Human sleep depth was traditionally assessed by scoring electro-encephalographic slow-wave amplitudes at the globally standardized C4-M1 electrode derivation. Since 2007, the American Association of Sleep Medicine (AASM) has accepted three additional derivations for the same purpose. These might well differ in slow wave amplitudes which would bias the scorings. Some derivations might also intro...

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea Full list of author information is available at the end of the article Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of q...

This paper provides a mathematical analysis of the relationship between vernacular and for-malised derivations of programs; in particular, when the vernacular derivations deploy general recursion. We introduce a calculus VPD to represent vernacular derivations and a constructive theory of operations and types, EOT , to represent formal derivations. We provide an intensional semantics for VPD wi...

Surprisingly, skew derivations rather than ordinary derivations are more basic (important) object in study of the Grassmann algebras. Let Λn = K⌊x1, . . . , xn⌋ be the Grassmann algebra over a commutative ring K with 12 ∈ K, and δ be a skew K-derivation of Λn. It is proved that δ is a unique sum δ = δ ev + δ of an even and odd skew derivation. Explicit formulae are given for δ and δ via the ele...