Semilinear response

On p-semilinear transformations

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...

Semilinear copulas

under some suitable assumptions on the generator f . The members of this family have some distinguished features that make them appealing for a variety of situations (presence of a singular component, non-trivial tail dependence, simulating algorithm); moreover, they can be interpreted as the dependence structures arising from a specific stochastic shock model [2, 3, 4]. Some novel statistical ...

Semilinear parabolic problems

Asymmetric semilinear copulas

We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1/16. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of Π...

Minimization of semilinear automata

We investigate finite deterministic automata in sets with non-homogeneous atoms: integers with successor. As there are uncount-ably many deterministic finite automata in this setting, we restrict our attention to automata with semilinear transition function. The main results is a minimization procedure for semilinear automata. The proof is subtle and refers to decidability of existential Presbu...