In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

We study the linear differential system associated with supersymmetric affine Toda field equations for Lie superalgebras, which has a purely odd simple root system. For an algebra, problem modified by conformal transformation leads to ordinary equation (ODE) that provides functional relations in integrable models. This is known as ODE/IM correspondence. superconformal are shown reduce couple of...