Abstract Expectiles are the solution to an asymmetric least squares minimization problem for univariate data. They resemble quantiles, and just like them, expectiles indexed by a level ? in unit interval. In present paper, we introduce discuss main properties of (multivariate) expectile regions, nested family sets, whose instance with 0 ? 1 ? 2 is built up all points projections lie between lev...

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...

Background: Radiotherapy is an important technique of cancer treatment using ionizing radiation. The determination of total dose in reference conditions is an important contribution to uncertainty that could achieve 2%. The source of this uncertainty comes from cavity theory that relates the in-air cavity dose and the dose to water. These correction factors are determined from Monte Carlo calcu...