abstract disc infiltrometer is one of those devices that used in recent years in measurement of hydraulic conductivity of entire soil. in order to analyze the data taken by disc infiltrometer a variety of methods based on wooding’s base analyze have been introduced. the objective of this study was to compare the performances of ankeny and weir methods for predicting soil hydraulic properties us...

Randall F. Ankeny,* Casey J. Ankeny,* Robert M. Nerem, and Hanjoong Jo Parker H. Petit Institute for Bioengineering and Bioscience and Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia; Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, Georgia; Department of Bio-inspired Science, Ewh...

In 1957 N.C. Ankeny provided a new proof of the three squares theorem using geometry of numbers. This paper generalizes Ankeny’s technique, proving exactly which integers are represented by x2 + 2y2 + 2z2 and x2 + y2 + 2z2 as well as proving su cient conditions for an integer to be represented by x2 + y2 + 3z2 and x2 + y2 + 7z2.

In this paper certain polynomial inequalities with restricted zeros are given, which generalize and refine some well-known due to Ankeny Rivlin, Dewan, Singh Mir, Wani Hussain others.

In this exposé, Pell’s equation is put in a geometric perspective, and a version of Artin’s primitive roots conjecture is formulated for hyperelliptic jacobians. Also explained are some recent results which throw new lights, having to do with Ankeny-Artin-Chowla’s conjecture, class number relations, and Cohen-Lenstra heuristics.

Abstract Pawsey’s PhD research saw him systematically explore the repertoire of methods (Ankeny, 2019) in ionospheric research. We will see later how this so strongly shaped his approach to early radio astronomy.

Let p be a prime congruent to 1 modulo 4, and let t, u be rational integers such that (t + u √ p )/2 is the fundamental unit of the real quadratic field Q(√p ). The Ankeny-Artin-Chowla conjecture (AAC conjecture) asserts that p will not divide u. This is equivalent to the assertion that p will not divide B(p−1)/2, where Bn denotes the nth Bernoulli number. Although first published in 1952, this...