The subcubic (O(n) for ω < 3) algorithms to multiply Boolean matrices do not provide the witnesses; namely, they compute C = AB but if Cij = 1 they do not find an index k (a witness) such that Aik = Bkj = 1. We design a deterministic algorithm for computing the matrix of witnesses that runs in Õ(n) time, where here Õ(n) denotes O(n(log n)). The subcubic methods to compute the shortest distances...

A generic algorithm is developed to reduce the problem of obtaining linear and nonlinear entanglement witnesses of a given quantum system, to convex optimization problem. This approach is completely general and can be applied for the entanglement detection of any N-partite quantum system. For this purpose, a map from convex space of separable density matrices to a convex region called feasible ...

Many of the pious bequest policies (Vaghf) !supportFootnotes]-->[1] at present time are denominated by old or ancient coins, the present value of which is not well known. Therefore, fixing the annual custodian fee for Vaghf is quite difficult. Moreover, the difficulty of evaluation of the present value of the dowry the husband has to pay to the bride after the marriage (Mahr) !supportFootno...