuclear SF Through Crystalline and Hyperfine Interaction Effects," Proc. Int. Conf., Laser 95 V.I. Corcoran and T.A. Goldman, eds., STS Press (1996) (with B. Balko, I. Kay, R. Vuduc).
  68. "Superfluorescence in the Presence of Inhomogeneous Broadening and Relaxation," Hyperfine Interactions 107 (1997), 369-379  (with B. Balko, I. Kay, J. Silk, R. Vaduc).
  69. "Sobolev Gradients and Boundary Conditions for Partial Differential Equations," Contemporary Mathematics 204 (1997), 171-181.
  70. "Snowflake Harmonics and Computer Graphics: Numerical Computation of Spectra on Fractal Drums," Int. J. Bifurcation and Chaos 6 (1996), 1185-1210  (with M. Lapidus, R. Renka, C. Griffith).
  71. "Continuous Steepest Descent in Higher Order Sobolev Spaces," Nonlinear Analysis 30 (1997), 3517-3520.
  72. "Laplacians and Sobolev Gradients," Proc. Am. Math. Soc.  126 (1998), 2053-2060.
  73. "Sobolev Gradients and the Ginzburg-Landau Equations," Siam J. Sci. Comp. 20 (1998), 582-590  (with R. Renka).
  74. "Recovery of Superfluorescence in Inhomogeneously Broadened Systems through Rapid Relaxation," Physical Rev. B. 55 (1997), 171-181 (with B. Balko, I. W. Kay, R. Vuduc).
  75. Sobolev Gradients and Differential Equations, Lecture Notes in Mathematics 1670, Springer-Verlag (1997).
  76. "Numerical Calculation of Singularities for Ginzburg-Landau Functionals," Elec. J. Differential Equations (1997), No. 10, 1-4  (with R. J. Renka).
  77. "Continuous Steeptest Descent in Higher Order Sobolev Spaces, Nonlinear Analysis 30 (1997), 3517 - 3519
  78. "An Inverse Function Theorem," Contemporary Mathematics, 221 (1998), 127-132  (with A. Castro).
  79. "Approximation of Eigenvalues on the Dirichlet Laplacian on a Fractal Drum," Proceedings of the Third IMACS International Symposium on Iterative Methods in Scientific Computation, July 9-12, 1997, Jackson Hole, Wyoming  (with R. J. Renka).
  80. "Spectral characterization of  solutions to linear differential equations," Proc. Am. Math. Soc., 128 (2000), 853-855.
  81. "Numerical Calculation of the Essential Spectrum of a Laplacian," Experimental Mathematics, 8 (1999), 301-308 (with R. J. Renka).
  82. "Continuous Newton's Method for Polynomials," Mathematical Intelligencer, 21 (1999), 18-23.
  83. "Linear Extension of Nonlinear Semigroups," Progress in Nonlinear Differential Equations 42 (2000), Birkhauser, 96-102, (with J.R. Dorroh).
  84. "Computational Simulation of Vortex Phenomena in Superconductors", J. Nonlinear Analysis 47 (2001), 3223-3229 (with R. Renka).
  85. "Una Sucesion de Problemas de Semigrupos", Universidad de los Andes, 2000
  86. "Critical Points of the Ginzburg-Landau Functional on Multiply Connected Domains", J. Experimental Mathematics 9 (2000) ,523-533  (With R.J. Renka).
  87. "Numerical approximation of critical points of the Ginzburg-Landau functional",  Nonlinear Analysis 47 (2001), 3259-3270 (with R.J. Renka).
  88. "An Inverse Function Theorem by Means of Continuous Newton's Method" , J. Nonlinear Analysis 47 (2001), 3259-3270 (with A. Castro).
  89. "A Complete Theory for Jointly Continuous Nonlinear Semigroups on a Complete Separable Metric Space", J. Applicable Analysis 78 (2001), 223-231.
  90. "A local inversion principle of the Nash-Moser type and applications to symmetric positive systems", SIAM J. Math. Anal. 33 (2001), 989-993 (with A. Castro).
  91. "Computational simulation of vortex phenomena in superconductors", Elec. J. Diff. Eqns, Conference 10 (2003),  241-250 . (with R.J. Renka).
  92. "A near minimal hypothesis Nash-Moser Theorem",  Int. J. Pure. Appl. Math.. 4 (2003), 269-280.
  93. "Integrated form of continuous Newton's method",Evolution Equations,  Dekker Lecture Notes in Pure Appl. Math. 234  (2003), 331-336).
  94. "Energy minimization using Sobolev gradients:  application to phase separation and ordering", J. Comp. Physics  189 (2003),88-97  (with S. Sial, T .Lookman,A. Saxena).
  95. Sobolev gradients:  Introduction, applications, problems, Contemporary Mathematics 257 (2004), 85-99  (with R..J. Renka).
  96. "Numerical determination of vortices in superconductors: simulation of cooling" Supercond. Sci. Technol 16 (2003), 1-4 (with R.J. Renka).
  97. "Boundary conditions, Sobolev gradients and gradient inequalities", Ulmer Seminare 2003 (2004), 336-345.
  98. "Numerical results for the Metropolis algorithm", J. Experimental Math 13 (2004) ,207-213 ( with P. Diaconis).
  99. "Least squares and chaotic behavior in initial value problems", J. Nonlinear Analy. Convexity 6 (2005), 65-70   (with R.J.Renka).
  100. Prospects for a central theory of partial differential equations, Math. Intelligencer 27 (2005), 47-55.
  101. Energy minimization using Sobolev gradients - finite element setting, Proc. World Conference on 21st Century M 2005, Lahore, Pakistan, eds. Chaudhary and Bhatti (with S. Sial, T. Lookman, A. Saxena).
  102. Energy minimization using Sobolev gradients:  application to phase separation and ordering, J. Comp. Phys 189 (2003), 88-97.
  103. The continuous Newtons method, inverse functions and Nash-Moser, American Math. Monthly 114 (2007).
  104. The divergence-free Jacobian conjecture in dimension two, Rocky Mountain J. Math 36 (2006), 265-271.
  105. Semidynamical systems and Hilberts fifth problem, Math. Intelligencer 30 (2008), 37-41.
  106. Newton's method in the context of gradients, Elec. J. Differential Equations 2007 (2007), 1-13 (with J. Karatson).
  107. Potential theory and applications to a constructive method for finding critical points of Ginzburg-Landau type equations, J. Nonlinear Analysis 69 (2008), 925-930 (with Parimah Kazemi).
  108. Potential theory for nonlinear semigroups, Ulmer Seminare 2007 (2007).
  109. The Tricomi equation: A case study for Sobolev gradients, Comm. Applied Nonlinear Analysis  (2008)., 1-8.
  110. Recursive Sobolev Gradient for stiff ode on long intervals, Int. J. Comp. Math. 85 (2008), 1727-1740. (with D. Mujeeb and S. Sial).
  111. The Reimann Hypothesis as a problem in differential equations. (preprint)
  112. Sobolev Gradients and Differential Equations, Springer Lecture Notes in Mathematics 1670, Second Edition, 2009.
  113. Lie generators for local semigroups, Contemporary Mathematics, 513 (2010).
  114. A Seqiemce of Problems on Semigroups, Springer Mathematical Problem Books, 2011.
  115. Numerical solution of Burgers equation, Appl. Math. Comp. 218 (2011),4017-4024. (with N. Raza and S. Sial).
  116. How to distinguish local semigroups from global semigroups, Discrete amd Continuous Dynamical Systems-A. 33 (2012)., preprint at  arXiv.org/abs/1109.2184
  117. A linear condition determining global or local existence for nonlinear problems, Central European Journal Mathematics, 11(8), 2013, 1361-1374 .(with John M. Neuberger and James Swift)..
  118. Numerical solutions of integro-differential equations using Sobolev gradient methods, International Journal of Computational Methods,  9 (2012) (with N. Raxa, S. Sial, M. Ahmad).
  119. Newton flow of the Reimann Zeta function: Separatrices control the appearence of zeros.  (with C Feiler ,H. Maier, W. Schleich). New Journal of Physics 16 (2014) 103023.

 

Revised 9 November 2014

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