87 citations · 163 across the 21 of their papers we have counts for
22 papers
Number of Real Critical Points of Cyclotomic Polynomials
Hoon Hong, Andrew J. Sommese
We study the number of real critical points of a cyclotomic polynomial , that is, the real roots of . As usual, one can, without losing generality, res…
Singular value decomposition of complexes
Danielle A. Brake, Jonathan D. Hauenstein, Frank-Olaf Schreyer +2
Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions t…
Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
Azat M. Gainutdinov, Wenrui Hao, Rafael I. Nepomechie +1
We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible…
Homotopy techniques for tensor decomposition and perfect identifiability
Jonathan D. Hauenstein, Luke Oeding, Giorgio Ottaviani +1
Let T be a general complex tensor of format . When the fraction is an integer, and a natural inequality (called balancedness) is satis…
Singular solutions, repeated roots and completeness for higher-spin chains
Wenrui Hao, Rafael I. Nepomechie, Andrew J. Sommese
We investigate the completeness of the solutions of the Bethe equations for the integrable spin-s isotropic (XXX) spin chain with periodic boundary conditions. Solutions containing…
On the completeness of solutions of Bethe's equations
Wenrui Hao, Rafael I. Nepomechie, Andrew J. Sommese
We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions wi…