Allen R. Miller (1942–2010) was an American mathematician. Miller was a major contributor to the field of

special functions Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...

, especially

confluent hypergeometric function In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular s ...

Biography

A native of Brooklyn, New York, Miller attended George W. Wingate High School and

Brooklyn College Brooklyn College is a public university in Brooklyn in New York City, United States. It is part of the City University of New York system and enrolls nearly 14,000 students on a campus in the Midwood and Flatbush sections of Brooklyn as of fall ...

, 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 research facility under the U.S. Army Ordnance Corps and later the U.S. Army Materiel Command that specialized in ballistics as well as vulnerability and lethality analysis. Situated at Aberdeen Pr ...

at the

Aberdeen Proving Ground Aberdeen Proving Ground (APG) is a U.S. Army facility located adjacent to Aberdeen, Harford County, Maryland, United States. More than 7,500 civilians and 5,000 military personnel work at APG. There are 11 major commands among the tenant units, ...

where he worked with physicist Jane Dewey. 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. Located in Washington, DC, it was founded in 1923 and conducts basic scientific research, appl ...

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 The George Washington University (GW or GWU) is a Private university, private University charter#Federal, federally-chartered research university in Washington, D.C., United States. Originally named Columbian College, it was chartered in 1821 by ...

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

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 Specular reflection, or regular reflection, is the mirror-like reflection (physics), reflection of waves, such as light, from a surface. The law of reflection states that a reflected ray (optics), ray of light emerges from the reflecting surf ...

on a sphere (

Alhazen's problem Alhazen's problem is a mathematical problem in optics concerning reflection in a spherical mirror. It asks for the point in the mirror where one given point reflects to another. The special case of a concave spherical mirror is also known as ...

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 Radar is a system that uses radio waves to determine the distance (''ranging''), direction (azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track aircraft ...

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 Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which information can be reliably transmitted over a communication channel. Following the terms of the noisy-channel coding ...

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