1 citations · 2 across the 6 of their papers we have counts for
6 papers
A note on mediated simplices
Victoria Powers, Bruce Reznick
Many homogeneous polynomials that arise in the study of sums of squares and Hilbert's 17th problem come from monomial substitutions into the arithmetic-geometric inequality. In 198…
Power index rankings in bicameral legislatures and the US legislative system
Victoria Powers
In this paper we study rankings induced by power indices of players in simple game models of bicameral legislatures. For a bicameral legislature where bills are passed with a simpl…
Polynomials non-negative on strips and half-strips
Ha Nguyen, Victoria Powers
In 2008, M. Marshall settled a long-standing open problem by showing that if f(x,y) is a polynomial that is non-negative on the strip [0,1] x R, then there exist sums of squares s(…
Rational certificates of positivity on compact semialgebraic sets
Victoria Powers
Schmüdgen's Theorem says that if a basic closed semialgebraic set K = {g_1 \geq 0, ..., g_s \geq 0} in R^n is compact, then any polynomial f which is strictly positive on K is in t…
Minimizing Polynomials Over Semialgebraic Sets
Jiawang Nie, James W. Demmel, Victoria Powers
This paper concerns a method for finding the minimum of a polynomial on a semialgebraic set, i.e., a set in $\re^m$ defined by finitely many polynomial equations and inequalities,…
A New Proof of Hilbert's Theorem on Ternary Quartics
Victoria Powers, Bruce Reznick, Claus Scheiderer +1
David Hilbert proved that a non-negative real quartic form f(x,y,z) is the sum of three squares of quadratic forms. We give a new proof which shows that if the complex plane curve…