We develop a new framework for investigating linear equivalence of divisors on graphs using a generalization of Gioan’s cycle-cocycle reversal system for partial orientations. An oriented version of Dhar’s burning algorithm is introduced and employed in the study of acyclicity for partial orientations. We then show that the Baker-Norine rank of a partially orientable divisor is one less than th...

The problem of estimating the location of one or more coherent point scatterers from the time-reversal matrix as computed from backscattered narrow or broadband multi-static data is investigated. For the case of homogeneous backgrounds it is shown that under very weak conditions and as long as the number of sensor elements exceeds the number of scatterers the time reversal matrix has a rank equ...

We report our theoretical results on spin conductivity in antiferromagnets by focusing the role of magnetic toroidal quadrupole (MTQ) electron systems. The MTQ is characterized as a time-reversal-odd rank-2 polar tensor degree freedom electrons, which distinct from conventional rank-1 and dipoles. Based microscopic sd model analysis for tetragonal system under both collinear noncollinear antife...

A great concern when utilizing the Analytic Hierarchy Process (AHP) is how final priority vector, resulting from inconsistent analysis, behaves compared with original ranking, consistent analysis. The AHP utilizes an inconsistency index to predict rank reversal. In addition of AHP, several authors have worked on developing alternative indexes, goal improving predictability However, indexes do n...