We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stabil...

let $a_1$, $a_2$ be unital banach algebras and $x$ be an $a_1$-$a_2$- module. applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $a_i$ into the dual space $a^*_i$ (for$i=1,2$) and such derivations  from  the triangular banach algebraof t...

In this paper, we will consider Hyers–Ulam–Rassias stability of multipliers and ring derivations between Banach algebras. As a corollary, we will prove superstability of ring derivations and multipliers. That is, approximate multipliers and approximate ring derivations are exact multipliers and ring derivations.

We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

In LI 31.2, J. Rubach proposes a modified version of OT that features derivations. In the present article I argue that, while some modification to the original formulation by Prince and Smolensky is needed, the correct one is not to re-introduce derivations, but rather to take fuller advantage of OT’s inherent parallelism. I propose that outputs must be related not only to inputs, but to other,...

We study δ-derivations – a construction simultaneously generalizing derivations and centroid. First, we compute δ-derivations of current Lie algebras and of modular Zassenhaus algebra. This enables us to provide examples of Lie algebras having 1 2 -derivations which are divisors of zero, thus answering negatively a question of Filippov. Second, we note that δ-derivations allow, in some circumst...

motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎it is shown‎ ‎that every lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎the definition of lie $n$-higher‎ ‎derivations on operator algebras and related pote...