Edward Neuman (born September 19, 1943 in

Rydułtowy Rydułtowy (german: Rydultau) is a town in southern Poland, in the Wodzisław County of the Silesian Voivodeship. Rydułtowy is in the south-western part of the Silesian Highland, on the Rybnik Plateau, in the Oświęcim-Racibórz Valley. A mini ...

Silesian Voivodeship Silesian Voivodeship, or Silesia Province ( pl, województwo śląskie ) is a voivodeship, or province, in southern Poland, centered on the historic region known as Upper Silesia ('), with Katowice serving as its capital. Despite the Silesian ...

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populous ...

) is a Polish-American mathematician, currently a professor emeritus of mathematics at

Southern Illinois University Carbondale Southern Illinois University (SIU or SIUC) is a public research university in Carbondale, Illinois. Founded in 1869, SIU is the oldest and flagship campus of the Southern Illinois University system. The university enrolls students from all 50 s ...

Academic career

Neuman received his Ph.D. in mathematics from the

University of Wrocław , ''Schlesische Friedrich-Wilhelms-Universität zu Breslau'' (before 1945) , free_label = Specialty programs , free = , colors = Blue , website uni.wroc.pl The University of Wrocław ( pl, Uniwersytet Wrocławski, U ...

in 1972 under the supervision of wmpl:Stefan Paszkowski. His dissertation was entitled "Projections in Uniform Polynomial Approximation." He held positions at the Institute of Mathematics and the Institute of Computer Sciences of the

University of Wroclaw A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the ...

, and the Institute of Applied Mathematics Bonn in Germany. In 1986, he took a permanent faculty position at

Southern Illinois University Southern Illinois University is a system of public universities in the southern region of the U.S. state of Illinois. Its headquarters is in Carbondale, Illinois. Board of trustees The university is governed by the nine member SIU Board of Tr ...

Contributions

Neuman has contributed 130 journal articles in computational mathematics and mathematical inequalities such as the Ky Fan inequality, on bivariate means, and mathematical approximations and expansions. Neuman also developed software for computing with spline functions and wrote several tutorials for the

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...

programing software. Among the mathematical concepts named after Edward Neuman are Neuman–Sándor Mean and Neuman Means, which are useful tools for advancing the theory 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 ...

including

Jacobi elliptic functions In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While tri ...

: * The

Neuman–Sándor mean In mathematics of special functions, the Neuman–Sándor mean ''M'', of two positive and unequal numbers ''a'' and ''b'', is defined as: : M(a,b) = \frac This mean interpolates the inequality of the unweighted arithmetic mean ''A'' = ...

* The Neuman Means of the first kind * The Neuman Means of the second kind

Awards and honors

Neuman has received an award for notable and creative achievement from the Poland's Secretary of Higher Education in 1983 and was named the Outstanding Teacher in 2001 in the College of Science at

. Neuman worked as a Validator for the original release and publication of the

National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

(NIST) Handbook and

Digital Library of Mathematical Functions The Digital Library of Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology (NIST) to develop a database of mathematical reference data for special functions and their applications. It is intend ...

. He serves on the Editorial Boards of the Journal of Inequalities in Pure and Applied Mathematics, the Journal of Inequalities and Special Functions, and Journal of Mathematical Inequalities.

Selected works

The most frequently cited works by Neuman include: * "On the Schwab–Borchardt mean" ''Math Pannon'' 14(2) (2003), 253–266. * "On the Schwab–Borchardt mean II" ''Math Pannon'' 17(1) (2006), 49–59. * "The weighted logarithmic mean" ''J. Math. Anal. Appl.'' 188 (1994), 885–900.

References

External links