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 A geometric program (GP) is an optimization problem of the form : \begin \mbox & f_0(x) \\ \mbox & f_i(x) \leq 1, \quad i=1, \ldots, m\\ & g_i(x) = 1, \quad i=1, \ldots, p, \end where f_0,\dots,f_m are posynomials and g_1,\dots,g_p are monomials. I ...

and other areas within

operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve deci ...

Education and career

Duffin obtained a

BSc A Bachelor of Science (BS, BSc, SB, or ScB; from the Latin ') is a bachelor's degree awarded for programs that generally last three to five years. The first university to admit a student to the degree of Bachelor of Science was the University ...

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

at the

University of Illinois The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...

, where he was elected to

Sigma Xi Sigma Xi, The Scientific Research Honor Society () is a highly prestigious, non-profit honor society for scientists and engineers. Sigma Xi was founded at Cornell University by a junior faculty member and a small group of graduate students in 1886 ...

in 1932. He stayed at Illinois for his PhD, which was advised by

Harold Mott-Smith Harold may refer to: People * Harold (given name), including a list of persons and fictional characters with the name * Harold (surname), surname in the English language * András Arató, known in meme culture as "Hide the Pain Harold" Arts a ...

and

David Bourgin David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". w ...

, producing a thesis entitled ''Galvanomagnetic and Thermomagnetic Phenomena'' (1935). Duffin lectured at

Purdue University Purdue University is a public land-grant research university in West Lafayette, Indiana, and the flagship campus of the Purdue University system. The university was founded in 1869 after Lafayette businessman John Purdue donated land and money ...

and Illinois before joining the Carnegie Institute in

Washington, D.C. ) , image_skyline = , image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, ...

during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

.Richard J. Duffin
from the

Institute for Operations Research and the Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger of ...

(INFORMS) His wartime work was devoted to the development of

navigation Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...

al equipment and

mine detector Demining or mine clearance is the process of removing land mines from an area. In military operations, the object is to rapidly clear a path through a minefield, and this is often done with devices such as mine plows and blast waves. By contra ...

s. In 1946, he became Professor of Mathematics at

Carnegie Mellon University Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology ...

. He wrote a letter of recommendation to Princeton University for

John Forbes Nash, Jr. John Forbes Nash Jr. (June 13, 1928 – May 23, 2015) was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow ga ...

, later a Nobel laureate. In 1949, Duffin and his student

Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions whi ...

developed a generalized method of synthesising networks without

transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...

s which were required in earlier methods. In 1967 Duffin joined with

Clarence Zener Clarence Melvin Zener (December 1, 1905 – July 2, 1993) was the American physicist who first (1934) described the property concerning the breakdown of electrical insulators. These findings were later exploited by Bell Labs in the development of ...

and Elmor Peterson to write ''Geometric Programming'' which developed a branch of

mathematical programming Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

by introducing a generalization of

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

s to

posynomial A posynomial, also known as a posinomial in some literature, is a function of the form : f(x_1, x_2, \dots, x_n) = \sum_^K c_k x_1^ \cdots x_n^ where all the coordinates x_i and coefficients c_k are positive real numbers, and the exponents a_ are ...

s 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." The methods of

are sometimes adapted for

convex optimization Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization probl ...

. Duffin would remain at Carnegie Mellon until his retirement in 1988. Duffin was also a consultant to

Westinghouse Electric Corporation The Westinghouse Electric Corporation was an American manufacturing company founded in 1886 by George Westinghouse. It was originally named "Westinghouse Electric & Manufacturing Company" and was renamed "Westinghouse Electric Corporation" in ...

. Duffin was inducted to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

in 1972 and to the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

in 1984. He was joint winner of the 1982

John von Neumann Theory Prize The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS) is awarded annually to an individual (or sometimes a group) who has made fundamental and sustained contributions to theory in operati ...

, and winner of

's Monie A. Ferst Award for 1984 in recognition of his ability as a teacher and communicator. He was elected to the 2002 class of

Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

s of the

Selected publications

* 1949: (with

) "Impedance synthesis without the use of transformers",

Journal of Applied Physics The ''Journal of Applied Physics'' is a peer-reviewed scientific journal with a focus on the physics of modern technology. The journal was originally established in 1931 under the name of ''Physics'', and was published by the American Physical So ...

20:816. * 1952: (with A. C. Schaeffer) * 1953: (with R. Bott) * 1956: * 1959: * 1962: * 1967: (with Elmor Peterson and

Clarence M. Zener Clarence Melvin Zener (December 1, 1905 – July 2, 1993) was the American physicist who first (1934) described the property concerning the breakdown of electrical insulators. These findings were later exploited by Bell Labs in the development of ...

) ''Geometric Programming'',

John Wiley & Sons John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in p ...

* 1974:

References

{{DEFAULTSORT:Duffin, Richard 1909 births 1996 deaths Scientists from Chicago 20th-century American physicists Grainger College of Engineering alumni Purdue University faculty Carnegie Mellon University faculty Fellows of the Institute for Operations Research and the Management Sciences Members of the United States National Academy of Sciences John von Neumann Theory Prize winners

Education and career

Selected publications

See also

References