2014/12/27 by Jakub Mareček, Jakub Marecek, Marecek, Jakub +5 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Formal Methods in Verification #Optimization and Control (math.OC) #Polynomial and algebraic computation #and Science (cs.CE) #cs.CE #math.OC
paper · pdf · doi:10.48550/arxiv.1412.8054
openalex publication_date 2014/12/27 · arxiv created 2016/11/15 · arxiv updated 2016/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Steady states of alternating-current (AC) circuits have been studied in considerable detail. In 1982, Baillieul and Byrnes derived an upper bound on the number of steady states in a loss-less AC circuit [IEEE TCAS, 29(11): 724--737] and conjectured that this bound holds for AC circuits in general. We prove this is indeed the case, among other results, by studying a certain multi-homogeneous structure in an algebraisation.