We show that the no betting characterisation of the existence of common priors over finite type spaces extends only partially to improper priors in the countably infinite state space context: the existence of a common prior implies the absence of a bounded agreeable bet, and the absence of a common improper prior implies the existence of a bounded agreeable bet. However, a type space that lacks...

The significant growth in the number of connections distributed generation (DG) units distribution networks increases operational complexity such networks. One complicating factors is improper action DG protection against islanding using an undervoltage relay event short-circuits feeders adjacent to connection. In this sense, study investigates through computer simulation which situations undue...

For a zero mean, proper, complex random vector x, the Hermitian covariance Exx is a complete second-order characterization. However, if the vector x is improper, it is correlated with its complex conjugate, meaning Exx 6= 0. This improper or complementary covariance must be accounted for in a complete second-order characterization. The improper covariance has been exploited for widely linear (W...

Improper choosability of planar graphs has been widely studied. In particular, Škrekovski investigated the smallest integer gk such that every planar graph of girth at least gk is k-improper 2-choosable. He proved [9] that 6 ≤ g1 ≤ 9; 5 ≤ g2 ≤ 7; 5 ≤ g3 ≤ 6 and ∀k ≥ 4, gk = 5. In this paper, we study the greatest real M(k, l) such that every graph of maximum average degree less than M(k, l) is ...