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- Ron Evans, John Greene
- Finite Fields and Their Applications
- 2009

We prove a general identity for a 3F2 hypergeometric function over a finite field Fq, where q is a power of an odd prime. A special case of this identity was proved by Greene and Stanton in 1986. As an application, we prove a finite field analogue of Clausen’s Theorem expressing a 3F2 as the square of a 2F1. As another application, we evaluate an infinite… (More)

We prove two general formulas for a two-parameter family of hypergeometric 3F2(z) functions over a finite field Fq , where q is a power of an odd prime. Each formula evaluates a 3F2 in terms of a 2F1 over Fq2 . As applications, we evaluate infinite one-parameter families of 3F2( 1 4 ) and 3F2(−1), thereby extending results of J. Greene–D. Stanton and K.… (More)

- Nanette R Boyle, T Steele Reynolds, Ron Evans, Michael Lynch, Ryan T Gill
- Biotechnology journal
- 2013

Recombineering has been an essential tool for genetic engineering in microbes for many years and has enabled faster, more efficient engineering than previous techniques. There have been numerous studies that focus on improving recombineering efficiency, which can be divided into three main areas: (i) optimizing the oligo used for recombineering to enhance… (More)

- Andrew Garst, Michael Lynch, Ron Evans, Ryan T Gill
- Microbial cell factories
- 2013

Rewiring and optimization of metabolic networks to enable the production of commercially valuable chemicals is a central goal of metabolic engineering. This prospect is challenged by the complexity of metabolic networks, lack of complete knowledge of gene function(s), and the vast combinatorial genotype space that is available for exploration and… (More)

- RON EVANS
- 2009

Let H denote the hypergeometric 3F2 function over Fp whose three numerator parameters are quadratic characters and whose two denominator parameters are trivial characters. In 1992, Koike posed the problem of evaluating H at the argument 1/4. This problem was solved by Ono in 1998. Ten years later, Evans and Greene extended Ono’s result by evaluating an… (More)

- Ron Evans, Lihua Huang
- 2014

We generalize two mind-switching problems that arise in connection with the popular sci-fi television series Futurama and Stargate SG-1. Optimal solutions to these problems are found by answering the following question about a permutation σ expressed as a product of nontrivial disjoint cycles. “When writing σ as a product of distinct transpositions none… (More)

For an odd prime p, define Hp(z) = ∑ u,v(mod p) ( uv(1−u)(1−v)(1−uvz) p ) , where z is an integer (mod p) and the summands are Legendre symbols. The function Hp(z) was explicitly evaluated for z = 1 by Evans (1981) and for z = −1 by Greene and Stanton (1986). Koike (1992) determined Hp(1/4)(mod p), and Ono (1998) evaluated Hp(z) for z = 1/4,−1/8, and 1/64.… (More)

- Ron Evans, Lihua Huang, Tuan Nguyen
- The American Mathematical Monthly
- 2014

An episode of the television series Futurama features a two-body mind-switching machine, which will not work more than once on the same pair of bodies. After the Futurama community engages in a mind-switching spree, the question is asked, “Can the switching be undone so as to restore all minds to their original bodies?” Ken Keeler found an algorithm that… (More)

Ocaliva, a synthetic bile acid analog with high affinity for the nuclear bile acid receptor FXR, is effective in treating primary biliary cholangitis, an autoimmune liver disease. It works in patients who fail to respond to or cannot tolerate conventional treatment with the natural bile acid ursodeoxycholic acid (UDCA).

- Ron Evans, John Greene
- 2017

A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p > 3. His proof required deep algebro-geometric techniques, and he expressed interest in finding a more straightforward direct proof. The first author recently gave such a proof of his… (More)