We use on-line partial-evaluation technology to generate partial derivations from natural (big-step) semantics deenitions. First, we reformat the big-step rules into a small-step form, and we extend big-step semantics to be higher-order, that is, we allow data structures like closures to contain partial derivations. Next, we apply a supercompilation algorithm to the transformed semantics, there...

Let R be an associative ring not necessarily with identity element. For any x, y ∈ R. Recall that R is prime if xRy = 0 implies x = 0 or y = 0, and is semiprime if xRx = 0 implies x = 0. Given an integer n ≥ 2, R is said to be n−torsion free if for x ∈ R, nx = 0 implies x = 0.An additive mapping d : R → R is called a derivation if d(xy) = d(x)y + yd(x) holds for all x, y ∈ R, and it is called a...

In this paper, we introduce the notion of multi-fuzzy normed spaces and establish an asymptotic behavior of the quadratic functional equations in the setup of such spaces. We then investigate the superstability of strongly higher derivations in the framework of multi-fuzzy Banach algebras

in this article, the notion of $n-$derivation is introduced for all integers $ngeq 2$. although all derivations are $n-$derivations,  in general these notions are not equivalent. some properties of ordinary derivations are  investigated for $n-$derivations. also, we show that under certain mild condition  $n-$derivations are derivations.

Recently, the algebraic theory of MV -algebras is intensively studied. In this paper, we extend the concept of derivation of $MV$-algebras and we give someillustrative examples. Moreover, as a generalization of derivations of $MV$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.Also, we investigate some properties of them.