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- John H. Conway, Ronald H. Hardin, N. J. A. Sloane
- Experimental Mathematics
- 1996
This paper addresses the question: how should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations… (More)
- Ronald H. Hardin, N. J. A. Sloane
- Discrete & Computational Geometry
- 1996
Evidence is presented to suggest that, in three dimensions, spherical 6-designs with N points exist for N = 24, 26, ≥ 28; 7-designs for N = 24, 30, 32, 34, ≥ 36; 8-designs for N = 36, 40, 42, ≥ 44;… (More)
By using totally isotropic subspaces in an orthogonal space Ω+(2i, 2), several infinite families of packings of 2k-dimensional subspaces of real 2i-dimensional space are constructed, some of which… (More)
- Ronald H. Hardin, N. J. A. Sloane
- Discrete Mathematics
- 1992
Hardin, R.H. and N.J.A. Sloane, New spherical 4-designs, Discrete Mathematics 106/107 (1992) 255-264. This paper gives a number of new spherical 4-designs, and presents numerical evidence that… (More)
- N. J. A. Sloane, Ronald H. Hardin, Tom Duff, John H. Conway
- Discrete & Computational Geometry
- 1995
What is the tightest packing of N equal nonoverlapping spheres, in the sense of having minimal energy, i.e., smallest second moment about the centroid? The putatively optimal arrangements are… (More)
By combining a modified version of Hooke and Jeeves’ pattern search with exact or Monte Carlo moment calculations, it is possible to find I-, Dand A-optimal (or nearly optimal) designs for a wide… (More)
- Ronald H. Hardin, Robert P. Kurshan, Sandeep K. Shukla, Moshe Y. Vardi
- CAV 1997
- 1997
- Dike N. Kalu, Ronald H. Hardin, Richard Cockerham, Byung Pal Yu
- Endocrinology
- 1984
Studies were carried out on SPF F344 male rats to evaluate the effects of aging and life-prolonging food restriction, without malnutrition, on rat skeleton and circulating PTH. Six-week-old F344 rats… (More)
Computer-generated designs in the sphere are described which have the minimal (or larger) number of runs for a full quadratic response-surface design. In the case of 3 factors, the designs have 10… (More)