Integrating Hasse–Schmidt derivations

Zero Derivations

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,...

Derivations and skew derivations of the Grassmann algebras

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...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

* 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...

Derivations NIP course

Q: Consider an uncorrelated (white) Gaussian signal s(t). Calculate its 3rd and 4th order moments, m3 = ⟨s(t1)s(t2)s(t3)⟩ and m4 = ⟨s(t1)s(t2)s(t3)s(t4)⟩. Confirm with simulation. The third moment m3 = ⟨s(t1)s(t2)s(t3)⟩ is zero. Namely, if t1 ̸= t2 ̸= t3 then m3 = ⟨s⟩ = 03 = 0. If t1 = t2 = t3, m3 = ⟨ s3 ⟩ = ́ N (0, σ2)x3dx = 0, as this is the integral over an odd function. For t1 = t2 ̸= t3, m3 = ...