2 results
A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues
-
- Journal:
- Canadian Mathematical Bulletin / Volume 49 / Issue 4 / 01 December 2006
- Published online by Cambridge University Press:
- 20 November 2018, pp. 560-577
- Print publication:
- 01 December 2006
-
- Article
-
- You have access
- Export citation
-
In this article we will show that there are infinitely many symmetric, integral 3 × 3 matrices, with zeros on the diagonal, whose eigenvalues are all integral. We will do this by proving that the rational points on a certain non-Kummer, singular
$\text{K3}$ surface are dense. We will also compute the entire Néron–Severi group of this surface and find all low degree curves on it.
Characterization of optimality for the abstract convex program with finite dimensional range
-
- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 30 / Issue 4 / April 1981
- Published online by Cambridge University Press:
- 09 April 2009, pp. 390-411
- Print publication:
- April 1981
-
- Article
-
- You have access
- Export citation
-
This paper presents characterizations of optimality for the abstract convex program
when S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S-convex (on Ω). These characterizations, which include a Lagrange multiplier theorem and do not presume any a priori constraint qualification, subsume those presently in the literature.
