Allen R. Miller (1942–2010) was an American mathematician. Miller was a major contributor to the field of special functions, especially confluent hypergeometric functions.

Biography

A native of Brooklyn, New York, Miller attended

George W. Wingate High School George W. Wingate High School is a defunct comprehensive high school in the Prospect Lefferts Gardens and Wingate neighborhoods of Brooklyn, New York City. It opened in 1956 and was closed down in June 2006 due to poor academic performance. Th ...

and

Brooklyn College Brooklyn College is a public university in Brooklyn, Brooklyn, New York. It is part of the City University of New York system and enrolls about 15,000 undergraduate and 2,800 graduate students on a 35-acre campus. Being New York City's first publ ...

, where he graduated in 1965 with a degree in mathematics. Miller began his professional career at the

Ballistics Research Laboratory The Ballistic Research Laboratory (BRL) was a leading U.S. Army research establishment situated at Aberdeen Proving Ground, Maryland that specialized in ballistics (interior, exterior, and terminal) as well as vulnerability and lethality analysis. ...

at the Aberdeen Proving Ground where he worked with physicist

Jane Dewey Jane Mary Dewey (July 11, 1900 – September 19, 1976) was an American physicist. Early life and education Jane Mary Dewey was born in Chicago, the daughter (and sixth child) of philosopher John Dewey and educator Alice Chipman Dewey. Her paren ...

. In 1967, he moved to the

Naval Research Laboratory The United States Naval Research Laboratory (NRL) is the corporate research laboratory for the United States Navy and the United States Marine Corps. It was founded in 1923 and conducts basic scientific research, applied research, technological ...

where he developed high-fidelity mathematical models of interactions between physical systems and electromagnetic fields. Unlike most pure mathematicians of the time, Miller implemented simulations of his models on early supercomputers. In the 1970s Miller was recognized not only as a leading mathematician but also as an expert on the

CRAY Cray Inc., a subsidiary of Hewlett Packard Enterprise, is an American supercomputer manufacturer headquartered in Seattle, Washington. It also manufactures systems for data storage and analytics. Several Cray supercomputer systems are listed ...

line of supercomputer. Miller maintained an academic affiliation with George Washington University as an adjunct professor after retiring from the Naval Research Laboratory in 1991. He published actively until his death from a heart embolism on August 15, 2010.

Special function theory

Miller made numerous contributions in the area of special functions and addressed several significant open problems. Notable among these include his work with Emanuel Vegh in formulating an exact closed-form solution for the grazing angle for specular reflection on a sphere ( Alhazen's problem).

Mathematical models

The Miller-Brown-Vegh model (developed at NRL) is commonly used to describe scattering from the ocean surface. It has been adopted in the US Navy's models for propagation over the ocean and appears in the Radar Handbook.

Computer security and information theory

Miller, with Ira S. Moskowitz, made several contributions to the mathematical analysis of covert channels in computer security. In particular he showed how special functions could simplify the closed form for the Shannon channel capacity and how the difference of divergent series could also be used to express channel capacity in certain physical situations that arise in anonymity networks.

Impact

Allen Miller published around 60 peer-reviewed journal articles and numerous other non-refereed technical reports and articles. His results have been applied in robotics, computer graphics, decision theory, and sensors. Miller received three Alan Berman Research Publication Awards from the

References

{{DEFAULTSORT:Miller, Allen R. 1943 births 2010 deaths 20th-century American mathematicians 21st-century American mathematicians Brooklyn College alumni