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Sorting vectors

Published online by Cambridge University Press:  24 October 2008

Rollo Davidson
Affiliation:
Trinity College, Cambridge

Extract

1. Introduction: In what follows, X will be a real inner-product linear space (inner product (x, y), norm |x| = (x, x)½); En will be n-dimensional real Euclidean space. We shall be dealing with sets {as: 1 ≤ s ≤ rk; r ≥ 1, k ≥ 2} of elements of X; we write a for the vector (a1; …, ark), and put . We suppose that |as| ≤ ∈ (< 0) for every s.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Cox, D. R. and Miller, H. D.The theory of stochastic processes (London: Methuen, 1965).Google Scholar
(2)Davidson, R.More Delphic theory and practice. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 191203.Google Scholar
(3)Rankin, R. A.The closest packing of spherical caps in n dimensions. Proc. Glasgow Math. Assoc. 2 (1955), 139144.CrossRefGoogle Scholar