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math.PR2009
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…
math.GM2009
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…
math.MG2009
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…