14 citations · 14 across the 7 of their papers we have counts for
7 papers
Polarizing Antiresonant Hollow-Core Fiber
Yuxi Wang, Charu Goel, Wonkeun Chang
Achieving robust single-polarization guidance in hollow-core fibers has remained a longstanding challenge, limiting their integration into precision photonic systems. Here, we repo…
Sums of squares of k-term forms
Charu Goel, Bruce Reznick
In this paper we study the cones corresponding to sums of squares of -ary -ic forms with at most terms. We show that these are strictly nested as increases, leading t…
On nonnegative invariant quartics in type A
Sebastian Debus, Charu Goel, Salma Kuhlmann +1
The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type A. As a first step to a classification…
A Refinement of Hilbert's 1888 Theorem: Separating Cones along the Veronese Variety
Charu Goel, Sarah Hess, Salma Kuhlmann
For , the cone of positive semi-definite (PSD) -ary -ic forms (i.e., homogeneous polynomials with real coefficients in var…
Intermediate Cones between the Cones of Positive Semidefinite Forms and Sums of Squares
Charu Goel, Sarah Hess, Salma Kuhlmann
The cone () of all positive semidefinite (PSD) real forms in variables of degree contains the subcone of those that…
The analogue of Hilbert's 1888 theorem for Even Symmetric Forms
Charu Goel, Salma Kuhlmann, Bruce Reznick
Hilbert proved in 1888 that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if or or , where is the number…
On the Choi-Lam analogue of Hilbert's 1888 theorem for Symmetric Forms
Charu Goel, Salma Kuhlmann, Bruce Reznick
A famous theorem of Hilbert from 1888 states that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if or or , w…