Mathematics Publications

Nonlinear Optimization

• Variable Metric Method for Minimization, Argonne National Laboratory Report 5990 (1959).
• Variance Algorithm for Minimization, Computer J., 10, pp 406-410 (1968).
• Variance Algorithms for Minimization, in Optimization, ed. R. Fletcher, Academic Press, New York (1969) pp 13-20.
• Optimally Conditioned Algorithms without Line Searches, Mathematical Programming, 9 (1975), pp. 1-30.
• New Least Squares Algorithms, J. Optimization Theory and Applications, 18 (1976), pp. 187-197.
• Optimization by Non-Linear Scaling, (Technical Report, Institutt for Teoretisk Fysikk, 7034 Trondheim NTH, Norway, 1976).
• Fast Least Squares Algorithms, American J. Physics, 45 (1977), pp. 260-262.
• Optimization by Non-linear Scaling, Chapter VI.2 in Numerical Software, ed. D.A.H.Jacobs, Academic Press, NY (1978).
• Conic Approximations and Collinear Scalings for Optimizers, SIAM J. Numerical Analysis, 17 (1980), pp. 268-281.
• Conjugate Directions for Conic Functions, Ch.1.3, Nonlinear Optimization, ed. M. J. D.Powell, Academic Press, NY (1982), pp 23-28.
• Evaluation of Step Directions in Optimization Algorithms, with Jorge Nocedal, ACM Transactions on Mathematical Software, 11 (1985), pp. 13-19.
• Variable Metric Method for Minimization, SIAM J. Optimization 1 (1991), pp. 1-17.
• Notation for Quasi-Newton Methods, with R.B. Mifflin and J.L. Nazareth, Optima, No. 32, (March 1991), pp. 3-4.
• Conjugate Directions in Perspective, Ch. 6, Linear and Nonlinear Conjugate Gradient-Related Methods, ed. Loyce Adams and J. L. Nazareth, SIAM, Philadelphia (1996), pp. 79-82.
• On a characterization of convexity-preserving maps, Davidon's collinear scalings and Karmarkar's projective transformations; with K. A. Ariyawansa and K. D. McKennon, Mathematical Programming, A 90 (2001), pp. 153-168.
• A characterization of convexity-preserving maps from a subset of a vector space into another vector space; with K. A. Ariyawansa and K. D. McKennon, J. London Mathematical Society (2) 64 (2001), pp. 179-190.

Logic and Nonstandard Analysis

• Computer Analysis of the Algebra of Relations, Argonne National Laboratory Technical Report 38 (1962).
• Near-Standard Analysis, International Conference of Mathematicians, Abstracts, August 1986, p. 28.
• Axioms for the Guests of Infinite Sets, Nonstandard Analysis Conference, Smith College, August 1988.

Physics Publications

Theoretical

• Proper Time Electron Formalism, Phys. Rev., 97 (1955), pp 1131-1138.
• Proper Time Quantum Electrodynamics, Phys. Rev., 97 (1955) pp 1139-1144.
• Causality in the Pion Proton Scattering, with H. L. Anderson and U.E. Kruse, Phys. Rev., 100, 339 (1955)
• Comparison of Spin Flip Dispersion Relations with Pion Nucleon Scattering Data, with M.L.Goldberger, Phys. Rev., 104, 1119 (1956)
• Dispersions in the Pion Proton Scattering, with H. L. Anderson and U. E. Kruse, Nuovo Cimento Supplemento, 4, 168 (1956)
• Elementary Particles with the Symmetry of the DeSitter Group, Proceedings of the Midwest Conference on Theoretical Physics (1959)
• Observables in Relativistic Quantum Mechanics, with Hans Ekstein, J. Math. Phys., 5, (1964) pp 1588-1594
• Time-Dependent Multipole Analysis, J. Physics A, 6, 1635-1646 (1973)
• Consequences of the Inertial Equivalence of Energy, Foundations of Physics, 5 (1975), pp. 525-542
• Quantum Physics of Single Systems, Il Nuovo Cimento, 36B (1976), pp. 34-40
• Single System and Ensemble Interpretation of Pure Quantum States, Physica Norvegica, 8 (1976), pp. 223-228
• A Lorentz Invariant Continuum Mechanics, Arkiv for Det Fysiske Seminar i Trondheim, No. 11, 1976

Experimental

• Scattering of Positive Pions by Hydrogen at 189 MEV, with Anderson, Glickman and Kruse, Phys. Rev., 100, 279 (1955)
• Machine Analysis of Pion Scattering by the Maximum Liklihood Method, with H.L. Anderson, Nuovo Cimento,5, 1238 (1957).
• Spin Momentum Correlation in the Beta Decay of Polarized Li8 Nuclei, with Burgy, Novev, Perlow and Ringo, Bull. Am. Phys. Soc., Series 11, 2, 2 (1957)
• A Method for Constrained Refinement of Crystal Structures, with J. P. Chesick, Acta. Cryst. (1975), A31, 586
• Application of a New Least Squares Method to Structure Refinement, with J. P. Chesick and C. Shoen, Acta. Cryst. (1976), A32, 120

Teaching

• Symmetry and Conservation in Introductory Physics, Amer. J. Phys, 26, 508 (1958)
• An Introduction to Dispersion Relations, with C. H. Holbrow, Amer. J. Phys., 38 (1964), pp 762-774
• Wstep do Relacji Dyspersyjnych (translation of preceding article into Polish), Postepy Fizyki, 16, 389 (1965)
• Symmetry, Proceedings of the Boulder Conference on Physics, Comm. on College Physics, 165 (1965)
• Algebraic Description of Motion, Amer. J. Physics, 42, 764 (1974)
• Kinematics and Dynamics of Elastic Rods, Am. J. Phys., 43 (1975), pp. 705-713