6 papers
Evolving the Euler rotation axis as a dynamical system, using the Euler vector and generalizations
John H. Elton, John R. Elton
Differential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is…
Householder Meets Student
John H. Elton, Andrew B. Gardner
The Householder algorithm for the QR factorization of a tall thin n x p full-rank matrix X has the added bonus of producing a matrix M with orthonormal columns that are a basis for…
Exact Solution to the Chow-Robbins Game for almost all n, using the Catalan Triangle
John H. Elton
The payoff in the Chow-Robbins coin-tossing game is the proportion of heads when you stop. Knowing when to stop to maximize expectation was addressed by Chow and Robbins(1965), who…
Notes on Feige's gumball machines problem
John H. Elton
We give a detailed proof, in the identically distributed case, of a conjecture of Feige about the maximum probability that the sum of n independent non-negative integer valued rand…
Indefinite quadratic forms and the invariance of the interval in Special Relativity
John H. Elton
A simple theorem on proportionality of indefinite real quadratic forms is proved, and is used to clarify the proof of the invariance of the interval in Special Relativity from Eins…
Ham Sandwich with Mayo: A Stronger Conclusion to the Classical Ham Sandwich Theorem
John H. Elton, Theodore P. Hill
The conclusion of the classical ham sandwich theorem of Banach and Steinhaus may be strengthened: there always exists a common bisecting hyperplane that touches each of the sets, t…