We explore a novel approach to compute the force between static quark and antiquark with lattice gauge theory directly. The is based on expectation values of Wilson loops or Polyakov chromoelectric field insertions. discuss theoretical technical aspects in detail, particular, how compensate large discretization errors multiplicative renormalization factor evaluation using multilevel algorithm. ...

Optimal power flow (OPF) problems are mathematical programs to determine how distribute over networks subject and operational constraints. In this article, we treat an OPF problem as operator that maps user demand generated power, allow the parameters take values in some admissible set. We formalize theoretic approach, define characterize restricted parameter sets under which mapping has a sing...