Richard Duffin

Richard James Duffin (1909 – October 29, 1996) was an American physicist, known for his contributions to electrical transmission theory and to the development of geometric programming and other areas within operations research.

Duffin obtained a BSc in physics at the University of Illinois, where he was elected to Sigma Xi in 1932.^[1] He stayed at Illinois for his PhD, which was advised by Harold Mott-Smith and David Bourgin, producing a thesis entitled Galvanomagnetic and Thermomagnetic Phenomena (1935).^[2]

Duffin lectured at Purdue University and Illinois before joining the Carnegie Institute in Washington, D.C. during World War II.^[3] His wartime work was devoted to the development of navigational equipment and mine detectors. In 1946, he became professor of mathematics at Carnegie Mellon University.^[1] He wrote a letter of recommendation to Princeton University for John Forbes Nash, Jr., later a Nobel laureate. In 1949, Duffin and his student Raoul Bott developed a generalized method of synthesising networks without transformers which were required in earlier methods.^[4]

In 1941, Duffin and A. C. Schaeffer put forward^[5] a conjecture in metric diophantine approximation which was resolved in 2020 by James Maynard and Dimitris Koukoulopoulos.^[6]

In 1967 Duffin joined with Clarence Zener and Elmor Peterson to write Geometric Programming which developed a branch of mathematical programming by introducing a generalization of polynomials to posynomials for engineering applications. Impressed with its innovations, a reviewer wrote, "common sense, ingenuity and originality in applying first principles are still competitive with other creative forms of the intellect."^[7] The methods of geometric programming are sometimes adapted for convex optimization.

Duffin would remain at Carnegie Mellon until his retirement in 1988.^[3] Duffin was also a consultant to Westinghouse Electric Corporation.^[3]

Duffin was inducted to the National Academy of Sciences in 1972^[8] and to the American Academy of Arts and Sciences in 1974^[9].^[10] He was joint winner of the 1982 John von Neumann Theory Prize,^[11] and winner of Sigma Xi's Monie A. Ferst Award for 1984 in recognition of his ability as a teacher and communicator.^[1] He was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences.^[12]

• 1949: (with Raoul Bott) "Impedance synthesis without the use of transformers", Journal of Applied Physics 20:816.
• 1952: (with A. C. Schaeffer) Duffin, R. J.; Schaeffer, A. C. (1952). "A class of nonharmonic Fourier series". Trans. Amer. Math. Soc. 72 (2): 341–366. doi:10.1090/s0002-9947-1952-0047179-6. MR 0047179.
• 1953: (with R. Bott) Bott, R.; Duffin, R. J. (1953). "On the algebra of networks". Transactions of the American Mathematical Society. 74: 99–109. doi:10.1090/s0002-9947-1953-0056573-x. MR 0056573.
• 1956: Duffin, R. J. (1956). "Exponential decays in nonlinear networks". Proc. Amer. Math. Soc. 7 (6): 1094–1106. doi:10.1090/s0002-9939-1956-0083366-8. MR 0083366.
• 1959: Duffin, R. J. (1959). "An analysis of the Wang algebra of networks". Trans. Amer. Math. Soc. 93: 114–131. doi:10.1090/s0002-9947-1959-0109161-6. MR 0109161.
• 1962: Duffin, R. J. (1962). "The reciprocal of a Fourier series". Proceedings of the American Mathematical Society. 13 (6): 965–970. doi:10.1090/s0002-9939-1962-0145259-x. MR 0145259.
• 1967: (with Elmor Peterson and Clarence M. Zener) Geometric Programming, John Wiley & Sons
• 1974: Duffin, R. J. (1974). "Some problems of mathematics and science". Bulletin of the American Mathematical Society. 80 (6): 1053–1070. doi:10.1090/s0002-9904-1974-13618-9. MR 0359436.

• Frame (linear algebra)
• Parallel addition
• Signomial
• Wang algebra