We classify integral rootless lattices which are sums of pairs of EE8-lattices (lattices isometric to √ 2 times the E8-lattice) and which define dihedral groups of orders less than or equal to 12. Most of these may be seen in the Leech lattice. Our classification may help understand Miyamoto involutions on lattice type vertex operator algebras and give a context for the dihedral groups which oc...

From the George Institute for Global Health, University of Oxford, Oxford, United Kingdom (R.N.); the University of Sydney, Sydney (R.N.); Makerere University College of Health Sciences, Kampala, Uganda (O.K.); and the Institute for Social and Health Sciences, University of South Africa, Johannesburg (O.K.). Address reprint requests to Dr. Norton at the George Institute for Global Health, New R...

Let p be a prime number and let k ≥ 2 be an integer such that k divides p − 1. Norton proved that the least k-th power non-residue modp is at most 3.9p log p unless k = 2 and p ≡ 3 (mod 4), in which case the bound is 4.7p log p. With a combinatorial idea and a little help from computing power, we improve the upper bounds to 0.9p log p and 1.1p log p, respectively.

Citation Zens, Timothy, Piotr Becla, Anuradha M. Agarwal, Lionel C. Kimerling, and Alvin Drehman. “Amorphous InSb and InAs[subscript 0.3]Sb[subscript 0.7] for long wavelength infrared detection.” In Infrared Technology and Applications XXXVII, edited by Bjørn F. Andresen, Gabor F. Fulop, and Paul R. Norton, 80123Y-80123Y-8. SPIE International Society for Optical Engineering, 2011. © (2011) COPY...

Katelyn N. Norton, Mark B. Badrov, Carly C. Barron, Neville Suskin, Armin Heinecke, and J. Kevin Shoemaker Neurovascular Research Laboratory, School of Kinesiology, University of Western Ontario, London, Ontario, Canada; Lawson Health Research Institute, University of Western Ontario, London, Ontario, Canada; Cardiac Rehabilitation Program, Division of Cardiology, University of Western Ontario,...

Abstract. We extend Norton-Borcherds-Koike’s replication formulae to super-replicable ones by working with the congruence groups Γ1(N) and find the product identities which characterize super-replicable functions. These will provide a clue for constructing certain new infinite dimensional Lie superalgebras whose denominator identities coincide with the above product identities. Therefore it cou...

C. JACYN BAKER1*, NORTON MOCK1, KENNETH L. DEAHL2, BRYAN BAILEY3 and DANIEL P. ROBERTS4 Microbiology and Plant Pathology Laboratory, ARS, United States Department of Agriculture, Beltsville, MD 20705, U.S.A., Vegetable Laboratory, ARS, United States Department of Agriculture, Beltsville, MD 20705, U.S.A., Alternate Crops and Systems Laboratory, ARS, United States Department of Agriculture, Belt...

The Nachtmann moment is employed to study the contribution of twist-3 operator to the nucleon spin structure functions. Target mass corrections to the CornwallNorton moments of the spin structure functions g1,2 are discussed. It is found that the corrections play a sizeable role to the contribution of the twist-3 d̃2 extracted from the Cornwall-Norton moments. PACS: 13.60.Hb, 12.38.Aw, 12.38Cy; ...

Application of the Aventech AIMMS20AQ airborne probe for turbulence measurements during the Convective Storm Initiation Project K. M. Beswick, M. W. Gallagher, A. R. Webb, E. G. Norton, and F. Perry School of Earth, Atmosphere and Environmental Sciences, University of Manchester, UK School of Earth and Environment, University of Leeds, UK Received: 13 November 2006 – Accepted: 11 January – Publ...

1. Leimgruber KL, Ward AF, Widness J, Norton MI, Olson KR, et al. (2014) Give What You Get: Capuchin Monkeys (Cebus apella) and 4-Year-Old Children Pay Forward Positive and Negative Outcomes to Conspecifics. PLoS ONE 9(1): e87035. doi:10.1371/journal.pone.0087035 Figure 3: Percentage of total trials in which monkeys and children paid forward positive and negative outcomes after receiving positi...