The diagonal of a multivariate power series F is the univariate power series Diag F generated by the diagonal terms of F . Diagonals form an important class of power series; they occur frequently in number theory, theoretical physics and enumerative combinatorics. We study algorithmic questions related to diagonals in the case where F is the Taylor expansion of a bivariate rational function. It...

In this paper, we propose an integration of compressive sensing (CS) and clustering in WSNs utilizing block diagonal matrices (BDMs) as the measurement matrices. Such an integration results in a significant reduction in the power consumption related to the data collection. The main idea is to partition a WSN into clusters, where each cluster head (CH) collects the sensor readings within its clu...

Recently, a very interesting behavior of crosstalk (XT) between diagonal cores (diagonal XT) in square-layout uncoupled four-core fiber (UC-4CF) that grows quadratically with length has been reported. In this paper, the intercore XT UC-4CFs is investigated on basis coupled-power theory. To make it easy to understand physical mechanism behavior, we derive an approximate solution equations. We sh...

Systems of linear diierential equations with constant coeecients, as well as Lotka{Volterra equations, with delays in the oo{diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.