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.
Richard Duffin | |
|---|---|
| Born | 1909 Chicago, Illinois, U.S. |
| Died | October 29, 1996 (aged 87) Pittsburgh, Pennsylvania, U.S. |
| Nationality | American |
| Alma mater | University of Illinois at Urbana-Champaign |
| Known for | Work on electrical network theory DKP algebra Duffin–Schaeffer conjecture Bott–Duffin synthesis |
| Awards | John von Neumann Theory Prize (1982) |
| Scientific career | |
| Fields | Physics |
| Institutions | Carnegie Mellon University Purdue University |
| Doctoral advisor | Harold Mott-Smith David Bourgin |
| Doctoral students | Raoul Bott Hans Weinberger |
Education and career
editDuffin 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]
Selected publications
edit- 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.
See also
editReferences
edit- ^ a b c C.I.J (1984). "Sigma Xi News". American Scientist. 72 (2): 124. JSTOR 27852522.
- ^ Richard Duffin at the Mathematics Genealogy Project.
- ^ a b c Richard J. Duffin from the Institute for Operations Research and the Management Sciences (INFORMS)
- ^ John H. Hubbard (2010) "The Bott-Duffin Synthesis of Electrical Circuits", pages 33–40 in A Celebration of the Mathematical Legacy of Raoul Bott, P. Robert Kotiuga editor, CRM Proceedings and Lecture Notes #50, American Mathematical Society
- ^ Duffin, R. J.; Schaeffer, A. C. (1941-06-01). "Khinchin's problem in metric Diophantine approximation". Duke Mathematical Journal. 8 (2): 243–255. doi:10.1215/S0012-7094-41-00818-9. JFM 67.0145.03. S2CID 122007220. Zbl 0025.11002.
- ^ Koukoulopoulos, Dimitris; Maynard, James (2020). "On the Duffin-Schaeffer conjecture". Annals of Mathematics. 192 (1): 251. arXiv:1907.04593. doi:10.4007/annals.2020.192.1.5. JSTOR 10.4007/annals.2020.192.1.5. S2CID 195874052.
- ^ Ben–Israel, Adi (1968). "Review of Geometric Programming—Theory and Applications. By R. J. Duffin, E. L. Peterson and C. Zener". SIAM Review. 10 (2): 235–236. doi:10.1137/1010047.
- ^ Dicke, William (November 10, 1996). "Richard Duffin, 87, Researcher In Many Areas of Mathematics". The New York Times. Retrieved March 30, 2015.
- ^ "Richard James Duffin | American Academy of Arts and Sciences". 9 February 2023.
- ^ "New Members Elected May 8, 1974". Records of the Academy. 1973–1974 (1973/1974): 69–72. 1973. JSTOR 3785536.
- ^ Assad, Arjang A.; Gass, Saul I., eds. (2011). Profiles in Operations Research: Pioneers and Innovators. New York, NY: Springer. p. 213. ISBN 978-1-441-96280-5.
- ^ Fellows: Alphabetical List, Institute for Operations Research and the Management Sciences, retrieved 2019-10-09