We show that there exist real numbers λ1, λ2, . . . , λn that occur as the eigenvalues of an entry-wise nonnegative n-by-n matrix but do not occur as the eigenvalues of a symmetric nonnegative n-by-n matrix. This solves a problem posed by Boyle and Handelman, Hershkowitz, and others. In the process, recent work by Boyle and Handelman that solves the nonnegative inverse eigenvalue problem by app...

This paper shows the findings of a research carried out with Colombian pre-service science teachers. In particular, it points results derived from application Didactic Sequence which ties up Nature Science (Nos) along historical models Law Boyle, such as philosophical controversy about vacuum, interest for experimental vacuum production and, finally, design air pump and works Boyle pressure. It...

Katherine Jones, Lady Ranelagh, worked at the heart of seventeenth-century scientific debates — in shadow her brother, Robert Boyle.

In their celebrated 1991 paper on the inverse eigenvalue problem for nonnegative matrices, Boyle and Handelman conjectured that if A is an (n+1)×(n+1) nonnegative matrix whose nonzero eigenvalues are: λ0 ≥ |λi|, i = 1, . . . , r, r ≤ n, then for all x ≥ λ0, (∗) r ∏ i=0 (x− λi) ≤ x − λ 0 . To date the status of this conjecture is that Ambikkumar and Drury (1997) showed that the conjecture is tru...